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Curated by: Mathemaniac (96 videos)
In short, you don't need a PhD to understand the math going on in the entire Dream cheating scandal; you just need patience and this video ;) Recently, a very popular Minecraft player Dream got caught cheating in his speedrunning attempt by the moderation team. The moderation team did a mathematical analysis, and Dream tried to debunk the math used by hiring an astrophysicist, but the math used in astrophysicist's paper was questionable at best. This video will explain ALL the math involved, including from both the moderation team and the astrophysicist, and doesn't offer any value judgement of the character of anyone involved. This hopefully can help you make an informed decision on who to trust / what to believe / what to think. If you watch this video just because you are a fan of this channel (good for you), this is also a very good opportunity of knowing the statistical tools for bias corrections, or just probability and statistics in general - binomial distribution, Fisher method, Bonferroni correction; or even just coding. This is quite possibly the longest video that I will EVER put on my channel. 00:00 Disclaimer 00:34 Background of the drama 03:41 Binomial distribution 05:46 Applying binomial distribution 08:12 Bias 1: Stopping criterion 12:02 Bias 2: Stream selection bias 14:08 Bias 3: Runner selection bias 15:24 Bias 4: p-hacking 17:25 Mod team math summary 18:03 Main criticism from astrophysicist 19:37 Minor criticisms from astrophysicist 21:14 Blatant mistake of astrophysicist 25:06 Outro and endcard stuff ***CORRECTIONS***: 2:40: p-values mean getting AT LEAST as lucky as these success rates, not just as lucky. 13:00: The streams aren't exactly independent, so this is not an exact answer, but it works as an overestimate nonetheless because they are positively correlated; if you are not convinced, you can also consider the Bonferroni correction, which is very close to this. 13:50: I said 1.19 * 10^(-12), but the figure shown on screen is correct: 1.19*10^(-11). 14:51: 1000 is the UPPER BOUND, not an estimation 19:30: This is based on the faulty assumption that all speedrun attempts are streamed. 24:20: The astrophysicist's 1 in 6300 is somewhat close to the chance of 18 heads in a row, or 19 of heads or tails in a row, so maybe some coding mistakes, or that he is exceptionally lucky in obtaining so many runs of 20 heads in his simulation. Also, the early stopping identified by the astrophysicist is not even true - in Dream's speedruns, he just throws a lot of gold to a lot of piglins in parallel to see what is traded. Further reading: 1) Markov Chain solution: https://bit.ly/3pHcrRo 2) Numpy.round/Numpy.around and numpy.random.uniform() function implementation https://bit.ly/3pGubN8 https://bit.ly/3pDA8dr 4) Fisher method of combining p-values: https://bit.ly/3pxjFaG 5) (not reading, but a video) Biases in statistical analysis in science: https://bit.ly/34Zex7D 6) Karl Jobst (another speedrunner) video on this situation, focusing on simulations: https://bit.ly/35072wX ***SOURCES*** Mod team original paper: https://mcspeedrun.com/dream.pdf Dream's astrophysicist paper: https://bit.ly/3nYQa1b Mod team rebuttal: https://mcspeedrun.com/dream/rebuttal.pdf Codes that I used in this video for calculation: https://bit.ly/2KGFLZN Loot table and Minecraft images: https://bit.ly/2KOg3Co https://bit.ly/34Z3Hyk https://bit.ly/2Jz7riB https://bit.ly/3rGndJD https://bit.ly/3o4WdBs https://bit.ly/3hJ2dxv https://bit.ly/3n3M0Uu https://bit.ly/2X09cZm https://bit.ly/3pEQMJW https://bit.ly/34Z3LOA Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels: https://forms.gle/QJ29hocF9uQAyZyH6 If you want to know more interesting Mathematics, stay tuned for the next video! SUBSCRIBE and see you in the next video! If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I will probably reveal how I did it in a potential subscriber milestone, so do subscribe! Social media: Facebook: https://www.facebook.com/mathemaniacyt Instagram: https://www.instagram.com/_mathemaniac_/ Twitter: https://twitter.com/mathemaniacyt Patreon: https://www.patreon.com/mathemaniac (support if you want to and can afford to!) For my contact email, check my About page on a PC. See you next time!