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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    Mathematical Answer: youtu.be/8Ko3TdPy0TU – Evorlor Jun 9 at 19:59
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    The simplest analysis is given by Matt Parker: if all humans on earth did something once a second for a century, we would have collectively done that 3x10^19 times, but Dream had a 1 in 2x10^22 run, so no freaking way. – Passer By Jun 10 at 1:48

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You can find an archived version of his confession here.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 Jun 8 at 1:17
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    Here is an actual quote from Dream "admitting" he cheated: "At this point I was lost, and I was fairly confused about the whole thing. Wondering what the other options were and exploring the possibilities. as much as I was confident that I didn't cheat, I had never explored the option that I possibly did." – BlueRaja - Danny Pflughoeft Jun 8 at 6:56
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    Matt Parker made a good video as well: youtube.com/watch?v=8Ko3TdPy0TU – luk2302 Jun 8 at 7:38
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    @BlueRaja-DannyPflughoeft That quote doesn't really say anything and there are parts of his statement where he did actually admit things. He did admit that "I ended up finding out that I HAD actually been using a disallowed modification..." and he goes on to explain that it increased spawn/drop rates and how he wasn't aware of it. This is certainly an admission that he had an unfair advantage due to game mods, but whether it's an admission of "cheating" is probably a matter of semantics. – NotThatGuy Jun 8 at 15:45
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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 Jun 9 at 13:21

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