Gamblers Fallacy definition | Psychology Glossary

define gambler's fallacy example

define gambler's fallacy example - win

Dream 😴💤 Investigation 👨‍🔬 Results 🔢 (dont know if this has been done before)

Speedrunning is a 👏👌 hobby in ☝ which people 😡👨 compete to complete 🚫 a 😱👌 video ♀ game 🏈🎲 as 🛠🍑 quickly 🆘⏰ as 😎 possible. 🔝 This paper 🤓 concerns speedruns of 💦 Minecraft: ⛏🚨 Java Edition, and, 👎😖 in 🚫 particular, speedruns of 🚨💦 the category known 💫 as 🍑💑 "Any% 🤣 Random 🎲🔀 Seed 👨🌾 Glitchless" (RSG) performed on 🔛 version 👧 1.16. 👸🏻 A 🅱 brief summary of 💦 the 👏🔍 relevant mechanics 💰 and speedrun strategies follows 🚗♀ for 👀 the unfamiliar reader. The 🗣 final 😪 boss 👨👨 of 👼💦 Minecraft ⛏ is located in 👄📥 an alternate dimension known as 🚫 The 🏕💦 End, 😣🔚 which 🙌😩 can be 🐝🐝 accessed using 🤳🏻 End ✋💯 Portals. An end 🖕✋ portal consists of 💰☹ twelve End Portal Frame blocks, 🌆🌇 a ⛄☝ random 🔀🔀 number 🎦 (usually 10-12) 🅾 of 💦 which 👏 must be filled 🔋😩 with 😍👫 an ☺ Eye 🤕 of 💦 Ender in 🚭👇 order to activate the portal. Thus, 👌🕵 the 🌞 runner is ☎👅 required ✅📋 to 👊💦 have ✊💪 up to twelve eyes 👀 of 💦 ender when 💕 they arrive at the 🤡🏻 portal to 💰🗣 be 😡🐝 able 💪💪 to 💦 enter The End and 👏👏 complete the game. 🏈🎮 In 📥 1.16, the ♀ only way 😓 to obtain an 👹 eye 👁 of ender is ❤♂ by crafting it, 🏃 which requires one Ender Pearl and one ☝👏 Blaze Powder. Ender pearls 🍬 can be 🐝🐝 obtained in several ⛓ ways, 💯😉 but 🏼🍑 the fastest is 🔥👌 to 💦👊 use a 🔥🐝 mechanic known 😝💫 as Bartering. In 🛌 a 🅱 barter, the 🔛 player 👨🎮 exchanges a 🏻👬 Gold 🤓🔦 Ingot with a 👍 Piglin (a humanoid creature 🐙 in the Nether dimension) for 👻 a randomly chosen item or 💰😫 group 🅱🅱 of 🚋👏 items. 🛡🛡 For 🏻🙃 each 👏 barter, there is 👅 about 🏫 a 5% chance ♂🙅 (in 📥👏 1.16.1) 🌱🚫 the piglin will 🤔 give 🏿 the 👏🕡 player ♀💰 ender pearls. 🍬🍬 Blaze powder is crafted out of 🏫 Blaze Rods, which are 😡💯 dropped 〽 by Blazes—a hostile mob. Upon being ❌ killed, each blaze has a 50% chance 😨 of 👨🎖 dropping one blaze rod. 🍆🍆 The 👏💛 main focus 😩 during 🚣🏃 the 🦉 beginning ➡😍 of 💦🔥 a 🔫👇 1.16 ⛈ RSG speedrun is to ✌💰 obtain (hopefully) 👏👏 12 🤓😣 eyes 👀 of 🍳👩 ender as 🙇 quickly ⏰ as 🏿 possible, by 🌈😈 bartering with 🆕👉 piglins and 🚕 killing blazes. These two 💏💏 parts of 😩💦 the 🏻🌊 speedrun route are 🔢🙏 the 👏💦 primary concern 😕 of this paper. 2 😂 Motivation ☑ Members 👨👨 of 😏 the 🏻 Minecraft ⛏ speedrunning communitya reviewed six consecutive livestreams of 😣 1.16 📣🔙 RSG speedrun attempts by 😈 Dreamb from 👩🛣 early October 2020. The 👶 data 💰💰 collected show 📺 that 🍆👀 42 of the 💬 262 piglin barters performed 🎭💃 throughout these streams yielded ender pearls, 🍬 and 💰🙋 211 of 🔧 the ⏰👀 305 killed blazes dropped blaze rods. These results 🔢 are 💇 exceptional, as 😠 the 😍🏽 expected proportion of 💦💦 ender pearl barters and 😵 blaze rod 🍆🍆 drops 💦😲 is 🙀 much, 😣👎 much lower. 🤓 An 👹💉 initially compelling counterclaim is 🍆😀 that 💦 top-level 🔼 RSG runners must 🙅 get 🍑 reasonably good 🏼💘 luck in 👌🏼 order to 💦💦 get a ♀👌 new 🎉🤤 personal best 👳👌 time 🕐⏰ in 👻😈 the 👨 first 🥇😂 place, 🏆🤤 so, while ♀👶 it 💯➡ is 🙈 surprising to 💦💀 see 👁 such 💦 an ➕ unlikely event, it 💯🦊 is perhaps 😍🏻 not 😥😅 unexpected. However, 🖐💯 upon 👦 further research, Dream’s 💭 observed drop 🏻👇 rates 💦 are substantially greater 👅👅 than 😽 those 👞👞 of 💦😰 other top-level 🔼 RSG runners—including, Illumina, Benex, Sizzler, and Vadikus. If ☔☔ nothing ♀🔫 else, 👴♀ the 😱🌈 drop 👇⤵ rates from 💋 Dream’s 💭💭 streams are 💓 so exceptional that 💯 they 🏽 ought to be 🐝 analyzed for 💰 the sake of it, 🔥 regardless of 💦 whether ☂☂ or not 🚫🚫 any one 😍 individual believes they 🏾 happened 🤔🤔 legitimately. aThe data 💾 were 😫😫 originally 🔙🔙 reported ♂ by MinecrAvenger and danhem9. bhttps://www.twitch.tv/dreamwastaken 3 3 😘🤔 Objectivity 🤖 The 🙀🐺 reader should 👫 note that the 🏻 authors of 💦 this 😎📍 document are solely 👞👞 motivated 🏿 by 😈 the presence 🙇 of exceptional empirical data, 📉💰 and 👏👎 that 😐🎢 any 👏 runner—regardless of 🏻😍 popularity, following, or 👉💰 skill— 😤 observed experiencing such unlikely events would 😏😎 be 😤 held to ✌💦 the 😼👌 same 😯 level 🔻🆙 of scrutiny. The 👊🅿 reader should 💦👍 also 🙇 note that 🤔🚟 the data 📉💰 presented are 🏻😩 extensively corrected for 🤔🎅 the 😫📚 existence 👌 of 🔴 any 🈸 bias. It 🔫😞 would 🍆😎 lack rigor and 💰💦 integrity for 💕😩 the 🗯 conclusions made 👆 in this 😏 report to 💦 substantiate the moderation 💯💯 team’s 🐒 decision if they 👥 were 👧👶 merely based 👌 on 🚟🔛 a surface-level 🍑🌎 analysis of the data. 📊 Indeed, these 🚱 corrections inherently skew the analysis in Dream’s 💭 favor. We 😂👦 aim to calculate not 🚫🖐 the 🍩💋 exact 👌👌 probability that 🏻👉 this 👈 streak 🔥 of 💯 luck 😄 occurred if Dream 💭 is 🔁 innocent, 😇😳 but 🍑 an upper bound 🤐🤐 on 🔛🔛 the probability; that is, 💦 we will 👊👻 arrive at 🚓😁 a value which 😡👏 we are certain is 😳🔮 greater 👅👅 than 👉 the 🅱💦 true probability. The 👦 goal 💦⚽ of 🏧👉 this ☝👈 document is to 💦⏸ present the unbiased, rigorous statistical analysis of the 👏🏼 data, 💰📉 as 😱🖕 well as an 🐎 analysis of the ♀🚨 Minecraft ⛏🚨 source 😔🏞 code, 😲😲 to conclusively determine whether or 💰➕ not 🚫 such an 🍎 event could be 👌😳 observed legitimately. 4 👌 Part 🏻 II 👩👩 Data The 📈💲 raw data 💾 (and its sources) 👉👉 from 🤤 which the 💰 following graphs were 👶 derived 🔜 can 💦💦 be 👏 found in 🍆 Appendix A. 🏿🅰 4 🙇 Piglin Bartering Figure 1: 🏫 Dream’s pearl barters, charted alongside various comparisons. The ✊ 99.9th 🤑 percentile line 🚫💨 represents one-in-a-thousand 💦 luck 😰🍀 (calculated 🚜🚜 using 📤📤 a 🥇➡ normal 🖖 approximation), which 🎓🙌 is already quite 💬🅰 unlikely—if not ♀ necessarily proof 💯📊 of anything. 😫 5 🍆 5 🍆🦐 Blaze Rod Drops 😲😲 Figure 2: ➡ The same for 🍆😱 blaze rod 🍆 drops. 💦 Part 👏 III Analysis 6 ❗ Methodology What ❓ follows 🏃🚗 is a thorough description 👿👿 of 😱 every aspect of our 🚟🅱 investigation in 👮 an 🍑 accessible manner. 🚁🚁 We 💰🔝 will begin 📦 with 👏👏 an 💸😯 introduction to the 👏👏 binomial distribution, and follow 👣 with 👏 adjustments 💰💰 to 🙅💊 account 💳 for 🔜🍆 sampling bias and 💰 other biases lowering the 👶 accuracy of 💦 the binomial distribution. Finally, 🙌 we 😂 will analyze Minecraft’s ⛏ code 😤 to justify the assumptions made 🙌💯 in our 👵💰 statistical model. 👄 To 🏻 strengthen 💪 our analysis to 💦🙏 the 💦👑 skeptical reader, we now 🍑 preemptively address 📪📫 expected 🤰🙄 criticisms and 👅👏 questions. Why 😩❓ are 🏻👀 you not 🏻 analyzing all of 😤💦 Dream’s runs? 💰💰 Doesn’t that introduce sampling bias? Yes. There is clearly 🤓😱 sampling bias in 👏 the 😦👌 data 📉 set, but 🤤🤚 its ⚜ presence 🏽 does 👏 not 🏼 invalidate our analysis. Sampling bias is a common 😍 problem in 👉👏 real-world ✨ statistical analysis, so if 🏿 it were 👩 impossible 🙇 to 🗣 account 💳 for, ⌛ then 🏿 every analysis of empirical data 💰 would be 🐝🍆 biased and 🏳👏 useless. ♀⏳ Consider flipping a 👌 coin 100 💯💯 times 🕛 and getting heads 🙉 50 👌 of 🔌 those times 💦 (a 🤣🤧 mostly 💁🙋 unremarkable result). Within 😱 those 100 coin flips, however, imagine 🤔 that 👏 20 of 👩 the 50 ⏳ heads 💤🙉 occurred back-toback somewhere within 😜 the 🙀➡ population. 👥 Despite 🙅♂ the 🐐☺ proportion overall being 😩 uninteresting, we 6 still would 😜 not expect 🤗🤗 20 📊 consecutive heads anywhere. Obviously, 🎳 choosing to 🔍 investigate the 👏 20 🔳🔳 heads 🙈🙊 introduces sampling bias—since we 👩 chose to ♂🙌 look 👀 at 🏠 those 😘 20 🎉🔳 flips because 💁😡 they were lucky, 🍀 we 👉💰 took a 👏 biased sample. However, 🖐🖐 we can instead discuss the probability that ☃👨 20 🆗🆗 or 💁🚫 more back-to-back 😡 heads occur 👻 at 👒😩 any 🚸 point in the 🔚 100 💯 flips. We 🏃👦 can use 👏 that 👆 value 💵💵 to 😠 place an 💰 upper bound 🤐🤐 on the probability that the 👏⛪ sample we chose could 🔒 possibly have 😣✅ been 👦 found 🚫👁 with 😣 a fair 👒 coin, regardless 🤷🤷 of how biased a 💰📖 method was 🅰 used to 🏽😩 choose the 🐆 sample. It’s 💦🏹 also 🙇🅱 worth 💵💸 noting that the choice to only 🕦 consider Dream’s 💭💭 most 💯😃 recent streak of 😳 1.16 🤜 streams is 👏 the 🔝 least arbitrary distinction we could 👌🚫 have 🙌👏 made. 👆 The 🖱🏋 metaphor of 🅱👶 "cherry-picking" 🍒 usually brings to ➡✌ mind 🤔 choosing from ➡ a wide ➡ number of 👩 options, but there ✔👇 were 🍑 at 🍆 most 💯 a 👌👌 small 😂🏼 handful of 🌹 options meaningfully equivalent to 💦 analyzing every 🏦 stream 💦 since 💦 Dream’s return to 💦♀ public 😪⛱ streaming. Note the 💌 importance of 😤💦 the 🔍 restriction that we ♀ must 🙅💰 analyze the 🍆😫 entire 🌲 six streams as a 💡👌 whole; 💰 true cherry-picking would 💭🌨 specifically select ❇ individual 🥖 barters to 💦💦 support 👍♀ a 👏 desired conclusion. How 🐼 do 👀 we 🅰 know this investigation isn’t biased? Concerns about 🤔 the 🏛👑 impartiality of the authors of 💦😊 this 😞 paper 🤓 have 👏😏 been raised 👧👧 in discussion about 🌈 the investigation. We 👨👩 do not think 💭 this 😞 is 🤔👐 a 🍾 significant issue; 🙅🏾 we have 😒 made 👆 an 😤 effort to be as 🍑 fair 👒 to 👸 Dream 💭💭 and ♂💰 thorough as 🖕🏿 possible in our investigation. Regardless, 🤷 it 💡💨 is a 👬 concern 😕😕 worth addressing. This 👈♂ paper 🤓 has 👏 been 😀 written to 💦✌ be 🙋🎮 as accessible as possible 🔝 to an ☺👏 audience without 🚫🚫 in-depth 👏 knowledge 📚😍 of statistics or programming. This 👈🔴 is 🔥🚫 primarily so 💯 that 👎👅 you 😍🙂 do not have 👃☣ to ✌💦 take our word 🙌 for 👻🎁 its accuracy. 👌 By 😈 reading 📖📲 the analysis, you should 👫😑 be able 💪💪 to 💦👉 understand 😷🤔 at 👌😠 least 👬🚫 on 🔥 a basic level why the ♂✅ statistical corrections we 👥❣ made 🤗😇 account 💳 for 💼 all ✊ the 😤 relevant biases. Additionally, ➕✏ as noted in 🙌 Section 3: 😧 Objectivity, 🤖🤖 we 👦💰 aimed not 🚫 to 😋💦 calculate the ➕💦 precise probability of 💦 Dream 😴 experiencing these 😤 events, but an 〰🦅 upper bound 🤐 on 🔛🏿 the 🅿😈 probability. This 🎄👉 makes 🤔 it ☠🤔 much 💘 more ✋ difficult for bias to 💦💦 have any 💦🍵 effect; 📣📣 if 👏 we 😀💰 correct ✅ for 🌍💕 the 🅱 largest amount 📉 of bias in 👏 the 🎁🚗 data that 🥁 there 🏿 could ❌😈 possibly be, 🏻 there is little 🐩👧 risk our 💩👶 analysis will 👊 be skewed due 👅👅 to 🍆📧 our 💰 bias causing us 🤵 to 💵💦 underestimate how 😱🗣 much 🙀💘 we ought to 💦 correct. ✅ We 👵👨 believe 💭😱 that, to ⏸ the extent any 📨 bias exists, these measures should be more 😏😏 than ☄ sufficient to ✌😤 account 💳💳 for it. 💱🤔 Additionally, ➕ note 📋 that we 👉🤠 are not 🚫 the only 😤 people 😣👥 capable of 🎆 analyzing these 🚑 events—if any 🌐 unbiased third 🤔🤔 party 👌 points 😘 out 😧📤 a 👌🥇 flaw in our 😻📸 statistical analysis or 🍆 notes 😚 a 👌 glitch that could potentially cause 🎗 these 💦🥜 events, they would, 💀 of course, be 😝💰 taken 🚀 seriously. 😒 What if 👏 Dream’s 💭 luck was balanced out ⚔ by 👷😗 getting bad 😤😩 luck 🍀🍀 off 😍 stream? This 👁 argument 🙅 is 💦😞 sort of 👍💯 similar to 👍 the 💰👈 gambler’s fallacy. Essentially, what 👏😱 happened to ♂ Dream 💭 at 🍆🍆 any time outside 😏🔥 of the 🎅👏 streams in 📥 question is 👏😩 entirely 💯 irrelevant to the 👀🍆 calculations 📊 we 👧 are 🅱♀ doing. 😧🏃 Getting bad 😞😩 luck at one 😥♿ point 🈯 in time 🕘 does not 🙅 make good 👌 luck 😟🏼 at a 👌🅰 different 💰💰 point ⬆⬆ in 🖕👏 time more 💯 likely. We 👥👓 do 😫 care about 👏 how 🤷👉 many 🏼💯 times 🤔🤔 he has streamed, since those 👉 are 👄 additional opportunities for 😏 Dream 💤💤 to 💦😣 have 🈶🌈 been noticed getting ➡ extremely 💛 lucky, 🍀 and 💰 if 🚀 he 😡👦 had gotten 🅱💦 similarly lucky 🍀🍀 during one 💯😫 of 💦💦 those 😘😖 streams an 🍑 investigation still 👉 would 💞 have 💴 occurred. However, what luck Dream actually 🤔 got 🏻😩 in 🛌 any 💦🍵 other 👳 instance 💯👉 is 🙀 irrelevant to this 😷 analysis, as it has 🤔👉 absolutely 💯🙅 no bearing on how 💯 likely the luck was 🔙 in this ⁉ instance. 🙄 7 💯💯 7 💯 The Binomial Distribution Note: 📝📋 If the 🌊🚀 reader is equipped with 👯👏 a ✨ basic understanding of 👏💦 statistical analysis and 💰🚄 the 🏼 binomial distribution, they ♂😈 may 🐝 skip to Section 8: 🅱✊ Addressing Bias. Note that 🤔😐 the ⛓🏻 explanations 📝📝 present 🎀🎀 here 💦💪 are sufficient for the 🔭 probability calculations 📊📉 performed throughout the rest 🚔🍑 of the 👽 paper, but 😮☝ are 💯 not 👎 exhaustive. Supplemental reading 📖📃 is 🙄❌ provided via 💰💰 footnotes where relevant. 7.1 💯 The Intuition Informally, if the outcome of a 👌 particular event can be described as "it either happens or 💁 it doesn’t", then 🤔 it 😐 can 🔫😡 be modeled with 😉 the 👏 binomial distributionc . For 👧🍆 example, imagine 💦👑 we 😊 wanted 👩 to 👉💦 compute the odds of 🏻 flipping a 💰 fair 😤👒 coind 10 times and 😘💛 having 😋 it 😏🥇 land ⬇ on heads exactly 😉😉 6 🤔 of those 🐥🐥 times. 🍆 Since a 😎👌 coin either lands on 🚟⬇ heads or it 🥊 doesn’t, we 👍👶 can 💦🗑 use 👏⚒ the 😫 formula for 🐻 the 🚟🎁 binomial distributione to determine the 🏆 chance 😨 of this 👈🍆 occurring. Since we 👨😂 flip the 💰👇 coin 10 🔟 times, 😆⏰ we say 🙊 푛 = 10, 🤑😰 and 💰 since 👨 we 💣😺 want exactly 6 💪 of 👀 those 👞🤔 flips to be 💎👼 heads, 🐵 푘 = 6. ❓ The ☝ chance of 🔴💦 a 👌💰 (fair) 👒 coin landing on 🔥 heads is 50%, so 푝 = 0.5. ➖ If we plug these 👳👈 values 👪💰 into 🤓 the binomial distribution formula, we 👨 get 🔟 P (6; 👧❗ 0.5, 😊 10) 😂 = 10 6 👆 0.5 6 💪🏠 (1 − 0.5) 😊💦 10−6 ≈ 0.205 👌 (1) ➗ To 💦 interpret this ❗ value, if ♂ we flip a ✋ coin 10 🔳💯 times, 🍆🕒 we 👦🌊 can expect 🤗🤗 to 💦 get exactly 😉 6 🤔 heads 🙊💤 about 👂☝ 20.5% 🆗🎉 of 🔝 the 👆🍆 time. 😵💯 To understand why 😳🤔 this 😂 formula yields the 👏 probability of 🍒💦 a binomial distribution, and 🙅 how 👹 to 👮⏬ generalize it, ✔ we 👧👮 break 🙇 down 👇👩 each 👋👋 term. 7.2 💯 Generalizing the 🌈 Binomial Distribution Generically, the probability of exactly 푘 successes with 👏😋 probability 푝 occurring in 👉 푛 trials (in 👏 our 💩 earlier example, 🔥🔥 푘 = 6 🕕 heads with 🎉🍨 probability 푝 = 0.5 💦😏 occurring in 🔝 푛 = 10 💯 flips) is 🔥 given 👈⤴ by ⏩ P (푘; 푝, 푛) = 푛 푘 푝 푘 (1 − 푝) 푛−푘 (2) ♀ We 😃 can deconstruct this 💯📉 formula term-by-term to understand why 😡 this represents the 📲 probability. Basically, 👎👎 this 👈 formula figures out how 💯 many ❔ distinct orderings of 🕯🅱 푘 successes and ➕➕ 푛 − 푘 failures meet 💯 the criteria, and 👏🤔 then 💯 sums the 👨😫 probability of 💯🏻 each orderingf . The 🎁🔝 notation 푛 푘 , read 📖 as 🏿💰 "푛 choose 푘", represents the binomial coefficientg , which is 🍏 the 🍆 number 🔢 of 🔴 ways ➕✔ we ❤🙋 can 🔫😠 observe 푘 successes in 🌤 푛 trials—the number 💦📱 of 🤖 ways, 💫💫 with 💰👏 푛 options for 🎅 trials ⚖⚖ to 💦 be successes, you ☠ could 🤷 "choose" 📥📥 푘 of 🗼👀 them. For example, there are 💨 two ✌ ways to 🐵⏸ observe 푘 = 1 👸 heads 💤 in 푛 = 2 coin flips. The head could occur on 🔛🔛 the first 🔢 flip, or 😩💁 it could 🤔 occur 👻👻 on the second 🕐🕐 flip. Therefore, 👏🎉 2 1 is 👮💦 equivalent to 👌 2. 🙈 With similar 💯 reasoning, 4 💦✌ 2 is equivalent to 6; ❗ there cThe binomial distribution also ➕ requires the assumption that ❗ we 👦👬 are ♀ observing discrete independent 🙅 random variables. Since 👨💦 piglin bartering and ➕ blaze drops 💦⬇ are 🏄 discrete independent random variables (see 👀👀 Section 9: Code Analysis), we ⚡ can 🔫 safely 🚦 make ✋ this 👈🎅 assumption. There ↗ are ⭐🙏 other 🙅✉ considerations about 💦 stopping 🆘🆘 rules which 😡 will 👙👏 be 📖🐝 addressed in 📥 Section 📦 8: 👊⚡ Addressing Bias. dA 👨😗 "fair coin" is 🔥💦 defined as 🍑🕛 one whose 🌄🌄 probability of 💦💦 landing on 🔛👇 heads 🐵 is 🔥 exactly 😉 the 💊🚟 same as 🏿🍑 its probability of 😤 landing on 🔛🔛 tails. We ♂ are 👶♀ also 👨 not considering the 🏽👏 probability that 🚟 the 👀👨 coin lands on 👋🔛 its 👤 side, which is entirely 👐 negligible for ⚠ this introductory-level explanation to 🗣✋ the 🔥👉 binomial distribution. ehttps://en.wikipedia.org/wiki/Binomial_distribution fFor an explanation of 💦👅 why ❓❓ this 👉 works, 💦 see 👀 https://www.youtube.com/watch?v=QE2uR6Z-NcU. 🐕 ghttps://en.wikipedia.org/wiki/Binomial_coefficient are 👶 6 unique ways 💯 to distribute 2 💦 successes (heads) 💤🙈 across 💰 4 trials ⚖ (coin flips). (These 🤤 are 🔢 1&2, 1&3, ♂ 1&4, 👷 2&3, 2&4, 💦❤ and 🤠 3&4.) As the first 👆 term represents the 💲👏 number 📟 of distinct orderings, the 👉 next 📅☃ two 💘 terms represent ✊ the 💦🏻 probability of ⛄💦 any 💦 one ♿ order. To find 🔎 this 🙋👏 probability, we simply take 🐥 the product of 💦 the probabilities of the 👏 events necessary to produce a 💰👌 given 👤⤴ ordering; that 😐 is, 💦 the product 👟👟 of the 👏👏 probability of 🚨👄 observing 푘 successes and 푛 − 푘 failures. Since 푝 is 🚟👮 the 🚧 probability of 💦 a ♂ given 👤 trial being 😑 successful, 📈📈 and there ✔ are 💓 푘 successful trials, 👨 we 👴👵 can account 💳 for the 💞🏾 successful 📈💪 trials 👨 with 🤝 the term 푝 푘 (푝 multiplied by itself 👈👈 푘 times)h ⌚😩 . Similarly, we 👌👦 account for 👷 the failures by 😈👨 raising 🅰🔝 the 🦏 probability of a 👏 failure to the power of 👏 the number 🎦 of 💦🌈 failures. As the 👑 only two 💏 possibilities 💡 in 👏 a 👏➡ given ⤵ trial are 🍑 success ☺🤑 and ☺ failure, and 👏 the 👩 probabilities must 💰🙋 sum 👀 to 1, the 👥♂ probability of a 👌 failure is ☎😜 (1 ♀ − 푝). It 🕘🍆 follows that, since 👨👨 each 👋👋 trial that is 🈁 not a 🍆🍞 success 💰💰 must be 🥜 a 🅰 failure, the 👏 number 🔢📞 of 🐶👨 failures is (푛 − 푘). Thus, the 💰💦 final term is (1 🕴 − 푝) 푛−푘 . Multiplying all 👌🤷 three terms together yields the 👏 probability of 🔴 a 💐 binomial distribution with 😂 a 💰👀 given 👤⤴ 푘, 푝, and 🎅 푛. 7.3 💯⏰ The Cumulative Distribution Function (CDF) It would be helpful 😲🤔 to 💦💦 have 💰👏 a 💰 way to 👏♂ compute the probability of 💀 observing 푘 or more successes. Intuitively, we can expect 🤗🤗 the 🚟😂 probability of observing exactly 푘 successes in 👮 푛 trials 👨👨 to ✌ be smaller than 😽💰 the 😼🤠 probability we 👥🏻 observe 푘 or 😤💰 more successes in the 💌🆘 same 🖕 푛 trials. Referring back 👌 to the 🌀👦 coin-flipping example, 🔥 if we 💏 wanted to 💦💰 compute the probability of ☹🏻 observing 6 or 🚫💰 more 😥 heads within 🎉 10 trials, 👨 then we ♂♂ can 💦💦 simply add 👈 together 😭🏿 the probabilities of 💦😔 observing exactly 😉😉 6 👆🤘 heads, 🐵 exactly 7 ❗⏰ heads, (...), exactly 😉😉 10 💯 heads, 🐵🐵 given by Õ 10 푘=6 ❗❗ 10 🅾 푘 0.5 😏➖ 푘 (1 🤜 − 0.5) 😲❌ 10−푘 😂 ≈ 0.377 ➖ (3) 😩 Indeed, this 👀👈 agrees with 😗 our intuition; it 😤 makes sense that it ❗☠ is more 👏💦 likely to get 6, 👧👆 7, 8, 9, 🈂 or 💀🍆 10 heads 😂 in 10 🅾 flips, than ♀🔪 it 💨 is 🈁 to ➡ get 🉐 exactly 😉😉 6 👏 heads in 📥👇 10 flips. The 👩 chance of receiving 푘 or 🙅 more 👆 successes is 🅱🍆 often 💰💰 referred to 💦💦 as 🛠👦 a ➡👏 푝-value. 💵 More specifically, 푝-values 👪💰 are 🚥 the chance ♂😨 of 🐙😤 observing 푘 or 👱🅱 more successes given the 👏😶 null hypothesis. While ⏳👶 that 👑 nuance is 🏻🗓 irrelevant if you 👈🗣 already 😃 know 🔞 for 🍆🌍 a fact 🏫 the 👨👏 coin is 🔥 fair, 😆✔ it 😩 is important 😍 to 😅💯 keep in 👌👏 mind 😲🤔 in this 😎👇 scenario—our entire goal ⚽😫 is, 😍 essentially, to 💦💦 analyze whether 📊 or not 😥 Dream 💭 is 👮💦 using 🏻🏻 a 💰🙀 biased coin. Armed 💪💪 with a 🏿 basic 🌑🚂 understanding of 💦 the binomial distribution, we 👨❤ will 🅱 now 😱🎅 discuss how 💯 this initial calculation must 😾 be corrected in order 📑 to 💦✌ be applied to 👉💦 Dream’s 💭💭 runs. 💰💰 hFor an 😤🤗 explanation of why this 😰👏 works, 👷 see 👁👁 https://www.youtube.com/watch?v=xSc4oLA9e8o. 😮 9 8 👊👊 Addressing Bias There ✔💦 are ❓ a 🏿 few 😋🔢 assumptions of 🔟 the 🅾 binomial distribution that 😟🔇 are 💰 violated 🍑 in this 👈 sample, some 🈯 of ☹😊 which were 👶 noted in 👏💉 the 😍👏 document Dream 💭💭 published 🤓 on October 27. This 👈 section 📦 accounts for ♿🤙 these 😍😱 violated assumptions, and 👏 proves computations that 😩💰 account 💳 for these 🚑🍆 biases. Note 👋 that 🤔 some 💯 of 🏿😤 these 😤 biases only apply to 😂 pearls, as 😅 blaze rod 🍆🍆 drops 😲💦 were 👶 examined in 😜👌 the same 💩👤 streams as pearls 🍬 due to the 🙆 pearl odds, which are 🏃🔢 independent 🙅 of the 🐐🅱 blaze rod drop ⤵ rate. This 👏 eliminates the 🚮 sampling bias from 💰 the decision to investigate the ✈🍃 pearl odds based 👌🤰 on 👇 the 🔯 fact that they 👩👧 are 💰 particularly lucky. 🍀 8.1 ✊🤔 Accounting for Optional Stopping 🆘🆘 The initial 💰 calculation for 🍆🍆 the 👏🎁 푝-value 💵💵 assumed that barters and rod 🍆 drops 💦 within sequences of 🥗💰 streams are 💩 binomially distributed, which 👏 is 😧💰 not 😅🏼 precisely true 🍆‼ (although 😛😛 likely a 💬👌 very ☣😔 good 👏👀 approximation). For the 🔚 data 💾 to be 👄 binomially distributed, the 🕵 stopping 🆘 rule—the 👨⚖ rule ⚖ by 😈👏 which 🎓👏 you 👨 decide 😱😱 when to 💦 stop 👮👋 collecting data—must 💰 be 👬🐝 independent of 💰 the contents of 🍒💦 the data. 📉📉 For instance, Dream may 📅 be more ⬆ likely to 💦 stop ✋✋ streaming for 🍆👨 the 🏻 day 🕑 after 🕑🅰 getting 😧😚 a particularly good 🏽 run, 🏃🏃 which is 🔁💦 more 🙅 likely to happen ♂♂ on ☝ a 📝 run 🏃 with 😍😍 good barters and ✊👏 blaze rods. Indeed, Dream 💭 did 🍆 stop speedrunning 1.16 🌅 RSG after 😡 achieving a 🐀👏 new 💌 personal best time. This ❓👆 will 🎤🙏 result in the 👏 data 💰💰 being at 👈 least slightly biased towards ⛪ showing better luck 🍀 for 🍅 Dream, 💭💭 and 👅 thus the data 📊📉 is not 🚫♂ perfectly binomial. To 👂⚔ account 💳💳 for 🅱 the 🗣😈 stopping 🆘🆘 rule, we will 🐼 correct ✅ for 👧🍀 the 🅱🌫 worst 👹👹 possible 🔝 (most 💯 biased) stopping 🆘 rule. Imagine 😎 that this investigation was being 🐝👏 conducted by Shifty Sam, a ✝😂 malicious investigator who is trying as hard ⛰ as 🏃 possible 🔝🔝 to 👉 report misleading data 💰💰 that 😐 will 👏 frame Dream. 💤💭 Since 👨 a 🙏👌 lower 😎 푝-value 💵💵 is ℹ more ❌ damning, Shifty Sam computes the cumulative 푝-value 👇💵 after 👀 every 💯 barter or 🕍 after every 🔪ⓜ blaze kill, 💀 and ☑💯 stops ❌ collecting datai once 🍆 he deems the 🛣 푝-value 💵 "low enough" 💦 to make 🖕 the 😹👏 strongest case 😎💯 against 🔫😤 Dream. 💭 This 😞😣 is 💦🔥 the 🍆 worst 👹👏 possible 🔝 stopping 🆘🆘 rule, since Shifty Sam will stop 🏿🤔 collecting data 📊 once 🔂 the 🌊👊 푝-value 💵 is arbitrarily 🤔 low 👇 enough (as 🎣 deemed by 🎨 him to be most 👉 convincing). It should be 🏳 abundantly clear 🔎 that this stopping 🆘 rule 👑 is far worse 🤢 than 🤢 whatever 🏿 stopping 🆘 rule ⚖⚖ Dream actually 👉 followed 😣 during 🚣 his 🥐🤔 runs. It may 🌌 not be 🎮🙋 immediately 👏 obvious how we 👩🌊 can ❓😬 calculate a 푝-value 💵 under ⬇ this 👮🏄 stopping 🆘🆘 rule. We 💰 cannot look directly ➡ at the number of 💦💦 success in 📅👌 the 👧➡ data, as that is 🔥 always 👌👉 going ▶🍆 to 😂 be 🐝 exceptional to 👏 this 👈 degree. What ❓👉 we can 💦 consider, ☺ however, 🤔🖐 is how 🤔🅱 quickly Shifty Sam reached 🕶 his 푝-value 💵 cutoff. Intuitively, we might 🅱♀ expect 🤗 Shifty Sam to spend a 💰 long 📏 time ‼⏱ waiting ⌚ for 🍆🔜 the data 💰 to reach his 😤😤 푝-value 💵💵 cutoff. To 🏼 put it another 🤒 way, it would 💯 certainly be 🐝 surprising, regardless of 🏿☹ how ⁉ shifty Sam is, 💰 to hear ✋ that 😐🗳 Dream got 🍸🎁 30 ✈ successful barters in 👇 a 🔫 row 💦 as soon 🔜 as 😱🍑 Shifty Sam started ▶ looking at 👸 the ⚕ data. 💰 Knowing 💭🤔 that 😩 Shifty Sam only 🕦🤠 decided to 😂 show 👨 you 💯 this data 📉 because it 💯💯 supported ✔ his 🅱‼ argument ♂🙅 would 😎 not really 😆🌈 make 🙋😬 that 🅱 any less ➖ surprising (concerns about 🍾 sampling bias aside—those 😤😤 will 👫🎬 be 💦🐝 addressed later). 🕑 Since 👨 the data reaching 👉 a 🍑 푝-value 💵 this 🐸 extreme so soon is 💯 somewhat surprising even 😂 if 💦👏 we know 😭💭 the 😆 data comes from 😂😲 Shifty Sam, we will 😜⚽ look at 🍆 the 🙌 probability that 😩🔕 Shifty Sam stops ✋ collecting data 💰 at 👨🍆 least as 🕘🅰 soon 🔜 as 👦 Dream 💭 stopped. ⚠ In 👏♀ other 🏭 words, if 🤔🅱 푛 is 💦✅ the 👏 number 😧☎ of trials 👨👨 in 👈 Dream’s 💭 data, our corrected 푝-value 💵👇 will 👏👏 be 😤 the probability that 👉 a series of 🔍 trials 👨 will, 🏼 at 🗽 any point 👇👉 on 🔛👇 or prior 🔙🔙 to 👅 the 푛th 🎃🥖 trial, have a binomial CDF 푝-value at 👨❤ least 🚫 as 🍑🏿 small 👌⏬ as the 👏 one 😫 for 👏🎁 Dream’s 💭 data. 🤓📊 iSince Shifty Sam here 😇 is 🅱 supposed 👏 to represent ✊ whatever 👆 caused Dream 💭💭 to choose 📥📥 to 🎀🏻 stop running 🏃🚫 1.16 RSG, suppose Shifty Sam is, say, Dream’s 💭💭 manager, and 💰➕ can 🔫 tell 💬😲 Dream 💭💭 when 🍑 to stop 🛑✋ or 🅱 continue 🔕 streaming. ⛵ 10 😂 Although 😛 that value 💵💵 could 🤔 be computed through 👉⏬ brute force, 🌕🏼 that approach would involve evaluating the 👏 probability and 🎉 푝-values 👪 for well 🤷 over 😈😏 2 😳 305 different 🈯👱 sequences—which is 🗓☝ obviously 🎳🙄 computationally intractable. As 🍑 such, 😆 we 🏃 used 🚟 a 😍😗 method that 🍆 allowed for 🔄 dealing 👦 with multiple sequences at 😂 once. The 🅱👉 exact algorithm is 💦 somewhat involved, so 💯 a 🌍😰 description 👿👿 has been included in 🚪 Appendix B 🅰😇 for interested 👅👅 readers. 8.2 ⚡ Sampling Bias in 🛌🖕 Stream 💦 Selection As 🙇 mentioned previously, we 🔫 chose to analyze Dream’s runs 💰 from 👉 the point ⬆👉 that 😐👏 he ♂ returned to streaming 😭😭 rather than 😻 all of 💰 his ‼💦 runs 💰 due to ♀➡ a 🅰🏻 belief that, 🤔 if 🤔👏 he 👉 cheated, 💏 it was 👨 likely from the 😄😈 point 👉⬆ of his return to 💦💦 streaming rather than 🅰 from 👊 his 💦👿 first ☝🥇 run. 😱 Although 😛 we 😱 cannot 🚫 be 🍆 entirely 👐👐 certain, 🤔🤔 it 👌 is 🚟😨 also ➕😨 likely that 😷😯 MinecrAvenger decided 🤔🤔 to 💦😱 investigate Dream’s 💭💭 streams due 👅👅 to 👏💰 noticing that ☠ they were 😉 unusually lucky. 🍀🍀 This, 🚮 of 🤤💦 course, 😂 means 🙄😏 that the streams investigated are not actually 😥 a 💰 true random 🔀 sample. Even ☎ if 👏 MinecrAvenger somehow 😆😆 chose streams to 👍 investigate 👏👏 at 🍆 complete 🚫 random, 🎲 we 💏🏼 are choosing to 💦🛏 investigate these 🈷🈷 streams due to the fact 📕 that 🍆 they 🙋 are lucky. 🤞 Thus, we 👨 cannot 😡🚫 treat this 🚙⬇ as a ➡🖼 true random 🔀 sample. To 🏻🏻 account for 👅 the 👏🌷 maximum possible amount 📉 of 🐣 sampling bias, imagine 🤔🤔 that Shifty Sam inspected every 👏 speedrun stream 💦 done by 🔥😈 Dream 💭 and 🌬 reported 🔫 whatever 💯 sequence of 💦 consecutive streams was the 😷 most ⬆ suspicious.j This would 🌨😵 produce the 👘😫 strongest possible 🔝 bias—or at 🍆🤠 least 😱😴 a 🐝☝ bias much 😂 stronger 💪 than there ✔💍 actually 😤 is—from 😂😍 the ✨ choice 😜 of 🐣 these particular Dream streams. Recall the example 🔥 of 🌹💰 investigating the 🤡🐐 20 🔳 back-to-back 😰 heads within 100 coin flips from 🅱 earlier. Much 😂💘 like 👋 you 👍👦 could calculate the 👏 probability of 🚑 20 consecutive heads 🐵🙉 occurring at any point in the 🅱 100 💯💯 flips, we 👨👦 can 🗑🔫 calculate the probability that ✔💄 Dream 💭💭 experienced 🤳 bartering luck 🍀 this 👏 unlikely in 👏🙌 any 💦 series 💓 of 💦🤓 consecutive streams. This 👈📣 would 👉 account 💳💳 for 💦 the 👏 bias from ➡ Shifty Sam, and 💛😮 thus 🏻 more 🙅➕ than account for ❓ the actual bias under ⬇ consideration. To calculate the 🔑🏥 chance 😱 that ⚪⚠ at 👌💯 least 👏😈 one sequence of 🙌😊 streams is 💯🌈 this lucky, 🍀 we 👧 first calculate the ✈🌜 chance ♂🚫 that 😟☘ no sequence is. 👏💦 Assuming independence, we 👦 can 🗑💪 do 👺 this by 😆 taking the 🅱 chance 🚫 that 🤢 a 🎮🍉 given ⤵👤 sequence isn’t sufficiently lucky (1 − 푝) to 💦🙌 the power 🏼 of the number 😯❤ of sequences, 푚. If 👏 an event 👐👐 occurs more 😩 than 😻 zero 👰👰 times, 🕐😆 then ❓👱 it 😏 must 🙋👏 have 😩👌 occurred at ❤🤣 least 👌 once, so 🆘 we can then 🙄➡ subtract (1 🥈 − 푝) 푚 from 🙃 one 🙏☝ to get 😛🍑 the 🎺🌊 chance that it occurs at least 🚫🚫 once, 🅱 giving 👸👸 1 − (1 − 푝) 푚. The number 🔢❤ of consecutive sequences consisting of at 😔🍆 least two 💏 streams from 😮💰 a 🅰 set of 😰 푛 streams is 👌👏 푛 2 , as you 👆 choose 📥📥 two 🎄 different 💰 streams to 👌👁 be 🤔 the 🔑👨 first ☝ and 🏽 last. Adding in 😏 the 푛 sequences consisting of 💦🐲 only one 🏻 stream, 💦💦 which ♀ were 👶 not 🚫🚫 included because 🏽🤔 the 👶🆘 first and last ⬅ stream 💦💦 are the 👨👏 same 🖕😂 stream, 💦 you get 😷 푛 2 + 푛 which 🏼👌 is equal to 푛(푛+1) ❄👸 2 . We 👦😍 can 🔫❗ now ❔ get an upper bound 푝푛 on ☝ the 🌎 푝-value across 👉👏 푛 streams, using 🤳 the ⬆ 푝-value 💵👇 derived 🔜🔜 from 👉💥 our 🌍 sample. 푝푛 ≤ 1 👊 − (1 💸 − 푝) 푛(푛+1) 👸 2 🏻 (4) 💦💦 At this point, 🈯📌 let 💂 us 👫 go ♂🏾 back and 👏🅱 analyze an 😚 earlier assumption we 👶🤔 made: 🏠💰 that 😤 the ♂🕍 푝-values 🅱💰 between sequences of 💦 streams are 😟 independent 🙅 of one another. 👯 This 👁👈 assumption is 😠 false—however, 👳👳 it 😢⌨ is 🙀👏 not ♂ false ❌ in a ☝ way ☝ that could cause 푝푛 to be ✅ greater than this ⬆ upper bound. 🤐 Consider the 😶👌 exact 👌 way 👟↕ in ⬇ which the sequences of 📆🏿 streams are 🔢 dependent on 🔛 one 😈🏼 another. Since 👨 they 🏼😕 all contain streams from the 👏🐺 same 🖕😯 set 📚➿ (those from Dream), some 🤔👨 of 💦 the 💰 data 💰📉 in 😂 each 👏👋 sequence will 👏💯 be 🅰👨 identical to 💱 that 💝 in other 👪 sequences. This 😋 lowers the chance 🚫 that 🔍 Shifty Sam jWe can 💦 safely 🚦🚦 assume ♀♀ the streams reported 🔫 would 🤕 be 🐝 consecutive—it would be extremely 💯😂 obvious that the 🔪😱 streams were 🙈👶 cherry-picked 🍞🍒 if ☔ Shifty Sam reported 👮🔫 the 👻 luck 🤞🍀 in, say, Dream’s 💤 first, 🥇 seventh, and 💦👌 tenth streams. Non-consecutive streams could 🔮 be 👏 reported 🔫👮 credibly in 👏👏 unusual circumstances, ❌ but that 👇🍆 possibility is essentially negligible. could find misleading data, as 🍑🍑 he 👨👨 has 🛒 less data 💰 to look 👀 through 🗺 for unlikely events. In technical terms, we 🔨♀ can 🔫 say 😵😩 the 🛩 푝-values 💰👪 of 💦🌾 the sequences of 😏 streams are positively dependent upon one ☝💯 another—they 🚪🏊 are 🚟🅱 positively correlated with each 👏👏 other. 💰 For 🏔 this 🔥 bound 🤐🤐 to fail, 🤧🤧 the 🏼⤴ sequences would ✅ need 👌 to be ❄🏻 negatively dependent. 8.3 Sampling Bias in Runner Selection In addition to 💦💰 these particular streams of 💦💦 Dream’s 💭 being analyzed due 👅👅 to their high 📓 proportion of 😂⛄ pearl barters, Dream was 🏻👏 initially analyzed out 🌌🉐 of 💦💦 all runners due 👅 to 😅 his experiencing unusually good 👼 luck. 😄😟 Much 😩 like ♂😄 we 📌 calculated 🚜🚜 the ⤴ chance of 💦👮 observing data as 👦 unlikely as 🤔💯 the data in ♂👏 question in any 🔥👏 sequence of streams, we ❣ will 👏💰 analyze the 👽 probability of observing data this 👁 unlikely from any 🌐 runner in ⬇ the Minecraft speedrunning community, using 📤 the same 🏆🤷 formula for the 🚑🐆 chance 🙅 of 💦 something 😅😳 occurring at 💯🍆 least ❗ once 💯💯 in a series 💓💓 of 💦👨 trials that 🏾🍜 we 👧👦 used 📅😏 earlier. This 😂 results 🔢 in 🛌 the following correction, where 푝푛 is 👅😝 the 푝-value corrected for 🍆 a community 👩👩 with 🙌👏 푛 runners, and 💰 푝 is 🌈 the 🌈 푝-value 💵💵 for Dream 💤 in 📥👸 particular: 푝푛 ≤ 1 🤜👀 − (1 ⛈ − 푝) 푛 (5) 🍆 Note 🎵 that, 😐 as 🅱🍑 we are 🔄⭐ discussing the 👩🕜 푝-value 💵💵 for 💦 data this ⬆ unlikely occurring to a runner within their 🍆⬅ entire 👏👏 speedrunning career, the 👻 size of their career is not 😖 relevant. Although 😛😛 a 🎁 runner may 🗓 be more ➕ likely to ⏸ experience 😋😋 six exceptionally lucky 🍀🍀 streams if 😂🤔 they 👥 stream 💦 more often, we 👬 already account 💳💳 for 👏 the amount they 👴🤷 stream when calculating 푝—in 🅱 other 👪 words, 🐎 if 🅱 someone 🕵👬 streams more 💯😩 than 💉⬆ Dream, 💭💭 they 😱 would 💀👌 need a 💻↘ luckier sequence of 👀💦 streams to have 👍♂ an 👅🏻 equally low 푝. 8.4 👊 P-hacking 👮 Perhaps 🤔🤔 Shifty Sam examined multiple types 🅱🅱 of 💦 random 🔀 events and 🍒💰 only ☝👃 picked the most 💯👥 significant ones. 💯 For 🤔🍆 instance, 👉 there could have 😤🅰 been 💴💫 analyses of flint drops 💦 or 🎡 iron golem drops, 💦💦 and ➕ only ☝💋 pearls and 😫 rods were reported ♂♂ due to those 👉 being the 👦👏 most 👉 significant—indeed, some 🍌 other 💰 barter items, as 🍑🍑 well 🤷🤕 as eye 👁😉 of 💦🏻 ender breaking rates, 💰 actually 🚟🚟 were 🙈 recorded. To ✌🅱 correct ✅✅ for 😣 this, 👈🏋 we take 🖐 the 👏🙀 probability of finding 🕵 each result at 🍴👉 least 🤸👌 once among 💰 an 🤔 upper bound ℎ on 👍🔛 the 👀💲 different ↔🈯 types 🅱🅱 of events that 🚟😐 could have 💯 been 👦🥜 analyzed. Unfortunately, 😭 the correction used 🚟🙄 for 👨🍆 selection across ➡ individuals and 👴👏 streams will 😳 not 🚫 work here. That 👋 correction requires either independent or 😤💰 positively dependent probabilities; however, 🤔💰 there 👌💾 are negatively dependent probabilities involved here. For 🔙🍆 instance, 🤔 the 👨 more pearl barters you 👆 receive, the 👏 less 😔 opportunities there are 😱💢 to 👮 receive 👉 an obsidian barter: your 👉👈 numbers of 🤑👏 pearl and obsidian barters are 🙏😊 negatively correlated. We can 💦 still correct ✅✅ for this, 👆 but 😠 it 💦 will 📌🤤 require 📜📜 a much 😩 looser upper bound than 😻 the 🤣 ones 💯💯 we 🏃 have 🈶😤 used 🙄🚟 previously. Remember that 🍆 the ⚰ probability of 👏 any one of a number 📱 of mutually exclusive events occurring is ✅👌 the sum of 💦 their 🍮 probabilities—for example, the chance of 💦💦 rolling 😋😋 either a 👌👀 two 🎄✌ or a five on a 🎉 six-sided die 🚦😪 is 🔥😩 1 6 ❗ + 1 😎 6 ❓ = 2 6 👆💪 . However, 🖐 this is 😂 not the 😦🚗 case 👅🤔 for 🎅🎁 non-mutually 🏆 exclusive events. Consider ☺🤔 the 💰 chance 🙅😨 of rolling either 😌 a 💰 number ❤📱 less than three 💁 or 🚻🙂 an 👹💶 even 🕚☎ number. The 🖥😃 chance 🙅😱 of 🔥 rolling a 🀄 number 🔢 less 📉 than 😽 three (1 👸 or ➕👉 2) is 🔥 2 6 ❗👧 and 👈 the chance 🚫 of rolling 💊 an even number (2, 🕔💦 4, or 🔮 6) ❓ is 😩 3 😗 6 💪❓ . Adding these 🍆 together 👫😄 would 👌 produce 5 ♥🏼 6 💪 . But this 👉 counts rolling 💊 a two ✌💏 twice, 👀✌ producing a number 🎦😧 higher than ⬆ the 👏🌌 true 💯 probability of 💦🔥 4 🏽💦 6 🕕❗ . This 👈 double-counting problem 🏻 is the 👧 reason ♀♀ why ⁉ adding together 👫👬 fails ⛔ for probabilities that 💖 are ❓💥 not 😖 mutually exclusive, so 🆙 it is 🗓 not a problem 🏻 that 😐 our probabilities are 🅱 not mutually exclusive: 12 the 🚟🌜 sum 👁👁 of 👏 the 🌧⚰ probabilities will 👏 still work 💵 as an ✒ upper bound. Thus, we 😱 have ⚠😎 the 🅱 followingk , where 😾🌎 푝ℎ is 😳 the 👊👏 푝-value corrected for ℎ comparisons, and 🌚 푝 is the 😂📱 initial 푝-value: 💵👇 푝ℎ ≤ 푝ℎ (6) We will ⚽ choose 📥 values 👪 for 🍆👅 these formulas and ➕ compute the 😱💦 final 😪🌠 results 🔢🔢 in 😏🏽 Part 💔 IV. However, 🤔 to ensure 💰💰 these computations are ♀ not 🚫 invalid due 👅👅 to 🔎 unusual behavior of 🗜 Minecraft’s random 🎲 number 💦😧 generation, 👪 we 👧 will 👊🅱 first 🏻 analyze Minecraft’s code. kThis is 💥👏 commonly known 💫 as 🙇 the 👏 Bonferroni correction. 13 😏😏 9 Code 😲😤 Analysis When 👌😂 discussing probabilities this 👁 low, ⬇👇 concerns about edge-case ⚔🗡 behavior in Minecraft’s random number generator ⁉ (RNG) are relevant. We 👨 have 👏♂ been working 👷 under ⬇ the ⛓ assumption that the results of 👪 piglin bartering and blaze drops 💦😲 are independent random 🔀🔀 variables, as 🍑 one would 😎 naively expect 🤗 if 👩😂 Minecraft’s ☄🍑 RNG were 👌👶 truly ⚡ random. 🎲 This would 👪💀 mean 🤔 that 🏻🙅 the 👧👏 variables cannot 👊 affect one another; that is, 💦🈶 past piglin barters and 👏 blaze drops tell 📟🗣 you 😕🏿 precisely nothing about future 🎆 ones. 💚 However, 💰🖐 it 💦 may 🤷📅 seem possible 🔝 that, 😐👉 in some 🐔 edge ⚔ cases, 💼 piglin barters or blaze drops fail 🤧🤧 independence in ways ✔🤔 which ✌👏 increase 💳💳 the 🗣🍫 probability of 🐣💦 observing Dream’s 😴💤 data. 💰💰 Here, 😶 we will 💍⚽ analyze how likely that 😝🍑 is 🈁 by 😈 inspecting Minecraft’s ⛏☄ code. 😲😲 Before 🍑😂 beginning 🆕😍 the 🕜❤ analysis, it 😽😉 is 🔥🍆 worth 💰💵 noting that 🙇🚟 if Minecraft’s RNG were 🍑😫 to ✌ fail ☠ in such a 😬 way ↕😇 that 😩💦 piglin barters and blaze drops could 🤔🤔 not 😠 be said 🗣 to 💦🔢 be 🏻👄 approximately ⭕ independent, 🙅 it 💧😩 would 😏🍆 still 🛑😻 be 📖 astonishingly unlikely for them 👬🎊 to fail in ⤵😜 exactly 😉😉 the ❤👏 way required to produce the observed data. 💾💰 The failure(s) would need to 😥👉 (1) occur repeatedly over the 🚗🍑 course 🏎 of 💦 six separate play sessions for 😏👨 Dream, (2) only 👨 occur 👻 to 👊➡ Dream 💭 out of all 😮😩 runners, (3) 😗 affect both bartering and 👏💦 blaze drops, 😲 and 👏 (4) 🕓 specifically 🔵🔵 bias the results 🔢 towards ⛪ piglins bartering ender pearls 🍬🍬 and 🍆🚄 blazes dropping blaze rods, rather ☑🙇 than 🔪🔺 towards some 💵 other barter item or blazes not ⛔♂ dropping rods. Although 😛 this 👈👌 may 🗓🗓 still be more 🤔💦 likely than the 👏👏 data 💰 occurring without a 🃏👦 flaw in 👉👏 Minecraft’s 🍑 RNG, even before analyzing the 🤥👢 code 😤 it 😩🙅 appears a 🅰 priori extremely unlikely. 9.1 Confirming the 👨💦 Probabilities Though 💥💭 the 🕍👏 probabilities we 😺 have ✊ been 🤤 using 🏻 thus 🕵 far 🌌 for 🕓 piglin and 🤔💦 blaze drop ⚰👇 rates 💯😂 in 👏 Minecraft ⛏🚨 1.16.1 🕴 are 🔢 publicly available 💢💢 information, 📚 it is important 😍 to 💰👌 identify exactly 😉😉 where 🌎🤷 these probabilities come 💦💧 from. 👉 The piglin bartering proportions are 🅱 determined by the piglin_bartering.json file 📂 found 🤔🔎 in the 👉🌎 1.16.1 🕛🏫 jar filel . As expected, exactly once 🏳 each 👏👏 barter, the 👨 game 🔥 selects an 😍👹 item from 💥💰 the 😜🙀 following weighted table: 🎲 Item Weight Book 💯 5 😂 Iron Boots 👞 8 ✊ Potion 10 Splash Potion 🍾 10 🔟 Iron Nugget 10 Nether Quartz 20 🔳 Glowstone Dust 20 🎊 Magma Cream 🍨🍨 20 Item Weight Ender Pearl 20 🔳 String 20 📊📊 Fire 🔥 Charge 40 Gravel 40 Leather 🐄🐄 40 Nether Brick 40 Obsidian 40 Crying 😣 Obsidian 40 Soul 😱 Sand 🏝 40 Table 1: 🗿 The 🌌 simplified contents of 🚨 piglin_bartering.json. Here 🍒 an item of 😓 weight 푛 is 👎🅱 푛 times more ✋🍗 likely than 🅰🔪 an 💶👏 item of 🛢💦 weight one. 😉 Additional information 📚 regarding enchantments, stack 📚📚 sizes, and 👏 potion 🍾🍾 effects not 😡❌ shown. 🚫 Since 👨👨 the 🏽👌 weights sum to 💦🌱 423, and 🎅 ender pearls have 🎁😑 a weight of 💦 20, 🔳🎉 the 👏 probability of 💦🔴 an ender pearl barter is ♻🅰 indeed 20 🔳🎊 423 as 🏿 expected (in 1.16.1, 👸 the 👉👏 version 👧 Dream 💭💭 used). 🎶 lTo read these 🔫🚟 files 📁📁 on 🏽 Windows, simply ⤵😡 rename 1.16.1.jar 🌸 to 💰💦 1.16.1.zip 🤜 and ⏱ navigate to data\minecraft\loot_tables. 💰💰 14 👦 Blaze drops are specified by a ❔🍒 file 📁 called blaze.json, an 👴 excerpt of which is 🙌 included below: 😫 1 " function ": " minecraft : set_count ", 2 💕 " count 💯🙌 ": { 3 👏🎆 "min": 🕑 0.0 , 4 "max": 1.0 , 5 " type ⌨✍ ": " minecraft 🍑🚨 : uniform " 6 🤔 } One 👆🤓 can 🔫 see 🙉 that, 👨👨 when the 👏🍤 player’s 🎮💰 weapon 🗡‼ does not ♀❌ have 👏 a looting enchantment, blazes select ❇ between 🏻 dropping either 😤😬 0 or 1 ❌⏰ rods using a uniform distribution. Thus, a rod 🍆🍆 drop 👇⚰ occurs with 🍨👏 probability 0.5 as expected. 🍆 9.2 💦 Setting 🌃 RNG Seeds Failures of 🌈👏 one of Minecraft’s ⛏☄ RNGs to 💦💱 behave randomly are 🏄🈶 not ❌ unheard of—the 💦🤤 most ☺💯 famous 😎😎 examples of 🍳💦 these 🚑❌ are ♂🙏 the RNG manipulation exploits found in 🔙➡ versions prior 🔙🔙 to 👌👌 1.13. 🕴👂 These ☀📀 all work on 👋 the ‼ same principle: 👴🏾 some part of Minecraft’s code resets an RNG being used 📅🆒 by 😈😈 other parts of the 🏠👇 code, causing predictable behavior. 😦
submitted by Alexjandro23 to emojipasta [link] [comments]

A note on statistics

Whenever the topic of gacha rolls comes up so does statistics. Often in these discussions I see misconceptions and misunderstandings. This is understandable; when you go beyond the absolute basics statistics gets very unintuitive very quickly. In this post I'll try to clarify the numbers so hopefuly we can all waste our SQ responsibly in the future. If you spot any mistakes please mention them!
Disclaimer: I'm on NA, so I assume a 0.7% chance of getting a rate-up SSR. On JP that went to 0.8% with 4th anniversary.
(Quick note - for most of my numbers I go to .1% precision. I think this is fine for our purposes, but treat these numbers as being +/-0.05%.)
Part 1: FAQ
Here I'll answer some questions that usually kick off a discussion in other threads. I fully expect that many people will already know a lot of this, but it's worth going over.
Q: I haven't got an SSR in forever. Surely I have to get one soon?
A: This is known as the Gambler's Fallacy and it's a classic. The short answer is no - the Gacha is under no obligation to give you an SSR out of pity. The Gacha does not know how many times you've rolled in the past. It does not know how many times you're willing to roll in the future. It does not know about "catalysts" and there is no "desire sensor". It does not care that this is your waifu and you'll give up the game if you don't get her. Beyond any memes or jokes each roll is an entirely independent event with a fixed probability of certain outcomes. Nothing more.
Q: The rate of getting an SSR is 1%. What does that mean?
A: It means the chance of getting an SSR from a single roll is 1%. This may sound pedantic, but it should be emphasised that that is exactly (and only) what it means.
Q: If I roll 100 times what is the chance of getting an SSR?
A: The chance of getting at least 1 SSR in 100 rolls is 63.4%.
Q: Across an infinite number of rolls, what are the chances of getting an SSR from any group of 100 rolls?
A: Mathematically this is the same question: 63.4%
Q: Shouldn't it be 50%?
A: No. The number of rolls needed for a 50% chance of at least 1 SSR is 69.
Q: If I do a ten-roll what is the chance of getting a rate up SSR?
A: 6.8%.
Q: If I roll 100 times what is the chance of getting a rate up SSR?
A: 50.5%
Q: If I roll 1000 times what is the chance of getting a rate up SSR?
A: 99.9%
Q: If I buy a max pack of SQ what's my chance of getting a rate up SSR?
A: 32.0%.
Q: The ten-roll and SQ questions, but for JP with its 11-roll and 0.8%.
A: 8.5% for an 11 roll. 38.2% for the max pack.
Q: What's the average number of rolls needed for a rate-up SSR?
A: Define 'Average'.
Q: Alright smartass - how many rolls do I need for a 50% chance of getting a rate-up SSR?
A: 99 (Well, 98.7)
Q: How many rolls do I need for a 90% chance of getting a rate-up SSR?
A: 328 (That's 984 SQ.)
Q: How many rolls do I need to guarantee a rate-up SSR?
A: Infinity. That's not just me being an arse, that's the mathematical answer.
Q: So how much quartz should I save for Skadi/JalteMerlin/My Waifu?
A: As much as you're comfortable with. Let's be honest - you will never get a 100% guarantee of getting who you're rolling for. It's entirely down to you how much SQ (and for some of us money) you're willing to put in. Personally I budget 150 rolls per rate-up SSR when I'm saving, which gives me a 65% chance. I fully expect some to take more and some to take less, but fingers crossed it'll balance out. That's my choice; you have to make yours.
A note on infinity:
Something I often see stated is that a 1% chance means that across an infinite number of rolls there's a 50% chance of getting an SSR from any group of 100. This is incorrect (as stated above). But it does beg the question of what an infinite number of rolls does mean. The core of it is that if you have an infinite number of rolls, 1% of those rolls will give you an SSR. Across all of infinity you will get exactly what the percentages indicate. But within that infinity you will have 'uneven runs'. There will be runs of a million rate-up SSRs in a row. There will be runs billions long with not a single gold servant to show for it. For my part I think any talk of infinity is rather academic - we don't have an infinite amount of SQ (or money!) to throw at the gacha.
Part 2: 150 roll breakdown.
In this section I'm going to look at a hypothetical run of 150 rolls and give the chances of certain outcomes. All numbers are percentages, I just didn't want to type out % so much. This ignores the guaranteed SR CE and R servant. Spook figures are for any spook, not a specific spook.
Cases SSR Spook Rate-Up SSR Rate-Up SR Specific non-event SSR CE Event SSR CE
0 63.7 34.9 10.4 90.6 1.4
1 28.8 36.9 23.7 9.0 6.1
2 6.4 19.4 26.9 0.4 13.1
3 1.0 6.7 20.2 0.01 18.6
4 0.1 1.7 11.3 0.0004 19.7
5+ 0.01 0.4 7.7 0.0001 41.1
Part 3: Formulae
Here are some of the mathematical explanations of how to generate probability numbers yourself, and links to some of the web pages you can use if you don't feel like doing it by hand.
Chance of getting at least one X% event in Y rolls:
1-(1-X)^Y e.g. chance of getting one rate-up SSR in 85 rolls is 1-0.993^85=0.450. You can type this into google and it'll do it for you.
Number of rolls needed for an Y% chance of an event with X% chance of happening:
Log(1-X)1-Y e.g. For a 70% chance of a rate-up SSR you need Log(0.993)0.3=171. Link to the site I use.
Chance of getting Z events with an X% chance in Y rolls:
Er... something something binomial distribution. I'll admit I don't understand the maths on this one but this site can do it for you. As an example of usage, if you want the chance of getting 5 rate-up SSRs out of 1000 rolls put in "0.007", "1000" and "5". The top box gives you the answer (0.128).
That's all from me. Good luck with your rolling!
Edit: Adding in rate-up SSR chances for 10-roll and max SQ buy, adding NA disclaimer and a couple of numbers for JP.
Edit2: For the rate-up SSR CE numbers I originally used 0.28% instead of the correct 2.8%. This is now fixed.
submitted by sgtkang to grandorder [link] [comments]

Epic Seven Quick-Start Guide

Epic Seven Quick-Start Guide
I think this is a great game and I've been lurking and participating in the daily question thread for a bit. Here's my attempt at passing that back up to the community.
​
Selective Summon:
Five main routes as of 3/25. I ordered them for amount of sanity cost vs payout.
​
Playing the Game:
​
Facts that you want to know about gearing up:
​
Guaranteed Gear - CabbageCZ
This topic really warrants a megaphone: the guaranteed gear will be what gets you through a lot of the progression hurdles.
​
Main Gear
Only upgrade red gear you find in abyss and lab for quite a long time (a month+). Use your resources wisely!
​
+12/+15 Your Right-Side Gear - CabbageCZ
A gear's +15 main-stat value is 5x the +0 value. It starts slow, but at higher ranks it jumps by a lot.
The difference between a +10 piece of gear and a +15 piece of gear is massive. Just the last few ranks make a huge difference, most of the power is in the last ranks. Prioritize +12, +15 on the top right side gear you have ASAP, it's a huge boost in power.
Sidenote: you should be watching the secret shop for jewelry/boots like a hawk when you unlock lv70/85 gear. The first +50/60% ATK or +50/60% HP gear will be a great power spike for your main healetank/DPS.
​
Artifacts
Artifacts are typically class specific gear that can drastically change how a unit functions. For the most part keep one of every artifact. You can find exceptions by searching reddit.
​
The Best 3 Star Artifacts: Daydream Joker (god tier PvE), Candlestick, Tonfa, Sheath. All of these are good even in endgame.
​
The Best 4 Star Artifacts:
​
The Best 5 Star Artifacts: Anything Soul Weaver. Rhianna & Luciella (Thief) best in slot almost all of the time. Uberius’s Tooth (Warrior). Song of Stars (Ranger) .
​
Again, I repeat that I don't feel that I'm doing the artifacts justice, all the while, my lists above are all sorts of hand waving magic. My suggestion would be taking some time and read the text on each artifact you own to really get the most out of your setups. (And further research through reddit!)
​
What is Farming in E7?
Farming in Epic 7 is a majority of the game. The goal is to get gold, exp, and catalysts for unit advancement.
Prioritize clearing Side Story Event: Always farm event currency in the Side Story Event mode, and with it, buy every item in the Side Story Event store.
​
AP Store
When you are done with Side Story: Farm Epic Catalysts using the AP Store, clearing as many Epic Catalysts as you can each week. This is the best gold, exp, and chance of catalyst vs stamina spent possible.
Friendly Advice: You are statistically unlikely to farm "Epic" catalysts and succeed in getting 1,2,... 15 of them from world maps. If you're farming with the expectation that you'll get them, you are setting yourself up for failure. (There is only 1 chance per drop typically on the boss monster. As opposed to non epics which have a chance to drop from the 5-11 other enemies on the map.)
The remainder of your epic catalyst will come "free" from Side Story and purchased from a Raid Store. I strongly advise for you to resist purchasing normal catalysts, and instead farming for them, or trading guild mates for them.
​
Promoting Units:
Always promote max level units before foddering away the unit. Units can only promote by being max level, they have to eat equal rarity units, but the food does not need max level. Much of the game is leveling fodder to feed.
​
Your first two 6* s should be your DPS, it's nice to have an AoE and a Single Target, optional. Lorina is a good choice here.
Your third should be either a support unit that buffs/debuffs, or your healer. Fourth should be which ever you didn't do.
​
What to do on the various maps:
​
World: Main story maps. Either carefully 3 star everything your first trip. Or come back and do it later. There is a second difficulty that continues the story when you beat 10-10. Clear everything for both difficulties. Prizes are generous especially on world difficulty.
​
Labyrinth: Look for little regions that stick out, go there for gold chests. Goal is to find them and push towards exit asap.
​
Raid: There is a 2 cost lab called Raid, try it as soon as you unlock it and prioritize it if you can beat it. The eventual goal is to finish all 5 bosses of the raid in 3 runs. That requires run 1 with 28 moral (1 boss and clearing towards next boss), run 2 with 33+ (2 boss clears), and run 3 with 28 moral (clear queen first then last boss). This will let you move units around to handle each boss mechanic.
​
Hell Raid: At the time of writing there are only two bosses. Only spend raid currency on buying the God Tier raid gear.
​
Abyss: Do it until you can't. First two life steal sets are huge power spikes for free. Push for them aggressively.
​
Altar: Clear as far as you can initially, farm them only when you need to.
​
Side Events: If possible, buy out the entire store every time. This is the best use of your stanima period. Farm normal with 1 of your own units, one helper, and 3 fodder for best rate of return. Hell is only good for burning all of your stamina for event currency and poor for exp and catalyst drop rate.
​
Hunts: Go as far as you can just to measure your progression. Beating Hunt 11 on auto battle is currently the same as "beating the game."
​
Event Battles: There is the regular battles which have a chance of dropping charms (NOT WORTH IT.) Do clear them for quest prizes once.
More importantly there are Limited Event Battles which have a chance to drop artifacts. Play until you get 1 event artifact. Then stop unless you're at the stage where you can clear hell, then max one out. Doesn't matter if you think it's good or not. It might be useful later.
​
Arena: Spend all resources fighting bots, it's okay, you'll reach a point in ladder climbing where this is what you'll do a lot of anyways.
The main two strats, are to have a speedster buff up team, then everyone else aoe's (called a cleave team). The other main team is the team that can survive a the first wave of cleaves with sheer stats or disruption, and wins from going second.
​
Upgrading Sanctuary Buildings:
​
Guild:
Join any guild ASAP! There's a shop in guild here with prizes you want. Donate aggressively to get them.
GvG - Play daily for prizes. Doesn't matter if you lose, just crash your teams and your fodder into things.
​
Shopping
There are a lot of currencies.
Skystone / Pack Store
​
Normal Store
​
Power of Knowledge Store
You get powder from selling 3* or better artifacts. Use guides to determine the "must haves" for your team.
​
Ancient Coin Store
​
Conquest Points Store
​
Friendship Store
​
How to get more Trasmit Stones / What to do with Friendship Bookmarks
Friendship bookmarks are used for low quality 10 summons. You get two types of junk, unit fodder, and artifact fodder.
The quest requires you to "skill up" an artifact, every so many times you do it, you'll get a quest complete for a bunch of silver transmit stones. The quest line goes up to 30. With your friendship points you can quickly front load all the silver transmit stones you'd otherwise have to wait months for.
​
Lobby
There are daily log in events you have to take part in, swipe left from the big banner button until you find your current weeks event.
​
Battle
​
Random Advice or Facts:
​
Molagora
You will hear horror stories about how limited and rare these guys are. Only three rules of thumb to follow here.
All other cases, don't buy it.
​
General Spinning Advice
Personally, I'm afraid of getting new units, they cost so much time and investment to add to my teams. This is what keeps my desire sensor in check. Until I fully built my current project, I tend not to want to divert my resources to another character.
That said! When first starting out, you do want to do a good amount of spins (maybe 200 bookmarks?) before saving up, it'll flesh out your artifact and utility heroes earlier on. But at some point you want to stop and begin to hoard for things you want/need.
In order to not be burned, you'll want to save 600 bookmarks for limited banners for the pity rate to kick in and get you the unit. You hope that you don't spend all 600, but the 121 spin club is a real thing. =(
When spinning on just regular character banners, be happy for the little things.
Generally don't save MoonLight ML summons, spend them right away. Mystic Summons (GvG currency) you can save until the rotation has what you need.
Spin all friendship bookmarks until you can't handle the fodder or artifact count. Ideally you use friendship summons to replenish fodder and farm transit stones.
​
Daily Rotation:
Then collect all reputation quests for the day.
​
If you have more time:
​
What is end game?
At this point you're just doing PvP, GvG, auto battling Hunt 11's, doing Hell Raid, and collecting free daily prizes from abyss (since you only need to complete it once).
​
TLDR: Spin for pretty much anything and beat the game with it. Do daily rotations. Game gives you enough stuff for gearing and promoting first four characters well. %based stats and speed are best stats. Spin early game, save mid to late game. Beat story, Beat Lab, Beat Abyss, Beat Side Story. Then grind ad nauseum and keep desire sensors in check.
​
Thank you for reading / bookmarking / commenting, whatever it is you did, I appreciate it!
submitted by PuzzleByron to EpicSeven [link] [comments]

"Fortune Favours" Ficlets - Daily Prompts February 2019

Hello, hello, and welcome to another month of FanFiction's Daily Prompts! In case you're new here, the idea is that there's one prompt every day of the month with a suggested wordcount of 100-500 words. You don't have to complete every prompt and you don't have to do them in order. You don't even have to share them here! But it's nice to see what other writers are up to on the sub even when we don't share fandoms, so I encourage it ;)
I had some trouble coming up with a theme for this month’s prompts, but I’ve been playing Persona 5 recently and one of the things I really enjoy about that series is the use of symbolism from Tarot Cards. And then I thought, hey, we’re just getting into a new year, why not have a month themed around fortunes and luck? Plus, “Fortune Favours February” is alliterative. Everyone loves alliteration.
Despite the theme, however, the point of this is exploring the symbolism of fortune-telling for our stories. We’ll also be playing with tropes relating to destiny and fate, as well as throwing some real curveballs at your characters with luck-of-the-draw prompts. I definitely cannot predict you the winning lottery numbers.
If these prompts don’t float your boat, or you just need more… feel free to check out the previous months: April, May, June, July, August, September, OCtober, November, December and January. If you do choose to write some of these prompts, you can post them in this thread so people will see them.
Some other guidelines:

February 1 | Fandom | “Title” | Rating | Offsite link/wordcount

Friday 1st – Heads or Tails. Your character has come to a crossroads and is stuck between two choices or routes, one of which is bad, and one of which is good (your character may or may not know which is which). Flip a coin or use a random number generator to choose which one your character is stuck with. Potential examples include: the character giving in to or resisting a self-destructive impulse; the wrong or right thing to say to a friend or ally; the safe or dangerous route; going out or staying in. Feel free to come up with your own ideas, of course. (500 words) Saturday 2nd – Trope: The Chosen One. A heroic archetype older than print, it’s time to put your own spin on the idea of “the chosen one”. Feel free to check out the related tropes on the tvtropes entry and subvert them if you wish! (300 words) Sunday 3rd – Readings: Tarot Cards. One of the more modern forms of fortune-telling, originally a card game, today the Tarot is popular because it’s replete with symbolism, each care from the Major and Minor arcana having potentially different meanings based on whether it’s in the reverse or upright position. There are various readings that can be done with Tarot cards, but let’s keep things simple for today. Pick one of the Major Arcana and write a character study based on that Arcana’s meaning. (400 words) Monday 4th – Oracles. Various people throughout history have claimed to have some special insight into the future. Some of them, like the Oracle of Delphi, had temples built for them, whilst others, like Cassandra, were disbelieved and scorned. Someone, whether through foresight or more mundane powers such as meteorology, has predicted a disaster. What response do they receive, and how do they feel about it? (300 words) Tuesday 5th – Oneiromancy, divination through dreams. Write a drabble about a dream your character has. This can be a dream as in a goal, or a dream they have when asleep. Actual divination not required, but have fun with foreshadowing and symbolism! (100 words) Wednesday 6th – Trope: Self-Fulfilling Prophecy. Another trope that dates back to (at least) the ancient Greeks, where doing your best to subvert a prophecy actually causes it to come true. Of course, the “prophecy” in this case doesn’t have to be a literal prophecy: this happens in the mundane world too, where rumours of a bank’s insolvency causes a run on the bank which actually does drive them into insolvency. So, what fate is your character meeting on the road they took to avoid it? (400 words) Thursday 7th – Lucky Sevens. Your character has gambled on something, metaphorically or literally, and this time they’ve come up trumps. Celebrate your character’s lucky break! (200 words) Friday 8th – Random trope! Hit the random trope button on the tvtropes homepage, and write something inspired by that trope. Feel free to pick the best of three in the event of getting a trope that you can’t write for whatever reason. Choose a suitable wordcount to aim for and away you go. Don’t forget to link us to the trope too! Saturday 9th – Readings: Tasseography, or divination from tea leaves. Often the symbols in tea leaf reading have different meanings than other forms of fortune telling, and the placement in the cup can influence the reading too. Let’s use this inspiration today to upset your character’s expectations. Is something they thought was far off coming upon them sooner than expected? Did they misinterpret another character’s actions in a serious way? Or, to go literally, maybe this tea party is really just not what they were expecting. (300 words) Sunday 10th – Make Your Own Luck. One of your characters doesn’t believe in coincidence or fate. Through hard work or outright cheating, they’re going to make things work out the way they want. (400 words) Monday 11th – Trope: Externally Validated Prophecy, when a character makes a prediction the audience knows will come true. This can be a Genre Savvy character who says something bad will happen if they split up in this haunted house, or someone in the past predicting an event the audience knows later happened. Or, in fanfiction, the future of the canon! You may also want to investigate It Will Never Catch On or This Is Going to Be Huge, best summed up as “The Titanic is unsinkable”—when a character makes a prediction the audience knows is wrong. (200 words) Tuesday 12th – Augury, divination through the flight of birds. Write a drabble inspired by birds or flight. Maybe your character feels like a caged bird, confined to one path, or feels free to choose their own destiny. Be as literal or metaphorical as you want! (100 words) Wednesday 13th – Break a Leg! Traditionally used in theatre as a way of wishing good luck, where it’s considered unlucky to actually say it aloud. We can do our own take on this today. Your character is wishing someone good luck, or being wished good luck, but for some reason the words can’t be said aloud. Why and what happens instead? Alternatively, your character needs all the luck in the world to pull off the performance of their lives! This could be a literal theatre performance or bluffing their way into the villain’s lair. Bonus points if you can combine the two somehow. (400 words) Thursday 14th – Unlucky in Love. Today is Valentine’s Day, but there’s enough lovey-dovey stuff out there in the world. Let’s spread angst and misery instead! The “love” can be romantic, platonic, familial, or other, but either way it’s not going well for your character right now. (300 words) Friday 15th – Wheel of Fortune. Your words today are “danger”, “spirit”, “horizon”, “mellow” and “penultimate”. Spin the wheel and see which one you get. Write a drabble inspired by that word. Include the word at least once. (100 words) Saturday 16th – Fortune Favours the Brave. You can’t get lucky if you never take risks. Today your character is taking the brave step of reaching out for something or someone. The question is, will the odds be in their favour? (300 words) Sunday 17th – Trope: Prophecy Twist. A trope Older Than Feudalism, used by everyone from the ancient Greeks to Shakespeare to Tolkien, yet it’s still an incredibly popular way to subvert audience expectations in works with a prophecy. Maybe your work doesn’t have a literal prophecy to subvert, but you can still utilise double meaning phrases and exact words (“I’ll give you everything that you deserve”) to set up a similar ‘twist’. (400 words) Monday 18th – Superstitious Minds. A superstition is a “pejorative term for any belief or practice that is considered irrational or supernatural”. Despite that, our society is full of superstitions, from collecting good luck in horseshoes to seven years of bad luck if you break a mirror, and people often have their own superstitions, such as a personal lucky number. What superstitions does your character have? (300 words) Tuesday 19th – Luck Comes in Threes. A reference to the old belief that luck, good or bad, comes in sets of three. Let’s get a snapshot of three instances of good or bad luck in your character’s life. (Set of three drabbles, 3 x 100 words) Wednesday 20th – Portent of Doom. Red skies at morning, sailors take warning. A variety of things are said to foretell death or danger, such as a grim, the wail of a banshee, or something celestial like a comet or an eclipse. Something in your story has a character or place marked for a terrible fate. What is it? (200 words) Thursday 21st – Readings: Chiromancy, or palm-reading. Today inspiration can literally be found in the palm of your hand – doubly so if you’re reading this on mobile. Check out the wikipedia entry for palm-reading and borrow one of its beliefs or symbols for your prompt today. Or, go literal and write something about hands! (300 words) Friday 22nd – Horoscope Help. Look up today’s horoscope for the astrological sign your character falls under. If you don’t know or they come from a canon with a different calendar to ours, feel free to use your own horoscope or pick one at random. I hope the future looks bright for your character, because at least one thing on that horoscope is coming true for them today. For bonus pats on the back, include everything in the horoscope. (500 words) Saturday 23rd – Lucky Men Need No Counsel. With enough luck, you don’t need good advice or wisdom. Luck is pulling through for someone today, and they’re getting away with something they really shouldn’t. The question is, when will that luck run out? (400 words) Sunday 24th – Gambler’s Fallacy. This is defined as “the mistaken belief that, if something happens more frequently than normal during a given period, it will happen less frequently in the future (or vice versa)”, normally associated with gamblers, hence the name. Maybe your character is a gambler, or maybe they’ve just suffered a string of bad coincidences, but their luck has got to turn around soon, right? Right?! (200 words) Monday 25th – Numerology, the practise of using numbers to find connections between coincidental events. What number has special significance to your character, whether good or bad? (100 words) Tuesday 26th – Be Careful What You Wish For. A common phrase applicable to every day life. Whether the “wish” is magical or not, something your character wanted is backfiring on them terribly today. (300 words) Wednesday 27th – Readings: Tarot Cards. I love them so much I did it twice. This time, use the reverse meaning of a Tarot Card for your prompt. (If you picked a reverse meaning last time, use the upright position instead.) You can use the same Tarot or choose another one if you like. Alternatively, you can explore the meanings of some of the Minor Arcana cards. (200 words) Thursday 28th – Trope: Screw Destiny. By now you’ve probably had it up to here with all these luck and fortune tropes. Well, feel free to channel all that frustration into our last prompt. Your character is facing impossible odds or something that seems predestined. Spit in the face of probability and kick destiny to the curb as your character says: Not this time. (400 words)
submitted by holliequ to FanFiction [link] [comments]

[I am worried] Gear inscriptions and layers of RNG on RNG and the potentially never-ending journey for our builds (Lack of inevitability.)

I'll start this post with some definitions I got from the stream so we're all on the same playing field. Some of my information might be a slight bit off because the stream just ended when I began to write this post and I'll try and edit to correct anything that is incorrect if someone points it out!

Definitions

1: Components: These are essentially your armoaccessory pieces that gives you bonuses to your abilities/damage/passives.
Components can have a max of 2 inscriptions on them.
We get 6 components we can use.
2: Inscriptions: These are secondary stats that are tied to components/equipment that can give bonuses such as +explosive damage or +hover time. The rarity of the gear will determine how many inscriptions are on the gear.
They said that there are approximately 100 inscriptions.
"Inscriptions on components are limited to a max of 2. So you can have 12 total inscriptions from components alone. Inscriptions on weapons and gear go up to 4. So you can have 20 total inscriptions from weapons and gear. That means, a grand total of 32 inscriptions that you can have." ​ (Thanks to Alizaea for the updated info.)
"Also worth mentioning the different "pools" for inscriptions. There's a primary damage pool, a traversal pool, a utility pool and who knows how many more. Point is, when you get loot it won't have 3 damage inscriptions, it'll have one from each of the different pools. So you'll can roll a gun with +10% assault rifle damage, +10% hover speed, and +10% pickup radius, but not one with +10% assault rifle damage, 10% ice damage, and +10% damage with shotguns."
"Inscriptions have pools they belong to. So there's a primary dmg pool with say 24 inscriptions, a utility pool with another bunch of inscriptions, a traversal pool etc. So a masterworked item can have like 4 inscriptions, each from a different pool."
(Thanks to Garginator850 for this updated info.)
Inscriptions from what I am pretty sure I heard can go from 5-10%.

Why I am concerned (It's not grind, it's that there is no inevitability.)

There is a lot of talk about builds and customization of gameplay.
I am a long term support player with a very specific build and playstyle in mind and I would go after stats such as (I have no idea if these are done):
  • Ability Duration (such as for windwall)
  • Freeze Duration
  • Freeze (The time-related stat shown on stream for the fire element.)
  • ICE AOE Size
  • ICE damage
  • Cooldown reduction
Let's go off of potentially 100 inscriptions. To get a specific single inscription on a piece of gear with 1 inscription is a 1/100 chance. To get one of these inscriptions on a piece of gear with 2 inscriptions is 1/50, so on and so forth.
For me to get 4 inscriptions on a single piece of gear that I want based on the list above I have a (6/100) * (6/100) * (6/100) * (6/100) = 0.001296% chance of that happening. Which means that is VERY unlikely to happen.
So while we have immense build power and a lot of control over gameplay style... the problem is now we have nested RNG in RNG in RNG. In video games that are online having the concept of "Best in slot" is an extremely prevalent and dominant theme of endgame gameplay. But when we are even talking about playstyles like mine where I am after gear that can enable a particular gameplay style it's admittedly pretty demoralizing to see that the chances of me ever fulfilling my build style is very close to 0.
I don't know if the ability gear has this or not, but I am 100% sure I saw it on components and weapons.
2 weapons with 4 inscriptions per = 8 inscriptions
6 components with 2 inscriptions per = 12 inscriptions
3 gear (aka abilities) with 4 inscriptions per = 12 inscriptions
= a total of 32 inscriptions.
Keep in mind for weapons and component, they have their own RNG tied to their own drop rates. Which have RNG on their stats (components can have various stats from what we saw in stream)... which then has RNG on their inscriptions.
Inscriptions can apparently go to 10% per inscription. That is 320% of stats sitting there.
That's 320% of stats... To me this is a very huge thing that can make or break a build. For instance 100% duration is DOUBLING the duration of a freeze or windwall. That is HUGE.
So we literally have RNG nested in RNG nested in RNG. It's not enough to just get the item with the stats you want. And the difference between player to player with builds will be INCREDIBLY VAST. 320% of stats sitting there is non-trivial.

Grind is not the issue, putting in effort is to be expected. But being on a helpless treadmill praying for RNG to go your way is not fun.

I expect grind. I want to be kept playing this game for years to come, sincerely. I am one of those people that gets into an MMORPG or online game and sticks to it for years. Like for FFXIV I was involved with that game all the way back to it's pre-release and am still subscribed and participate in it's "hardcore" raid scene.
So to me grind isn't an issue. But the issue is there is NO INEVITABILITY.
I am fine putting in grind but for me RNG has consistently proven itself to be a very unkind game mechanic and that it often breeds resentment and helplessness in games where you are going out trying to achieve something even roughly like what you may have envisioned like I did above. After the like 100th time killing a raid, not getting that ideal piece of gear is extremely draining. I have been there before and it's not fun, it's hands down one of the most demoralizing experiences I have ever had in gaming and has resulted in me actually quitting games in the past because of it.
Again, it's not the fact that there is grind. It is the fact that there is no inevitability. There is no way to slowly grind up and know "hey even if I don't get this piece of gear after my 100th run, I can cash in "tokens" and get the stats I want.
Now multiply this over 6 components.
Now add in weapons.
I don't know if the ability gear has this or not, but I am 100% sure I saw it on components and weapons. Regardless we have 2 weapons, 6 components = 8 pieces of gear which have their own RNG tied to their drop rates, to the base stats on the components and the rest.
To reiterate over my example above. If I wanted 6 stats out of the 100 that is a 6/100 chance of getting one.
6/100 multiplied by 4 inscription slots = 0.06 * 0.06 * 0.06 * 0.06 = 0.00001296 or 0.001296%. For just the inscriptions on a component. Now that component probably has 100 or so primary stats so we have another 6% chance at that even being the right set of stats. Then we have 6 components to do that with.
That alone is such an alarmingly distressing amount of RNG I don't know what to say other than concern about the ability for us to actually have a build.
That gets into my next point.

Inevitability

I've played way too many games for way too many years but consistently for me and many other it's felt better overall to be able to grind LONGER for something and put in more effort but have a guaranteed outcome that we are working towards rather than stabbing into the aether.
No, crafting a weapon over and over and over for a RNG roll isn't inevitability (especially a legendary one... I doubt collecting the materials for a legendary weapon is trivial!). There is with RNG no guarantee you will ever get your roll and that is actually a fallacy. https://en.wikipedia.org/wiki/Gambler%27s_fallacy
FFXIV: For the MMORPG FFXIV there are "primal raids" that people can grind and kill 100 times and each time they collect a token. They can eventually trade in 100 of these tokens for a mount that has a small chance of dropping (and smaller chance you successfully beat your team mates for the roll for it!).
This gives players inevitability that eventually after grinding for 100+ times that they will eventually get this mount. That it's fine and not all hope is lost and that they aren't just funneling in time into the abyss for an RNG drop that they are fighting with 7 other people over. This gives a lot of people more reason to keep sticking to the content and grind through that 100 times.
On the flip side I will bring up an example of where FFXIV also failed with loot,
Diadem:
This system looks the most similar to the system we will have in Anthem and that is what worries me. With Diadem you did a bunch of events and had a chance at absolute BiS gear....
...That had it's stats tied to RNG. I'll choose probably one of the most kind and gentle posts about the playerbase's opinion on this (You can bet there were many more "spicy" / "exciting" posts on this. But I will advocate for the gentler...
https://www.reddit.com/ffxiv/comments/611aah/diadem_20_analysis_and_final_opinions/
_"So long as you worked hard and had some skill, you could get whatever you wanted. That’s what the “American Dream” really is, Yoshida.
So, enter Diadem. What changed? An alternative gear progression model was introduced – pure and complete luck.
With Diadem gear, luck is the only thing that matters. Sure, you can increase your chances through hard work but it’s no different from ARR pony farming or HW bird farming before the introduction of the 99 token trade-ins. I think quite a few people can share their nightmares about that endless spiral of despair. You can farm Diadem endlessly but without any luck, you’ll never get a respectable piece of i265 gear or an i280 weapon. And, if you do get lucky, you suddenly have a piece of gear that no alternative obtained purely through hard-work and/or skill can compete with.
To be fair, RNG is not necessarily bad. Aquapolis is heavily RNG-based. PotD accursed hoard rewards are heavily RNG-based. Wondrous Tails is heavily RNG-based. The difference is that regardless of RNG, all of those still followed the law of effort and reward. Even their rarest rewards had a defined gil price that you could work towards. Someone could get lucky with WT and get an Ornate Ironworks Apron of Crafting. As an alternative, you can pay gil to just buy it or overmeld grade V materia to achieve the same level of power.
In more than a few discussions regarding gear progression, the Diablo franchise has been referenced. To start, I just want to clear up one fallacy. Diablo has never been based on RNG. In both D1 and D2, you had trade and markets. Even if the piece of gear you wanted didn’t drop or roll with the proper stats, you could trade for it or buy it. Even in its much maligned state of release, D3 also offered you the ability to circumvent RNG through the auction house. Since the auction-house’s removal and the change to a more individualized loot system, D3 has continually made changes to temper its RNG. They buffed drop rates, gave drops a character specific bias, changed gambling to be a viable means of targeted gear rolling, added the limited ability to reroll secondary stats, etc. They’ve gone out of their way to revert to a hybridized model of work/skill and reward.
Pure RNG is antiquated design and has no place in a vertical progression MMO. It’s not like FFXIV doesn’t understand this. With Alexander’s shift to a hybrid token loot system, they abandoned the more RNG loot system from Coil. They added token trade-ins to help negate the RNG from EX-trials. They’ve actively tried to mitigate the impact of RNG. It’s baffling that Diadem sticks out like such a sore thumb."_
This rubbed many people the wrong way and honestly Diadem was a complete failure that I haven't heard about in over a year if not longer. The content was dead on arrival and infuriated people to the point where myself and many others just didn't do the content because the RNG grind was helpless

This is something I am very passionate about and was gearing to make YT content related to this.

I am a build fanatic and love to figure out playstyles and determine how we can play unique from each other and how to determine synergies. I am absolutely that person that min-maxes their gear and loves to try new and unique things. For me the OPTIONS of the builds and all of the various stats is extremely exciting. I see so much room now for being able to POTENTIALLY run a wild number of builds (if we get the gear, which is my concern here).
Want to fly more and go for a like flying rocket launcher build? We can clearly do that.
Want to do a more supportive freeze build like me? Clearly that's an option (YAY!)
Want to focus on ability spamming with cooldown reduction and the like? From what I've seen in the stream, you can most likely do that too!
Want to do X, Z, Y? Probably can do that too!
I want to emphasize that's FANTASTIC and gets me very excited to gear up to do content on this game!
I truly didn't want to end this post on a negative note, but I am concerned because I am one of these people that loves going and figuring out new builds and trying out new stuff and making things happen.
This would certainly be along the same lines as the MANY Warframe build guide videos such as this one (picked one at random) : https://www.youtube.com/watch?v=jSeryg_8EnA
I'm struggling to imagine a world with these RNG mechanics where I can say "hey just slot up your javelin with a component like 1,2,3,4,5,6 and equip weapon 78 and weapon 32 and do X Y Z".

In closing

I sincerely hope that there is some mechanic introduced where we can grind for some sense of inevitability on our gear. Since builds and playstyle are UNDENIABLY a core part of this game I sincerely am hoping that there are some mechanics for us to grind for (I am not advocating for getting our ideal build in a day or a week or even a month).
Like I understand the fundamental idea of keeping people in a gameplay loop, but that can be done with mechanics that give players a sense of progression and that they aren't just throwing their hands up into the air praying for RNG to have Mercy on them.
Sure people will get lucky, that's the nature of things. But I am sure that someone who wanted to play a DPS Interceptor would be VERY unhappy to get a gear that would be my personal playstyle's "best in slot".
And that's the beauty of the build system here, we have a lot of flexibility. But we need a way to reliably GET the build.
submitted by bearLover23 to AnthemTheGame [link] [comments]

CMV: The political ideology I propose herein would be a vast improvement for America, reunify the country if people at large bought into it, and protect human rights better than either major party.

I'm considering writing a book proposing a new political ideology, and thought I would use Reddit for feedback!
The core of this proposed political ideology is neither Democratic, not Republican, nor Libertarian, but has elements of it that would appeal to a cross-section of the population, I believe.
The main focus of the ideology is reliance on logic instead of emotion, and protecting human rights. This is a common aim among all Americans to differing extents, but few agree how to go about it. In this post I'll just focus on a few aspects of my ideology, but in large part it has to do with maximally restricting government's ability to dictate personal actions. This is something Libertarians fundamentally agree with (though their desire to eradicate business and environmental regulations as well turn many non-libertarians off), and should also appeal to small-government conservatives and human-rights Democrats.
"Big Ideas": -The government does have an important role to play. They should protect the commons (environment), provide a social safety net, guard out borders, create a business environment that is fair and competitive, collect and distribute taxes, and ensure the safety of their citizens. We reject the far-libertarian view that everything should be privatized. -That said, as far as human rights go, eliminating the excesses of the criminal justice system is inextricably linked to ensuring the rights of the citizens from intrusion by their government. -Criminal laws are nothing more than threats from our government. Remember, pieces of paper do not have the power to physically prevent a murder - all they do is say "If you do Action X, we will ruin your life." This is justified sometimes, but we should never forget the true nature of laws as threats, and view them as a necessary evil at best. -Illegalizing any personal action is inherently an intrusion into personal freedom by government. That is not to say it is never justified, but it should always be viewed with extreme skepticism. -The right to engage in personal actions which do not cause harm is fundamental, not subject to the whims of public opinion. This is a key difference in this ideology. -A general principle is that "If a personal action is legal in at least one upscale, western first-world country (being here defined as the US, Canada, Australia, and any country that is both in the EU and was not part of the Warsaw Pact), it almost certainly should be legal." The rationale being that if an upscale country can function without banning something, it's almost certain that it's not necessary to ban it for society to function.
Part 1:
"if x (where "x" is a "personal action" (ie, an activity a citizen can choose to engage in - not a business regulation or something of that nature)) does not harm anybody and does not have the potential to harm anybody, or alternatively if x has the potential to harm only those willingly engaging in x, then engaging in x is a fundamental human right which no governing body has the right to prohibit no matter how popular or unpopular x is, and attempting to do so is a crime against humanity and should be punished as such.
Attempts to demonstrate "X is harmful" or "X has the potential to be harmful" must rely specifically on actions that are a direct consequence of X, and not those of tangentially-related events or a "slippery slope." For instance, arguing that gambling should be illegal or restricted because some gamblers "fuel their habit" by robbing banks is in invalid argument - it's the bank-robbing that is causing the harm to nonparticipant third parties, not the gambling. Similarly, those who argue that violent video games should be illegal or restricted because some of their players commit violent crimes are using an invalid argument - the actual violence is the cause of harm, not the game. Arguing that certain hard drugs should be illegal because their users inherently become violent towards non-participants may in some instances be a more compelling argument (because the argument claims that the violent tendencies are an inherent, inevitable consequence of action X and not just something a subset of participants do), but should still be viewed with skepticism. It is the absolute responsibility of those attempting to restrict or ban X to prove beyond any doubt that X is harmful or has the potential to be harmful.
If x does have the potential to cause harm to those not willingly participating in x, then x is likely not a fundamental human right and is subject to popular opinion - however, mitigating factors should be considered which could tip the scales in favor of keeping x legal. Example: Driving. Driving heavy automobiles at fast speeds has the potential to cause harm, even to those not willingly engaging in x (eg, protesters walking on the sidewalks near roads). Driving is therefore not a fundamental human right, but a myriad of obvious mitigating factors tip the scales in favor of keeping driving legal."
Example 1: Should prostitution be legal? From the above statement, we can see that the only two people substantially impacted by the act are also involved and consenting to the act, and it seems nearly impossible to prove that it is causing definitive harm to nonparticipant third parties. As such, it should be legal, but this ideology breaks from most by saying not just that it "should" be legal, as if the support of the people is required, by rather defining it as a fundamental human right that it would be a crime for any politician to try to circumvent. Public opinion has no bearing.
Also notice that a common erroneous argument applied here is that "legalizing prostitution would encourage human trafficking." I'll refer to this as the "subset fallacy" - the reasoning is attempting to reference something that sometimes occurs alongside Action X(prostitution), and using it to try to make a law that affects Action X itself, rather than the subset. Rather, this reasoning only justifies laws that ban human trafficking, not prostitution. The fact that legal prostitution makes human trafficking "easier" is immaterial.
Example 2: Should driving 70 MPH on the highway be legal?
First, note that as the roads are paid with tax dollars for public use, this is not strictly a "personal action." Thus, public opinion does matter. The people should be able to decide what rules they would like for their publicly-funded roads, and there is no "right" to drive at any given speed. Naturally, being allowed to drive 70 MPH on private property (with consent of the property owner) is a fundamental human right.
Part 2: The role of taxes
(There is a lot more to do with defining rights, limiting governmental scope as far as criminalizing actions, and other such things, but to keep things short here I wanted to skip ahead to another part of the ideology I find interesting.)
-There is no right to avoid paying taxes, and as such taxes should largely be determined by popular opinion. That said, there are some guidelines lawmakers should be obliged to follow when creating tax code:
-No stratified income tax shall be such that those in higher tax brackets feel unduly punished for their marginal additional income (IE, if income up to $200k is taxed at 25% and income over $200k is taxed at 50%, the value of dollars earned over $200k goes down too much, too fast. This principle is of course subjective, as it is not protecting a fundamental right, but followers of this ideology would keep it in mind when creating tax law or debating tax policy
-No income should be taxed at an amount greater than 100% of actual earnings
-(Most critically and most interesting) Taxes are a tool to be used to offset negative externalities, but are NOT a tool to use for social engineering.
Example: The government wants fewer people to gamble, so they impose a 5% tax on all gambling winnings. This tax would NOT be permitted. A tax cannot be used to induce action or deter action alone.
Example: The government is concerned that an increase in soda intake will increase the burden on the public healthcare system in the future, and want to impose a tax to recoup their losses. They estimate (through careful analysis with healthcare professionals and other relevant field experts, and would of course be required to provide proof of their calculations for the tax to be permitted) that for each soda consumed, a person is .002% more likely to develop a condition that requires reliance on Medicare or other governmental assistance later in life, calculated across society at large. It's also estimated that the average cost of these conditions to government is $30,000 per person. By multiplying 30,000 by .002 percent, the government decides to tax sugary drinks at an amount no greater than $0.60 per liter to offset the costs they later expect to incur from the activity. This tax WOULD be permitted, and is a perfect example of how things would work in a logic-based political system.
There's much more, but there's a basic introduction! I look forward to hearing your thoughts (also, if anyone has a name for this ideology, feel free to suggest it!)
This is a footnote from the CMV moderators. We'd like to remind you of a couple of things. Firstly, please read through our rules. If you see a comment that has broken one, it is more effective to report it than downvote it. Speaking of which, downvotes don't change views! Any questions or concerns? Feel free to message us. Happy CMVing!
submitted by yogokitty to changemyview [link] [comments]

I Would Literally Rather Write My Dissertation: Gambling With Time

tl;dr: Overwatch is a gambling mechanic wrapped in a FPS hybrid.
Gambling
A swarm of controversy surrounded Overwatch following the Star Wars Battlefront II loot box scandal, such that Overwatch's loot box system was ultimately disabled for Belgian players. However, the true gambling mechanic lies at the heart of the matchmaking system. While a variety of features of the matchmaker's functionality have been revealed, there is no way to know precisely how the matchmaking algorithm operates beyond what information has been made publicly available - if you think Blizzard is going to release proprietary details of their matchmaking algorithm, you're kidding yourself.
Emerging research in HCI attempts to describe naive philosophies that users create to explain the behavior of algorithms, e.g. Facebook trending timeline, Twitter feeds, etc. Multiplayer matchmaking algorithms are no exception and result in folk theories that gaming communities adopt to provide causal attributions for the behavior that they see on screen. Importantly, these theories are non-veridical and, in many cases, non-diagnostic.
How is it that users are expected to behave rationally and remain contented by a system that does not provide sufficient information about it's underlying processes, while simultaneously requiring a shared understanding of those processes in order to satisfy a win condition? Stated alternatively, how is it possible for users to be satisfied with Overwatch if users are not provided a complete description of how performance is measured?
I would argue there is not a possible solution in the current state of the game.
Balance
Not knowing the full extent of how user behavior is measured, or used, results in a decision to play that is only partially informed. While almost any multiplayer matchmaking game is ultimately a gamble, Overwatch extends this metaphor further by introducing dozens of variables that explode geometrically at runtime; 50% win rate is desirable given the total number of variables that must be compensated to approach fairness, but not enjoyable.
FPS titles like Halo, CS:GO, Call of Duty, Destiny, etc. do not suffer the same burden that Overwatch does in terms of matchmaking 'fairness', simply because the number of variables that must be constrained is, by comparison, well-defined. I would argue that this is the reason "low-effort" heroes like Moira or Brigitte were introduced into the game; to balance the win-rate for a gaming environment that includes casual and serious players with different gaming philosophies.
For example, there are users in the Overwatch community that accept a 1v1 between a projectile / hitscan character and an auto-aim character is a reasonable [fair] contest, while there are others that do not. Similarly, there are users that believe Brigitte is an acceptable solution to the meta implications of high-mobility characters in Overwatch, while others do not. How is it possible to reconcile such disparate beliefs in the same gaming environment without forcing some evenness onto the player base? I would argue that currently no such method exists.
Issues
The best suggestion - after two years of development - is the addition of a role-queue system, which would theoretically address many of the balance issues in Overwatch, but would likely introduce new problems that could be equally undesirable, or worse.
There is no fundamental issue in Overwatch, there are several (this list is not exhaustive).
It is not possible to align all of these features without resulting in a misperception of fairness in a group that is uninformed about what constitutes a fair winning strategy.
Conclusions
Users that participate in competitive game modes in Overwatch are motivated by the prospect of increasing rank, but in doing so, that user is engaging in a gambling behavior. In Overwatch, players believe their performance will affect their ability to increase rank, but in fact, the probability of success [per match] is predicted before the match ever starts. The probability of long runs of wins / losses in competitive matchmaking will likely be underestimated, or attributed to the user's unique performance, vis-à-vis the Gambler's fallacy and fundamental attribution error, respectively. Thus, users will continue to attribute performance gains to their own agency, when in fact, performance gains are simply the outcome of an optimization problem.
submitted by cjwidd to Overwatch [link] [comments]

Games and Theory: Cognitive biases Part 13

While I have been busy these past couple of years, and my work here has been neglected somewhat, I have recently decided to try to once again dedicate some time to this sub, and my contributions here within.
While I can't and won't guarantee a return to form, I will try my best to maintain the standard of content which you all have come to expect from me. With that being said, there inevitably will be some what of a teething phase, due to the self referential nature of my work and my current lack of familiarity to it. This is unfortunately an inexorable truth to defining unthread ground. The further we escape that which has come before the more we must define what we have come to know for ourselves.
"The neglect of probability, a type of cognitive bias, is the tendency to completely disregard probability when making a decision under uncertainty and is one simple way in which people regularly violate the normative rules for decision making. Small risks are typically either neglected entirely or hugely overrated. The continuum between the extremes is ignored."
"There are many related ways in which people violate the normative rules of decision making with regard to probability including the hindsight bias, the neglect of prior base rates effect, and the gamblers fallacy. However, this bias is different in that rather than incorrectly using probability, the actor completely disregards it."
A perfect reference to this would be the anti-vaxxer movement, they believe that a vaccine will cause autism.
Lets pretend if that were true. Vaccines prevent the contraction, of in many cases life threatening illnesses. If we assume both were 100% effectual, and risk of contracting the illness was 50% over a life time. I think I'd rather take a 100% chance of autism, over a 50% chance of death. But the statistics are far more complex than that.
"Measles affects about 20 million people a year, primarily in the developing areas of Africa and Asia. It causes the most vaccine-preventable deaths of any disease. It resulted in about 96,000 deaths in 2013, down from 545,000 deaths in 1990. In 1980, the disease was estimated to have caused 2.6 million deaths per year. Most of those who are infected and who die are less than five years old..."
"...Before Immunisation in the United States, between three and four million cases occurred each year."
in 1980 before vaccination the population of America was 225million. So about 2%~ of the population each year contracted this one illness alone.
"A new government survey of parents suggests that 1 in 45 children, ages 3 through 17, have been diagnosed with autism spectrum disorder (ASD). This is notably higher than the official government estimate of 1 in 68 American children with autism, by the Centres for Disease Control and Prevention (CDC)"
1/45 or 2/90 is again for as much as it matters around 2%~ of the population.
So if all vaccines caused autism, with absolute certainty in 2% of the population, but without vaccines we would have 2% of the population getting infected with this one specific illness alone. There would still be enough president, to warrant mandatory vaccination.
this is of course assuming that there even was any connection with vaccination and autism, which there is not
if we then consider the lack of documentation correlating autism with vaccinations, and the statistical advantage and benefits caused by all the vaccinations for various other illnesses. Well its even more statistically advantageous, to vaccinate your kid whether you believe the anti vax agenda or not. It is this statistical benefit that is neglected, by those who follow the anti-vax movement.
This can be exploited by bringing attention to as yet unrecognised favourable statistics, or using an emotive issue, to detract from unfavourable statistics. The emotive issue doesn't even have to be related to the topic. A presidential candidate can reference an important statistic and raise an important issue, and an opposing candidate can simply ignore it and attack the others character, bypassing the need for an appropriate response entirely.
"The normalcy bias, or normality bias, is a mental state people enter when facing a disaster. It causes people to underestimate both the possibility of a disaster and its possible effects. This may result in situations where people fail to adequately prepare and, on a larger scale, the failure of governments to include the populace in its disaster preparations.
The assumption that is made in the case of the normalcy bias is that since a disaster never has occurred, it never will occur. It can result in the inability of people to cope with a disaster once it occurs. People with a normalcy bias have difficulties reacting to something they have not experienced before. People also tend to interpret warnings in the most optimistic way possible, seizing on any ambiguities to infer a less serious situation."
Despite being unassuming this bias is actually one of the most venomous, and counter productive biases to society as a whole and one which I spend most of my time fighting. It benefits from Ambiguity effect / Backfire effect / Belief bias / Confirmation bias as well as many other previously discussed biases.
Events known to some as black swan event's is the area in which I mostly operate;
"The black swan theory or theory of black swan events is a metaphor that describes an event that comes as a surprise, has a major effect, and is often inappropriately rationalised after the fact with the benefit of hindsight."
Sometimes as a contingency planner and sometimes in event resolution. Simply bringing peoples attention to pending events, to line up funding to resolve them can be an undertaking in and of itself. Even more if there is no evidence that an event is pending, or when it's potential is merely suspected. As I often say, people will always do what they want most, and with the recently mentioned "Neglect of probability" people will rather not spend money on something that "might" happen.
A great example of this is the Japanese engineer, who requested the tsunami wall near the fukushima daiichi nuclear power plant be twice as big. At the time there had only been one major tsunami documented the 2001 tsunami in Indonesia. Before that, they were even considered myth, and held a place amongst the alien pyramids, and crop circle documentaries on discovery.
In hind sight, anyone would mention with the right information, that yeah all coastal nuclear power plants should have a large wall surrounding them. But trying to get a government, or anyone, to pay out of hand, for something that "might happen" that can be written off as statistically improbable. Well you might get someone saying "should we build massive dome's to prevent asteroid impacts too?"
On a more intimate level, people who may have an unwanted pregnancy in their relationship, taking multiple tests, because the original result wasn't satisfactory, as if its some kind of quantum pregnancy in which observation will change the result. Or even people who lack home or car insurance.
This can be exploited with shock and awe styled social engineering, large over arching plans executed nearly instantly, relying on things like disbelief and the bystander effect.
In a way the fictitious man gambit exploits this. Initially before you have ascended to the exceptional state, people will disbelieve your ability to be capable of exceptional feats. Imagine for instance the news, someone has done something, robbed a bank, killed someone, been a secret millionaire, comments from people are always how they were so normal, they didn't think they were capable of such things and so on. Normal people are expected to be normal, and thus, disbelief will protect you and your machinations. Equally, exceptional people are expected to be exceptional, this is also "normal" for them, Someone who is known to win races, or teams who are known to win games, are expected to continue to win, but this expectation of success can be falsely attributed to feats far beyond the skill set of the person/people in review. If for instance we found out tomorrow tom cruise was going to be an astronaut or was going to be vice president to some candidate. We would just accept this as being normal, he is an exceptional person, we assume he can do exceptional things, as being normal.
"The omission bias is an alleged type of cognitive bias. It is the tendency to judge harmful actions as worse, or less moral than equally harmful omissions (inactions) because actions are more obvious than inactions. It is contentious as to whether this represents a systematic error in thinking, or is supported by a substantive moral theory. For a consequentialist, judging harmful actions as worse than inaction would indeed be inconsistent, but deontological ethics may, and normally does, draw a moral distinction between doing and allowing. The bias is usually showcased through the trolley problem."
The Trolley problem is a thought experiment in ethics. The general form of the problem is this: There is a runaway trolley barrelling down the railway tracks. Ahead, on the tracks, there are five people tied up and unable to move. The trolley is headed straight for them. You are standing some distance off in the train yard, next to a lever. If you pull this lever, the trolley will switch to a different set of tracks. However, you notice that there is one person on the side track. You have two options: (1) Do nothing, and the trolley kills the five people on the main track. (2) Pull the lever, diverting the trolley onto the side track where it will kill one person. Which is the most ethical choice?
In one scenario, John, a tennis player, would be facing a tough opponent the next day in a decisive match. John knows his opponent is allergic to a food substance. Subjects were presented with two conditions: John recommends the food containing the allergen to hurt his opponent's performance, or the opponent himself orders the allergic food, and John says nothing. A majority of people judged that John's action of recommending the allergic food as being more immoral than John's inaction of not informing the opponent of the allergic substance.
This can be exploited in the very basic form of Lying through omission, as people find it less offensive, which considering omission's can't really be contradicted, and also written off as forgetfulness, is generally considered a more advantageous practice.
In other aspects, it itself can have attention brought to it, so as to sway someone's behaviour in a favourable manner. Highlighting or undermining the potential of options presented can also serve to magnify the potential of this bias. Manipulating Ambiguity effect / Anchoring / Attentional bias / and Confirmation bias
The current American presidential election is rife with this, in so that, "if you do not vote, Y will become president" depending on either candidate is framed, either one being vilified enough the other becomes the only option. Anchoring bias, and confirmation bias, will take it from there, as an indifferent centrist person, becomes imbued with a sense of necessity in their point of view, and a sense of discomfort, even cognitive dissonance, when exposed to contradicting information.
"The outcome bias is an error made in evaluating the quality of a decision when the outcome of that decision is already known. Specifically, the outcome effect occurs when the same "behaviour produces more ethical condemnation when it happens to produce bad rather than good outcome, even if the outcome is determined by chance."
While similar to the hindsight bias, the two phenomena are markedly different. The hindsight bias focuses on memory distortion to flavour the actor, while the outcome bias focuses exclusively on weighting the past outcome heavier than other pieces of information in deciding if a past decision was correct."
The tendency to judge a decision by its eventual outcome instead of based on the quality of the decision, is almost the opposite to Normalcy bias as mentioned above. Frustratingly, they happen at different stages of an event, so there is very little counterbalance.
The phrase "if you have done something right, its as if you have done nothing at all" is almost a mantra in the field in which I operate. Not unlike the humble sys admin, getting yelled at by his boss. "what are we paying you for" when all is well and "what are we paying you for" when anything breaks. Being dismissed as a doomsayer when you recognise the need for something, and characterised as a snake oil salesman when things go awry, can be frustrating to say the least.
Again recognising the fukushima daiichi incident, its very easy, as I did above, to blame the local government or the authority figure concerned, for not having the foresight to spend money on a taller wall. When it could be statistically improbable for it to have happened in the first place, and statistically unlucky for it to have happened at all. The people in charge of making these decisions, have plenty of engineers, mathematicians and statisticians on hand, to divine what is and is not a reasonable expense and safety measure, Otherwise we might just have those meteorite domes over every nuclear power plant and important buildings. In the end, even a broken clock is right twice a day.
With all that being said, Outcome bias, can be great to undermine those in leadership or positions of authority, it is frankly a lot easier to undermine someone's decision making ability, when you have no decisions of your own to make, or easier than making those decisions yourself. The glass castle gambit indulges this bias fairly well, and to a lesser extent the ridik ulass gambit does too, as stated in the past the ridik ulass gambit is playing to draw not to win, a potential key component in this, is moving second, in a reactionary capacity rather than a pre-emptive manner. In a position of leadership, if you do nothing, you can't really be faulted or undermined for making mistakes. This behaviour also benefits from Omission bias, as mentioned above, in that faults through inaction will be judged less harshly than faults caused by action.
When all is said and done, its easy to do nothing, This can cause you in a leadership position to become comfortable doing nothing, allowing your leadership to stagnate. Which can be a dangerous habit to form. A man with everything to lose, has little to gain, and a man with nothing to lose has everything to gain. Stagnant leadership often gives way to the younger, the ignorant, more ambitious, and if you are too afraid to lose what you got, you can easily lose it all through inaction.
I originally posted this post here as I had a sub created and dedicated to this sort of content. As I have not posted new content there or else where in nearly 2 years, I felt it useful to post here, and as some people don't like following links, I decided to post it directly here too.
submitted by ridik_ulass to SocialEngineering [link] [comments]

Question about the Gambler's Fallacy.

This is kind of a deep question that will probably result in talking about Hume's skepticism, but I'll ask about it anyway.
I want someone to define very clearly what exactly the "Gambler's Fallacy" is with very clearly defined terms. This is what the Wikipedia link defines it as....
"The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the mistaken belief that, if something happens more frequently than normal during some period, it will happen less frequently in the future, or that, if something happens less frequently than normal during some period, it will happen more frequently in the future (presumably as a means of balancing nature). In situations where what is being observed is truly random (i.e., independent trials of a random process), this belief, though appealing to the human mind, is false."
Key terms: "Mistaken","Belief", "false", "memory", "conditional", "unconditional".
I think a major issue for me is whether or not mathematical claims about probability are considered "analytical a priori", "synthetic a priori" or "a posteriori".
Basically my question is, could someone please define the gambler's fallacy in the most precise language possible for me? Because as of now I think that the way this concept is phrased is that it is a combination of various ideas and is problematic. This is almost a Wittgenstein language thing.
For example. It seems like in order for the "gambler's fallacy" to make sense you have to hold the belief that mathematics and the universe are the same and independent of the human mind. That is, in order for something to be "true" or "false" you need a comparison, which means a universal truth (as Bertrand Russel would phrase it). That is, an objective reality to which you can compare things to. Which would lead to epistemological problems, and eventually logical problems of basically analytic/synthetic apriori aposteriori claims.
That is, the gambler's fallacy is comparing a person's "belief" or "interpretation" with the objective reality of the various instances/coin tosses/events. But if the individual's "beliefs" or "interpretations" DO match up with that objective reality, are those beliefs/interpretations really "false" or "true"? Even if it is "accidental" or the "logic" cannot be replicated in every single instance possible to get the same exact results.
The problem with attempting to replicate an experiment every single time is that you are arguably never able to replicate the same EXACT experiment because various things change: time, space, angles, objects, people, etc. Trying to apply logic in the world would lead to inductive reasoning problems.
[edit] If you can repeat experiments and get the same exact thing, you also risk determinism. Which then possibly challenges the idea of "random" events even being possible.
Thus I think the Gambler's fallacy is most likely a hindsight bias thing, or even pseudo math/logic, especially when contrasted with things like the Law of Large Numbers, or reversion to the mean.
Maybe I don't understand the concept very well. If that's the case please enlighten me.
submitted by Humble_Person to askphilosophy [link] [comments]

define gambler's fallacy example video

- YouTube Equivocation (Logical Fallacy) - YouTube 31 logical fallacies in 8 minutes - YouTube How We’re Fooled By Statistics - YouTube Commercial Fallacies - YouTube CRITICAL THINKING - Fallacies: Fallacy of Composition ... Fallacies In Commercials - YouTube The gambler's fallacy - YouTube Are you Begging the Question? - Gentleman Thinker - YouTube

A gambler's fallacy is a heuristic in which a person thinks the probability of an outcome has changed, when in reality, it has stayed the same. If a coin is flipped 10 times and lands on "heads" everytime, a person employing gambler's fallacy would believe the probability of the coin landing on "heads" the 11th time would be very low. Gamblers' fallacy definition at Dictionary.com, a free online dictionary with pronunciation, synonyms and translation. Look it up now! The gambler’s fallacy, also known as the negative recency effect and the reactive inhibition principle, refers to a common mistake in human judgment. It is the belief that, for random independent events, the lower the frequency of an outcome in the recent past, the greater is the likelihood of that outcome in the future. Gambler’s fallacy, also known as the fallacy of maturing chances, or the Monte Carlo fallacy, is a variation of the law of averages, where one makes the false assumption that if a certain event/effect occurs repeatedly, the opposite is bound to occur soon. Gambler's Fallacy Stating an event as more or less likely to happen later on due to the amount of times that it has occurred previously. Example: Because some people have been accused of witchcraft, more people are likely to be accused. Gambler's fallacy occurs when one believes that random happenings are more or less likely to occur because of the frequency with which they have occurred in the past. Examples of Gambler's Fallacy: 1. That team has won the coin toss for the last three games. The gambler's fallacy is the belief that the chances of something happening with a fixed probability become higher or lower as the process is repeated. Learn about the gambler's fallacy, and see... What is the Gambler's Fallacy? Also known as the Monte Carlo Fallacy, the Gambler's Fallacy occurs when an individual erroneously believes that a certain random event is less likely or more likely,... In an article in the Journal of Risk and Uncertainty (1994), Dek Terrell defines the gambler's fallacy as "the belief that the probability of an event is decreased when the event has occurred recently." In practice, the results of a random event (such as the toss of a coin) have no effect on future random events. The Gambler’s fallacy is when you believe that the past performance of independent events will have an effect on a further independent event. 13. What is a prior probability? A prior probability is something’s probability that everything else will be equal. 14. How does the overlooking prior probabilities fallacy cause problems?

define gambler's fallacy example top

[index] [4244] [4387] [5328] [9614] [6130] [1370] [7493] [8920] [1693] [2549]

- YouTube

I learned about fallacies recently, and it's nice to have a way to put a name to ways in which we don't think or argue logically.Follow up video: Chesterton'... A description of the Logical Fallacy known as Equivocation (Fallacy February & 90 Second Philosophy). Information for this video gathered from The Stanford E... About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators ... About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators ... Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. Is punishment or reward more effective as feedback? Do new medical treatments really work? What about streaks in sport? Without considering regression to the... In this video, Paul Henne (Duke University) describes the fallacy of composition, an informal fallacy that arises when we assume that some whole has the same... Flip a coin five times, and if you get five heads, you may begin to expect the next flip to land on tails. The "gambler's fallacy" doesn't just affect bets a... A common philosophical mistake! Have you told somebody that they've begged the question? Did you use the term correctly?Gentleman Thinker playlist: https://w...

define gambler's fallacy example

Copyright © 2024 casinos.betsstore.online