While I cannot provide a solid yes or no answer to "did Dream cheat," I have provided several other things which may prove useful. My analysis may be applicable to any Bernoulli process where we do not know the true rate. If we have a hypothesis that the rate is a specific value, and no strong alternative hypothesis, then the two Python routines posterior_H_fair() and BF_H_fair_H_cheat() can be invoked to generate a Bayes factor for reasonable mathematical definitions of those hypotheses. Both routines run quite fast; most of this notebook was developed on an Asus Transformer, and the slowest cell takes about thirty seconds to execute. Both routines are also quite flexible, as they allow arbitrary Beta priors to be supplied and have arbitrary precision so that math overflow isn't a problem. This makes those routines applicable well beyond the simple question of "did Dream cheat?"
I have also tried to make it as easy as possible to build another analysis on top of this one. If, for instance, you do not agree with my definition of
For instance, one idea not explored here is heirarchical models. The PE report attempted to build such a model for Ender pearl barters using Monte Carlo simulations, but a better approach is to invoke Stan or emcee to build and sample from the posterior. This would allow you to test the success rate of barters, the number of Ender pearls dropped per successful barter, and the amount of gold a speedrunner could gather simultaneously. Rather than assert whether the speedrunner's goal was ten or twelve Ender pearls, as the PE report's simulation does, they can be free parameters in the model that the MCMC engine will explore for you.
At minimum, I at least hope to have provided a different and more rigorous approach towards analyzing whether or not a speedrunner modified their game.