[00:00] This year, the Fox TV channel debuted a new reality show called The Snake. It was a show hosted by Jim Jeffries where people had to either be or not be the Snake, I don't know.
[00:12] So, don't panic if you didn't. The point is enough people did that when they had a final challenge that involved rolling custom dice to get snake eyes when the probabilities looked a little bit suspect.
[00:29] In the finale episode, the final six contestants had to roll these weird kind of custom dice things. And the first person to get snake eyes went straight to the final.
[00:45] The next four people to get snake eyes got to stay in the game. And the very last player who didn't get snake eyes was going to get kicked off the show. Round one, all six contestants roll double nothing.
[01:00] Not a single snake eye to be seen, 11.2% chance of that happening. A single snake eye. Nothing.
[01:14] The first one, we have a winner. The last two rolls in that round also nothing. Round three. The remaining five contestants, two of them get snake eyes.
[01:28] Two from five. Incredible. In what we believe to be round four, the three remaining contestants all roll absolutely nothing. There's only two contestants left and they both roll not snake eyes. A snake eye and a blank.
[01:46] And the final unlabelled round, maybe six, who knows? One of the contestants rolls snake eyes. That's five contestants rolling snake eyes in, if you count them, 24 rolls.
[02:00] Five contestants all got snake eyes in 24 rolls. Come on. That, that feels like it happened real quick, but what are the odds?
[02:12] In a very literal sense, we can work out the probability by thinking first of all, Now, if we got 24 rolls, we know the last one has to be snake eyes 'cos that's where we stopped.
[02:27] And then the other four snake eyes can be anywhere in the other position. Choose four snake eyes is 8,855 possible ways that can happen.
[02:41] And the probability of each of those is just the probability of snake eyes. That's 1/(6^2). And the probability of not getting snake eyes is 35 out of 36.
[03:00] So to get five snake eyes, that's 1 over 36 the power of five. And to not get the other 19 of them, that's 35 over 36 all to the power of 19.
[03:16] five snake eyes in 24 rolls is 0.00857%, it's pretty small. Now, that's the exact percentage for 24 rolls, but that's actually not what we care about.
[03:32] If they had done it in 23 rolls or 25 rolls, I'd still be making this video. It's because it's a weirdly small number.
[03:44] How fewer rolls would there have to have been in the show And I thought I'd split it into two.
[03:56] I think 25 or under, definitely; 50 and under, probably. Instead of working out every single one of those and adding them all up, I just ran some simulations. I ran literally millions of rounds of this part of The Snake.
[04:12] That's the frequency that any set number of rolls, the likelihood of that happening were you to just start a game of snake eyes on The Snake.
[04:24] So I can tell you the probability of the game ending in 25 or fewer rolls is 0.055%.
[04:37] That's small! Even 50 or fewer rolls, which is our I probably would make this video, is 1.24%. So for the game to have been over that quickly
[04:53] or anything remotely similar in terms of how fast it ended extremely unlikely. So technically we have option zero: they just got very lucky. They didn't think through how unlikely rolling that many snake eyes was.
[05:08] But then you wouldn't believe it. They got super lucky, it happened real quick, nice and neat, done.
[05:20] So, to explore other options, we're going to recreate the finale of The Snake. And I've invited different canonical versions of myself from other videos to join us.
[05:34] So, uh first of all, we have Space Matt. [Matt] We've got Beard Matt. [Matt] Future Matt, We all love Future Matt
[05:46] [Future Matt] Yes, reporting live from tomorrow. [Business Matt] I'm the mat you normally skip over, but this time I get to be in the real video. Although, while I'm here, saily.com/standupmaths for a new SIM, more on it later.
[06:00] [Matt 2] It's me from the second channel, I'm basically the same. [Matt] So, we all had a bit of a think, this is so ridiculous, And we came up with some ideas for how they could have made the show if it wasn't just pure luck.
[06:16] And we'll start with one of the least likely explanations. [Business Matt] Yeah, I mean, I hate to be the one who sounds like a LinkedIn post,
[06:28] There are several ways they could have faked this. What if there's like an electromagnet that can turn on and off bits of metal in the dice?
[06:41] There's like a literal puppet master or CGI, they dice aren't... Okay, You know what? We actually passed the footage on to a magic expert to analyse it.
[06:54] And the answer is no, like it doesn't look like it's been faked in terms of trickery at all. You just need one disgruntled contestant or someone on the crew and the whole thing gets rumbled.
[07:10] It's happened on other shows and they would have to commit to the fact it's no longer, I know it's reality TV, but no longer a fair game. It would be a very expensive thing to do.
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[08:55] [Matt] Thanks for that Business Matt. So, if we rule out trickery, uh next round of theories are what if these aren't real dice? They're ridiculous crates and they never claim that these are perfectly fair dice.
[09:14] So, we thought maybe they're slightly biased. And, uh, I I believe Space Matt has some theories for what could have happened. [Space Matt] Yes, I do. In fact, I think there's two different ways they could have been biased.
[09:28] First up, deliberate ways they could have skewed the odds. So, the crates that they're using as dice, we assume there's only a single snake eye on each one.
[09:42] What if at some point they swap out one of these for a crate with two snake eyes and they're just very careful to never show both of those faces at once?
[09:54] Well, I ran the numbers, I got a new distribution for if there's three snake eyes in total. And the probability of doing it in 25 or fewer rolls goes all the way up to 1.1%. 50 or fewer rolls, it's now 14.3%. Still not super high.
[10:10] If you add two more, one on each dice, now we're talking the probability of 25 or fewer rolls is 13.7%, the probability of 50 or fewer rolls is roughly 2/3, it's like 66.5%.
[10:24] the fact there were two snake eyes on each mini crate dice. What if they accidentally biased the dice?
[10:36] So, for example, oh, just floating by here in Maths Space is a blank version of one of the crates. And in theory, fair dice.
[10:49] But what if when you're 3D printing your crate, you accidentally. Oh, look! It's another one that's been squashed in a single dimension. Now, this is exaggerated, but the idea is these two faces are now more likely,
[11:06] So, if the snake eye was on one of these, maybe, you know, not this bad, but slightly, it's more likely. I worked out if you want a 50% chance of being 25 or fewer rolls,
[11:25] this would have to be 43% chance on each of these faces. I mean, I don't want to get side-tracked again by how thin that would have to be for that to happen.
[11:39] And if you want a 50% chance of doing it in 50, that's a bit more generous rolls. You still need 31% chance on these faces and 9.5 on the others.
[11:51] Now, while we can speculate about if maybe this happened. Oh, look at it go. What we do know definitely happened was if you take a very close look at the crates. The face that they put the snake's eye on they flattened it to make it look...
[12:09] I mean, just I guess it's easier to draw on but that means they had to remove a bit of material. and that actually makes the snake eye face a little bit lighter.
[12:21] we left that in because I wanted them to be, I mean Main Matt, wanted them to be fair, but the ones in the show do have some material missing
[12:33] which would have made it ever so slightly biased to come up snake eyes. In all of these situations.; however, because we can see the dice and it might be slightly off but not much,
[12:45] [Matt] Right, so, it's a factor, but it's not everything. There's something else going on.
[12:57] [Matt] Right, so, now we're down to what I think a lot of us were suspecting. Maybe they just rolled the dice over and over again and made it look a lot quicker. So, to have a closer look at that, we go now to Beard Matt.
[13:13] demonstrates that getting five snake eyes in under 25 or 50 rolls very unlikely. Well, you get snake eyes once every 36 rolls on average.
[13:28] And if you want five of them, it's just 5*36. Like the exact midpoint of that plot is 180 rolls on average. What is the rest of that weird distribution?
[13:43] Well, by the time you've done 100 rolls, there's a 15% chance that you've got your five snake eyes. 180 is halfway, 50%, 200 rolls is 65%.
[13:56] 300 rolls is up at 92%. And by 400 rolls, 99% chance that you're done. So, so maybe that's what they did.
[14:11] I mean, would reality show contestants just sit there rolling dice Who am I kidding? Of course they would.
[14:25] So, we're going to do it. We've got an Australian comedian in a jungle-esque environment. We have a rustic table bounce precariously on bits of a pallet.
[14:37] And using these special dice and a variety of hilarious cast members from previous videos, And we're going to get to the bottom of the snake stats.
[14:51] Between me and the five other Matts, that's effectively six people in this competition. And the last person to get Snake Eyes, kicked off the channel.
[15:06] We'll see what happens, here we go. Roll number 1. [Future Matt] I mean, for me, this is a lot less exciting because I already know who lost, but it's not me. [Beard Matt] All right, my turn. Here we go.
[15:24] [Business Matt] Time to take care of some business. [Matt Two] Two eyes for Matt Two. Here we go. [Matt] Here we go.
[15:39] [Dice roll clatters across all Matts] [Dice roll clatters across all Matts] Ahh, hah-hah, no one's going to beat that.
[15:56] [Dice roll clatters across all Matts]
[16:12] [Beard Matt] Snake eyes! All right. Once again, Beard Matt is successful. [Dice roll clatters across all Matts]
[16:24] [Dice roll clatters across all Matts]
[16:40] [Dice roll clatters across all Matts]
[16:58] [Dice roll clatters across all Matts] [Business Matt] Now in theory only half of it should be knocked out by now, but I guess that's about right.
[17:14] [Dice roll clatters across all Matts] Ha, ha-ha! Take that, Future Matt.
[17:26] I'll be back tomorrow. [Matt] We did a combined 125 rolls to get five snake eyes.
[17:39] Now, that is way faster than I expected, but still, I mean, totally plausible. I mean, I know I roll a lot of things for a long time, I get that.
[17:52] That's okay. I can believe that some highly motivated reality TV contestants and some TV execs, who had written themselves into a probability corner, would just hunker down and keep rolling the dice.
[18:08] And at no point do they specify how many rolls per round. So, and at one point they stop telling us what round it is. We only see 24 rolls, but they don't promise that's all that happened.
[18:23] So, I would say unless we get any more information, I'm going to say, yeah, they they just rolled a bunch. It's technically completely fair and for the purposes of pacing,
[18:35] they edited it down strictly within the ambiguity in how they set up the game. We won't know for sure, however, unless we speak to someone involved in the production. So, if anyone knows anyone involved in making Fox's, The Snake,
[18:53] I mean on the record or anonymous, get in touch. Thank you to all the other Matts for what a dream collaboration this has been. I guess I'll link to all of your videos; links' links below to everyone involved in this, uh, in this video.
[19:12] Uh, and that's it. Um, like I, I guess we, we reality TV show wave goodbye. [SUM theme plays]