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...

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!

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