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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 Bartering Luck Dream - Illumina Expected 99.9%ile 50 40 30 20 10 100 200 300 Cumulative Gold Ingots Figure 1: Dream's pearl barters, charted alongside various comparisons. The 99.9th percentile line represents one-in-a-thousand luck, which is already quite unlikely-if not necessarily proof of anything. Cumulative Pearl Trades

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Piglin Bartering: Dream vs. Other Speedrunners Graph


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Origin Entry: Dream Speedrun Cheating Controversy

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9 Conclusions If you are asking about the hypothesis that Dream was using modifications for the six streams in question, then the ender pearl barter probability was 3 x 10-10 to 3 × 10-9 depending on how you implement the stopping criterion; let's choose 10-10. The blaze rod probability was 3 x 10-8. Combining these two probabilities using Equation 2 gives 1.2 × 10-16, Adding in the correction (by multiplying) for 100,000 possible sets of 11 streams to investigate in 1,000 different ways gives a investigation gives 10-8 or a 1 in 100 million chance. That is, there is a 1 in 100 million chance that a livestream in the Minecraft speedrunning community got as lucky this year on two separate random modes as Dream did in these six streams. That is extraordinarily low, though not nearly as low (by a factor of 75000) as concluded by the MST Report (1 in 7.5 trillion). The main things that increased the probability are: 1) using a Barter Stopping criterion (factor of about 100) and 2) using 100 times as many livestreams and 10 times as high a p-hacking correction, for which I have provided specific justification. If you are asking about the hypothesis that Dream was using modifications for all eleven streams, the probabilities are much higher because the other five streams had more typical results. The ender pearl probability goes up to 3 x 10-4 and the blaze rod probability goes up to 10-6. Combining these gives 7 x 10-9 and adding the 10$ boost gives 0.7 or 1 in 2. Note that my corrections are designed for low p- values, so this may not be fully accurate, but this inaccuracy would not affect the conclusion that this case is completely consistent with expectations. That is, an investigation of all the similar Minecraft livestreams that picked a runner who had unusual luck in two different ways would produce results as unusual as Dream's in these 11 streams. Note that for speedrunners to reach high positions on the leaderboard requires excellent skill and luck. These answers are extremely different, which is unsurprising because the ender pearl and blaze rod success rate is very different between the first five and last six streams. How should you decide between the case with eleven streams and the case with six streams? It depends on what you think the probability is that Dream would make a modification at that point (as compared to any other point) without being influenced by the actual probabilities. It was a natural breaking point in the timeline of streams independent of the fact that it was probabilistically extremely different, which argues for the six-stream hypothesis. If you allow the streak of streams/runs to be any length up to N (instead of choosing 6 or 11 in advance), then another correction of N° should be included. Using N ~ 10 gives a corrected probability of 1 in 10 million . This does not account for the fact that "lucky streaks" should be treated somewhat differently which would increase the odds, potentially up to 1 in a million. So if you think "if Dream would have chosen to modify his numbers then this is the only place within the eleven stream set that Dream would have modified them", then you should lean toward the 1 in 100 million case. If you think Dream could have chosen to modify his numbers in between any stream, then these odds should come down substantially to 1 in a 10 million. If you think that if Dream modifying things, he would only have done it at the beginning of all eleven streams in question, then the data show no statistically significant evidence that Dream was modifying the probabilities, given that he was investigated after it was noticed that he was lucky. Since the eleven-stream probability is so much higher, even if you think that (independent of the prob- abilities calculated after seeing the streams) there is a 100-to-1 chance Dream modified before the final six streams instead of before all eleven streams, the six stream case provides a negligible correction and the prob- ability becomes just 1/100. That is, external evidence that the probabilities were modified at this specific point would be needed to produce a significant probability of cheating. Even in the worst case, the probabilities are not so extreme as to completely rule out any chance that Dream used the unmodified probabilities. If you have independent high-probability reasoning to suppose that the game was modified by Dream before his final six runs, then the low probability of that hypothesis even after correcting for other biases suggests an alternative explanation. There are reasonable explanations for Dream's ender pearl and blaze rod probability, potentially including extreme "luck", but the validity and probability of those explanations depend on explanations beyond the scope of this document. One alternative explanation is that Dream (intentionally or unintentionally) cheated, though I disagree that the situation suggests that this is an unavoidable conclusion. In any case, the conclusion of the MST Report that there is, at best, a 1 in 7.5 trillion chance that Dream did not cheat is to0 extreme for multiple reasons that have been discussed in this document. 9The MST Report computes this in a different way: choosing the number of 11-stream livestreamers and then choosen any of 11*(11+1)/2 subsets from these streams. In addition to the possible issues mentioned above, this correction is pretty strongly dependent on the somewhat arbitrary choice of 11 (which is potentially relevant to Dream, but may not be universal). I instead propose that you take consider all sets of consecutive livestreams of a certain length, which leads to a correction of the number of livestreams times the number of plausible lengths
PIGLIN ON HIS WAY TO TO GIVE DREAM HIS ENDER PEARL COLLECTION
When you rig a Minecraft mob vote by getting your impressionable fans to vote for the most useless and most easily forgettable mob so that your speedruns won't get affected by a newly added mob but later on you get exposed for cheating on your speedruns with solid proof so your efforts in rigging a Minecraft mob vote was all for nothing now that you are looked at as a lying cheater in the speedrunning community
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