Game Theory: Did Dream FAKE His Speedrun? A Final Analysis.

oh hey matt oh hey you it's me robert we sat next to each other for like three semesters in college yeah richard robert robert yeah how have you been what are you doing these days? Are you done with college I guess not technically since I'm a professor now professor humor anyway what are you doing? Well, my life definitely took an unexpected turn. I'm, actually, I'm a professional YouTuber now, oh God, don't tell me you're setting your backyard couches on fire, no, no. those people are the worst no, I have a show where I actually talk about video

game

s, well someone got lucky, so what do you do all day?

It's about what you'd expect playing video

game

s, making fun of video games, reading 29-page articles on binomial distributions. in a Minecraft

speedrun

ning series oh wait, not really, no, I'm just kidding, only part of the article is about the binomial distribution, the other sections describe modular arithmetic and the properties of congruent linear generators. Hello Internet, welcome to game

theory

, the program that speeds up. scientific topics for the benefit of those with short attention spans but still manages to be longer than a Minecraft

speedrun

. It's true that as of November 3, the Minecraft 1.16 speedrunning world record is 14 minutes, 39 seconds, and 520 milliseconds.

Milliseconds, that's how granular we are. Get here, people, and that should show you that Minecraft speedrunning is serious business, which is probably why a Minecraft speedrunning controversy set the Internet alight throughout December, because what better way to cap off a packed year? from crazy headlines that people taking the most relaxing in the world. game and turn it into a warzone

dream

smp excluded of course that thing is always a warzone in the best way possible but say when the minecraft speedrunning team puts together a 29 page document claiming that

dream

cheated while speedrunning in minecraft and dream in turn hires an anonymous astrophysicist to offer a 19-page rebuttal, all of it related to sampling bias and the binomial distribution and computer modeling and statistics.

It's a very important thing when people bring out latex. You know, it's serious. I'm glad maybe. one of you has that reference for everyone else, I'm not talking about latex, plastic, I'm talking about latex, document preparation software that allows academics to include all those strange mathematical symbols in their documents, because if you have ever tried to use them. word, it doesn't work, so why am I here? Well, honestly, I wasn't sure I wanted to cover this. I don't want to insert myself unnecessarily into the drama. Besides, this is the future. Matpat is coming. We're wrapping up this episode now. release in about a week, but Dream just issued his

final

word on the matter on Twitter.

I don't want this video to be seen as beating a dead horse or reopening old wounds. It just took me a long time to work through the calculations. Videos take forever to edit, and while I could have archived the episode and taken control of this one now that the discussion is officially over, I think being late to the party is actually a good thing, since there are a lot of interesting takeaways from Everyone Anyway, I'll talk about all of this later in the script, I just wanted to let you know that I recognize that this is coming very late and I think this video, especially the conclusion, is still very valid now, let's go back to the episode as it was personally written.

All my experiences with Dream have been very positive. It's been fantastic working with Dream on both our collaboration video and as a guest on our charity livestream last year. Also, I really admire the work he and the team are doing at Dream smp, but it's not every day that people are excited to talk about statistics and many of these discussions have been very technical and complex in a way that is quite difficult to understand. if you're not comfortable with math, and honestly, that's the whole reason I created game

theory

. This program was originally designed to be a place where I could discuss a lot of big, seemingly complex topics and fun, more digestible ways nowadays, mostly these are big, complex topics like the fnaf timeline, but also things like physics and history and yes, even mathematics.

You want to know more about the games you love without having to put in the effort on your own, now you can play and learn, we have created the tangential learning experience of game theory games, oh what a shame, it's so bad, it's so bad that It's blinding me anyway. Jokes aside, I was lucky enough to have teachers who made me excited to learn and who were good at explaining things, but I know other people aren't as lucky, so I always wanted this channel to be the place for whoever found it to explain why. These types of topics are actually a lot more fascinating than you think and this is absolutely one of those situations, it's also one of those situations where I think we might all be missing the most important point at hand, but I'll get to that one.

A little later I understand that we are all fine here, I am not trying to attack anyone, this is purely for education, there is a lot of misinformation circulating here and like that old shameful game theory promotion said that knowledge is power, oh , I played the embarrassing promo again, what was it? I think so, I think it's worth starting from the beginning. Dream is a Minecraft speedrunner who's a bit reductionist since he does a lot more than just speedrunning these days, but when he first appeared here on Game Theory he introduced himself by saying I'm a dream.

I own Minecraft Speed, so yeah, I'm going to follow that dream anyway. At various points in Minecraft history Speedrunning held world records in March 2020, completing a Minecraft 1.14 run in 32 minutes and 21 seconds, which at the time was a world record by 16 seconds, broken several days later, by so Dream came back to claim the crown with a time of 26 minutes and 44 seconds. In June, he once again claimed the title of world record holder with a Minecraft run of 1.15. in 22 minutes and 4 seconds, in fact, the Dream Day race is actually the fastest 1.15 race on record, although in an interesting twist, it's not actually number one in the standings, as there are five people who actually have completed Minecraft 1.14 with faster times, why?

Well, 1.14 and 1.15 are similar enough to group them together as a single category, although a fun fact is that 1.15 is actually considered harder for speedrunning due to the removal of a cheat that allows you to infinitely resupply villagers and even in the midst of the current scandal. Dreams 1.15 remains in the rankings without any dispute over its authenticity or validity and this brings us to the controversy that did not begin until last October when Dreams began playing Minecraft 1.16, which is the one with the inferior update, an update that was sufficiently large as for core. Mechanics to include it as a completely separate category of speedrun.

In the best of these races, Dream was able to complete the game with an impressive time of 19 minutes and 24 seconds, putting him in fourth place in the standings; However, it also meant that he was very lucky. In fact, during his October speed running livestreams, Dream got so lucky that he attracted the attention of several people who began to wonder if his livestreams were proof of more than just good luck. If Dream had really modified the game, a lot of people might be now. wondering at this point why scrutinize the dream in particular after all, while his 19 minute 24 second run was certainly impressive and very fortunate that it is far from the fastest Minecraft speedrun in the books, of In fact, it's several minutes behind the 15 minute 12 second run that was the previous world record at the time, so if you're looking for suspiciously good luck, why wouldn't you focus on the fastest times?

As the Minecraft speedrunning team explained in their 29-page report, the problem wasn't with any of the dream speedruns in particular, rather it was abnormally high drop rates of key items across multiple consecutive live streams, which types of key items, so one of the biggest bottlenecks in any Minecraft speedrun is creating ender eyes to use the

final

portal to reach the end, which requires both ender pearls. and fire dust to craft, hence the importance of these two particular items and the dream in these six live streams in question was getting them at suspiciously high rates; Specifically, the research team noted that between 42 and 262 pig trades made throughout these broadcasts, ender pearls were obtained and 211 of the 305 fire kills dropped fire rods, this means that for this specific set of speed racing, the dream had a pearl bartering success rate of 16 when the actual rate is actually much closer to 4.7 percent and a fire rod drop rate of 69.2 percent when The actual drop rate is 50.

That may not seem like a big deal after all, a drop rate of 16 is obviously higher than 4.7, but are the numbers really that different to warrant a cheating investigation? I mean, these are random events after all, sometimes you just get lucky. Well, to illustrate this moment of the surprise test, which is more likely to be flipping a coin 10 times and getting heads at least seven times or flipping a coin a hundred times and getting heads at least 60 times, pause the video if you need to. Think about it, scroll down to the comments section to post your response, and while you're there, consider subscribing.

It's that red button right below the video. It's really satisfying to click and I cover a lot of aspects of Minecraft history. I've probably put more story into this game than Anyway, Mojang has you all ready with his answer. Great, his probability of flipping a coin 10 times and getting heads seven or more times is 17. His probability of flipping a coin a hundred times and getting heads 60 or more times is 2.84, yeah. It is much less likely now that the result may seem counterintuitive at first, but as your data set gets larger and larger, it is more likely to reflect the actual probabilities which, when talking about coin tosses, are 50 x 50.

You want an even higher probability For example, your chances of flipping a coin ten times and getting heads eight or more times five point four seven percent are actually significantly greater than your chances of flipping the same coin 10,000 times and getting heads. 51 or more, all you're talking about is 5 100 percent, more than half the chance of that happening is 2.32 at a glance, you could say, hey, 51 chance, that's only one percent out of 50, why would it be so unlikely? But this is a phenomenon that is described in statistics as regression towards the mean or sometimes a return to mediocrity, which is how I like to describe most of the content in the YouTube trends tab.

Oh, dive into YouTube's trending tab. Look, this episode will end up in the trending tab on YouTube. So how does all this apply to Minecraft, for example. You only have a 4.7 chance of getting an ender pearl from a piglen barter. You might get lucky and get an ender pearl after, say, four tries, leaving you with a drop rate of 25, but the more times you try, the closer and closer you'll get. the actual drop rate of 4.7 percent and when you're talking about 20+ hours of live streams and hundreds of barter attempts, you would expect the number to be much closer to the expected value, which and I'll just call this fact. out means that if there was cheating in this situation, it was the fact that the dream showed his work that got him flagged, it wasn't the individual record setting race that set off alarm bells, it was that plus the other 20 hours or so. more career. attempts broadcast online around it, an individual race would not have had enough drops to show any kind of manipulation or subtle bias;

In other words, if there was cheating involved and this was just an individual run that occurred offline, completely removed from any context and was then presented for consideration, none of this would have happened, there would be no way to verify the validity of the run. Unless of course I'm missing something here, I just thought it was an interesting loophole that this whole situation came up with that should probably be closed. Now let's think about an extreme example of luck winning the lottery. The chances of you purchasing a lottery ticket and winning the Mega Millions jackpot are approximately 1 in 300 million.

Those are incredibly low odds, but obviously some people are lucky enough toto win the lottery. I want a lottery that is great and it wouldn't make sense to track down the lottery winner and ask that person about cheating. On the other hand, if the same person were to win the jackpot multiple times, that's when fraud investigators will start investigating. This involved example illustrates one of Dream's first responses upon being selected for the review: he simply won the lottery, got very lucky, and by looking at only those cases of extreme luck, the review team saw skewed numbers in his response.

Instead of taking a truly random sample, the sample starts when luck seems unsuccessful and the sample ends as soon as I reach my personal best goal of 19 minutes, although this may be promoted as a random set of data, it is definitely not the end of quote. a problem known as sampling bias which refers to the fact that dream speed racing streams were not chosen at random for review, people spent hours analyzing the data specifically because someone noticed that they seemed to be luckier than normal and obviously if you test someone specifically because they seem to be getting lucky when you look closely at the results, they will appear luckier than normal, so to combat bias, what everyone has been calculating and discussing in their huge papers research is the probabilities of this luck happening, not specifically for dreaming. but literally every minecraft player alive knows the old saying about how if a monkey presses random keys on a typewriter for an infinite amount of time, he will eventually write the complete works of shakespeare;

It's based on the idea that something super is almost guaranteed to happen given enough time and enough tries, and it's a real theory, a statistic. The theory is called the infinite monkey theorem anyway, the same thing applies here. The luck of the dream was extreme, but how extreme was it? Both the Minecraft speedrunning team and the anonymous astrophysicists who were hired by Dream to write a rebuttal have submitted their numbers, but people seem to be confusing those numbers. I quote directly from the original report, the Minecraft speedrunning team came up with a number of 1 in 7.5 billion, well that number is basically what they say, hey, let's say there are a thousand Minecraft speedrunner monkeys on a thousand keyboards, there are still only one in 7.5 trillion chance of recreating the luck we saw in dream broadcasts, conversely, dreams that the odds are 1 in 100 million, the number 1 in 10 million is very much discarded in the refutation of dreams, but it's actually a different number, comparing the two is actually like comparing apples to oranges if you're looking for the best comparison: it's the sprint racing teams, one in 7.5 billion, versus the astrophysicists, 1 in 100 million, but that still leaves us with a huge difference in the calculations, why is it so good no matter how much I would like it to be?

It's not something that has one big answer, but many smaller answers, what you know is why these arguments occur in 20+ page documents. It includes things like differences in the application of detention criteria, different estimates for the total number of people alive. transmits other differences to account for sampling bias and differences in accounting for e.g. piracy bias. We've already covered the discussion of sampling bias in broad strokes and are about to address the latest p-piracy issue, but as you can see, it's a lot. more than I really want to go into here if you want to get into the nitty-gritty, I highly recommend the mathematicians video which breaks down all the arguments point by point from a deeply statistical mathematical perspective, good job mathematician, keep up the good work, but all.

I just hope this illustrates the broader point here: this is a complex topic with many different questions to consider, all using numbers that are, at best, rough estimates that are very flexible, which brings us to the last point. which I want to talk about. about p-hacking bias p-hacking is sometimes also known as data dredging. It is basically the practice of looking for patterns and selectively presenting data to reach a conclusion. It's pretty much the principle this channel was founded on, for example watch our marioismental series of episodes from a long time ago in the channel's history in these episodes I reviewed hundreds of mario games to present the viewer with curated data points to take them to the conclusion that yes, mario is indeed a sociopath and to get there, i ignore decades of him. act heroically and selflessly to save the mushroom kingdom although to be honest to this day this is one of the theories i still believe i just can't ignore the fact that mario whips dk in his first games or le grinds luigi's foot when he wins in the tennis match anyway this process is sometimes described as post-dictation, you get it, it's the opposite of predicting instead of proposing a hypothesis and then doing an experiment that confirms the hypothesis, You start with a pile of data and then use the data to generate a hypothesis to explain it after the fact, so how does this apply to our Minecraft speedrunning controversy?

Well, in any Minecraft game there are many sources of randomness, but so far we've only been looking at two pearl exchanges. and blaze rod drops, but what about other sources of luck, like blaze spawn frequency or how many piglets you can actually trade with? These are also random just because two variables happen to be higher than you would expect. Do we know that we're not just cherry-picking the data to come to the conclusion that cheating happened well? It all depends on the number of variables if there are only ten factors to consider and two are unusual then yes it's hard to deny it.

There's something fishy going on, but if there are, say, thousands of possible variables, then it's very easy to pick two of them and get a false correlation. In fact, there's a really fun website dedicated to exactly this, for example, did you know? The decline in divorce rates in Maine is actually related to the decline in people consuming margarine. It is true that there is a 99 correlation between the data points. The graph doesn't lie, but obviously our conclusion is that divorce and margarine have no relationship, unless, of course, marriages are suffering. to poor butter substitute choices, but when you look at a lot of data you can come to pretty much any conclusion and that's the other major point of contention between Dream and the speedrunning team: how many rng sources are there that could be manipulated as possible cheat sources how big is this data set the minecraft speedrunning team made a generous quote unquote estimate of 10 different factors your words are not mine dream claimed it was closer to 37. and honestly the frustrating thing about this is that there really is no clear answer because it's not just about how many variables there are but also how measurable those variables are.

I mention all of this one to explain it a little more clearly and two to point out that some of these calculations and differences between the numbers are based on numbers that come from assumptions that may seem a little arbitrary and that's where there is room for debate, but everything This, as good as it is to talk about statistics, I think you are missing the point, yes, it is essential to maintain integrity in speedrun. Boards are one hundred percent absolutely important, but are we sure this is a game that should have a speedrun board in the first place for all the back-and-forth over this topic?

One thing that is not up for discussion here is the reliance on luck in Minecraft 1.16. speedrunning well, the nether update was beloved by many minecraft players outside of the speedrunning community, myself included, given the large amount of theoretical material it added to the game, the speedrunning community hasn't exactly welcomed it with open arms and has led to a bit of a split with Minecraft 1.16 considered so different from previous versions as to warrant its own leaderboard, the update substantially changes the amount of time needed to complete Minecraft under ideal conditions while I'm recording this, the speedrun The fastest Minecraft pre-1.16 has a completion time of 19 minutes 36 seconds, while with version 1.16 the fastest time is only 14 minutes 36 seconds, so why would 1.16 be so divisive?

Well it all comes down to how fast you go in 1.16. Which makes the 1.16 speed much faster. As much as 5 minutes compared to previous versions of Minecraft, it has nothing to do with tricks like bunny jumps or diagonal bridges or other methods that Minecraft speedrunners have spent years perfecting, it has everything to do with what we've been talking about all this time. Random events and more specifically the piglin barter ending the pearl trade is where Minecraft 1.16's extra speed comes from compared to previous versions and unlike bunny jumping or bridge jumping, this is not the kind of stuff you can get better at by practicing if the barter system gives you the items you need it mostly comes down to pure randomness and bad luck can ruin the most skilled runs now obviously rg has been a big part of it of speedrunning and especially Minecraft speedrunning from the beginning - after all, the most popular category of speedrunning involves playing in worlds generated from a random seed - but many runners find that kind of randomness interesting, the kind that forces you to improvise along the way.

To me, sprints like that test the most important skill you can have as a player. something I call sight reading, a game that has enough fundamental skill and knowledge of the game mechanics that you can just dive into it and know what to do to achieve a solid time no matter what curveballs the game throws at you, but barter rng doesn't really challenge the player in that way, it's more like a slot machine where you just throw gold at an npc and hope for the best and the swing times it can create is massively greater than many other rng items From the past. maybe even break sprinting, which begs the question: does it counteract the underlying goal of what it is to be a sprinter?

It is not surprising that Dream's exceptional luck is undoubtedly one of the most striking and controversial parts of this entire incident, after all, he is a youtuber with More than 15 million subscribers and even more who are not subscribed to his channel, but that doesn't change the fact that with version 1.16 Minecraft has become a game where your ability to set a world record depends mostly on chance, it's partly a measure. of your skill absolutely, but arguably the most important thing being tested is your patience. Do you have the perseverance to keep playing for the hundreds or thousands of hours it takes for the rng to bless you with the luck you need to get the best time?

It's even worth investing those hundreds or thousands of hours when the most important factor in your success is something that is completely out of your control, so what would be the alternative perhaps a more accurate annual indicator of the best speed runner for that version of the sport? The game would be a speed racing tournament that would place two or more players on the same random world seed and see who can roll with the punches, the best, who can use their knowledge of the game to get to the end of the end as fast as they can. you can.

I'd probably have to make piglet trading off-limits, but would that be any different from a Smash Brothers tournament where certain characters can't be used due to an imbalance or are broken? I don't know, it's just an idea I wanted to put forward. and hell, I really enjoy seeing a competitive version of Minecraft because let's face it, if that comes out of all this controversy, well, I'd definitely call that a silver lining, well, that and everyone being forced to learn statistics so they can talk about it, but Hey, like I said before, learning is and should always be fun and lucky for us.

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