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The speedrunner Dream has recently been accused of cheating in his Minecraft Java v1.16 glitchless speedrun.

How did the Minecraft Java speedrunning mods calculate if Dream cheated?

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The Short Summarized Answer

These are the relevant facts.

These were drop rates for two items important to the speedrun attempts over the course of six livestreams.

Ender pearls are obtained 4.7% of the time. Out of 262 rolls they were obtained 42 times.

Blaze rods are obtained 50% of the time. Out of 305 rolls the were obtained 211 times.

The probability of being at least this lucky in each case can be modelled by a binomial distribution.

For the ender pearls this probability is 0.00000000000565319.

For the blaze rods this probability is 0.00000000000879143.

These probabilities are independent so the chances of both occurring is their product, 0.000000000000000000000049699624 or 1 in 20 sextillion.

You can do some adjustments for biases but they don't even come close to reaching a reasonable probability.

The Long In-Depth Answer

This video sums up the decision behind the mod's actions, based on a paper made studying how incredibly statistically unlikely his run ended up being. You can either watch the video or read the paper to understand the reasoning behind their actions.

Did Dream cheat?

Yes, he's actually admitted to doing so. Here's the relevant clicky. In a recently deleted tweet he posted a confession of sorts that revealed he had "inadvertently" used mods to enhance the drop rate of ender pearls and blaze rods.

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You can find an archived version of his confession here. The relevant paragraph in regards to cheating in his run:

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After considering this, I ended up finding out that I HAD actually been using a disallowed modification during ~6 of my live streams on Twitch. At the time we were just starting to record videos on 1.16 and we had just hired a developer to help with coding mods for videos because me and George had no experience with mods only plugins. One of the mods that they were working on was an overall recording mod, that I have used in every video (with updates and improvements) since around the speedrun controversy.

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    +1 Good Answer. Karl Jobsts video on this subject is worth watching as well.
    – Wipqozn ♦
    Commented Jun 8, 2021 at 1:17
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    Matt Parker made a good video as well: youtube.com/watch?v=8Ko3TdPy0TU
    – luk2302
    Commented Jun 8, 2021 at 7:38
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    @NotThatGuy Dream cleared his mod folder before submitting it to the mods. He admitted doing so. From that point on, at least, he was aware that he used modifications of some sort. That he "wasn't aware" of what those mods did is... strange, to say the least.
    – T. Sar
    Commented Jun 9, 2021 at 13:21
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    ...especially that he specifically commissioned the custom mod to modify these drop rates "to make his videos more interesting." Did he forget he paid money to have a mod made that did just what the moderators accused him of?
    – SF.
    Commented Jun 9, 2021 at 19:53
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    @justhalf those aren't irrelevant folders, however. Moderatorss ask those folders because it is easy to put mods that change details in the game to make it easier to pull off a speedrun. Those are proof that you did or didn't cheat. More so, if you aren't cheating, those folders will most likely be empty by default or contain speed-run approved mods, like timers or stuff like that. There is very little reason to clear a mod folder at all, more so when it is standard procedure to check those files in case of a cheating situation.
    – T. Sar
    Commented Jun 10, 2021 at 13:47

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