Lo que los casinos OCULTAN de la ruleta: la VERDAD matemática

[00:10] win at casino roulette? That's what we're going to analyze in today's video. Before we begin, there's a concept called Expected Value that we need to understand very well because it's fundamental to the entire

[00:24] analysis we're going to do. I'll explain it with an example. Imagine the following game: we have two players, A and B, and they're playing by flipping a coin. The coin is perfectly balanced, meaning that 50% of the time it lands on heads and

[00:37] 50% of the time it lands on tails. They do the following: when it lands on heads, B pays A following: when it lands on heads, B pays A 1.20, and when it lands on tails, B pays A

[00:49] 1. Do you think this is a fair game? Intuitively, it's clear that it isn't, but we can confirm this with expected value. Let's calculate it. In this Let's calculate it. In this case, we would have the expected value of A.

[01:04] When A wins, they win 1.20. What is their probability of winning? Since the coin is perfectly balanced, they have a 50% chance, one half. Now, when A loses, they lose one euro. What is their probability of losing? The same, one half. If you do

[01:22] losing? The same, one half. If you do these calculations, you'll see that this gives these calculations, you'll see that this gives average, player A wins this amount per spin, but notice what happens to player

[01:38] to player B. When B wins, they win one euro, and this happens half the time. But when they lose, they lose 20 euros, which also happens half the time. In this case, their expected value is negative. That is,

[01:52] on average, they are losing on each spin. And you might say, "Yes, but if I play three times, if I quit, then I 've won." True, but the law of 've won." True, but the law of large numbers tells us that the more

[02:07] we evaluate a random experiment, the closer we get to the theoretical result. That is, the more people play, the more true it becomes that, on average, player A wins 10 cents per spin and player B loses 10 cents. This general idea is what we'll use to

[02:23] evaluate the strategies in Roulette. You can see the roulette wheel projected here; it has 37 slots, that is, the numbers from 0 to 36. Besides betting on one number, you can bet on two, three, or as many as you want. You can bet on red, black, even,

[02:38] want. You can bet on red, black, even, odd, dozens, columns. Great! Let's evaluate the expected value of all these types of bets. Let's start with the most basic one. I'm betting on 19 because I like that number. What are my

[02:52] chances of winning, and above all, what is my expected value if I consistently what is my expected value if I consistently bet on that number? Let's calculate the expected value of a straight bet. How much do you win if you get a straight bet right? You win

[03:07] 35 chips. What is the probability of getting it right? One in 37, because I'm betting on one of the 37 squares. How much do I lose? I lose one chip. When do I lose? I

[03:21] lose if the ball lands on any of the remaining 36 numbers. Now, what is the value of this? This value is

[03:38] negative, which means that in the long run, we're going to lose on average per long run, we're going to lose on average per bet. In this case, 2.7 cents or 0.27 chips. If we imagine that these chips are worth 1 euro, then that's 2.7

[03:54] cents. Let's evaluate another strategy. Let's suppose I want something more balanced. I'm going to bet on colors. Perfect. So, if I bet on red or black, what is the probability of getting it right? There are 18 red numbers and 18 black numbers,

[04:11] but friends, there's also zero, and zero isn't any color. So what are the odds? I get paid one chip when I win, and I win 18 one chip when I win, and I win 18 out of 37 times. When I lose, I lose one chip.

[04:27] But it turns out there are 18 numbers of the opposite color plus zero, that is, 19 opposite color plus zero, that is, 19 out of 37. Do you know what number this will give? It's

[04:39] out of 37. Do you know what number this will give? It's negative, 0.027, slightly tilted in favor of the casino. Let's calculate another one: a

[04:57] paid two chips when I win, so two times 12 gives 37. When I lose, what do I lose? Well, I lose my chip. How many numbers do I have that make me lose? I have 24 plus zero.

[05:10] Again, zero isn't even, it isn't odd, it isn't red, it isn't black, it doesn't belong to any column, it doesn't belong to any dozen. I would have 25 out of 37. And

[05:24] to any dozen. I would have 25 out of 37. And guess what value it gives? possible combinations, you'll realize that the roulette wheel is

[05:39] very, very, very slightly tilted in favor of the casino. If you keep betting on the same thing at the casino, all you'll favor of the casino. If you keep betting on the same thing at the casino, all you'll a little bit on each spin. Of course, you could quit after winning twice,

[05:54] but that won't make you rich, and it wouldn't make much sense anyway. What if you lose? This is where one of the most talked-about roulette strategies comes in: the Martingale. The Martingale is a

[06:09] super interesting strategy, and in theory— I emphasize, in theory—it's correct. What does it I emphasize, in theory—it's correct. What does it consist of? First, we have to find something with a probability close to 50% to bet on. Let's say

[06:23] to 50% to bet on. Let's say we bet on red. Great! I put one chip on red, but it doesn't come up; it comes up black. What do I do? I repeat my bet, but I double my chips on red. It still doesn't come up red. No problem. I double my chips on red,

[06:37] chips on red. It still doesn't come up red. No problem. I double my chips on red, Great! I've won four chips! Perfect! But it turns out I've invested three. That is,

[06:50] after doing this sequence, my result is plus one chip. In other words, I've recovered my initial investment and gained one chip. Hey, this is great!

[07:02] No, because in the end, if I constantly bet on one color, I keep doubling my bets, and that's what I get. If the roulette wheel is balanced, the color will come up sooner rather than later, and I'll recover my winnings and gain a chip. Okay, let me explain why it doesn't work. There are

[07:19] two limitations. The first is that you do n't have infinite capital; that is, it grows super fast. Let's do a quick sequence: 1 2 4 8 16

[07:34] 32 64 128. And we have 2 3 4 5 6 7 8 spins. You might say, "Wow, but why did black come up eight times again?" Law of

[07:49] large numbers: The more a random phenomenon is observed or repeated, the closer it will come to the theoretical result. Yes, but also, all these irregularities will occur more often. That is, if you observe a phenomenon of

[08:05] this type long enough, you'll see that these kinds of things, however improbable, end up happening. If you ever go to a casino and ask a casino employee if they've ever seen 20 reds in a row, they'll most likely say

[08:20] seen everything. Why? Because they've observed many, many, many spins. But even if we had infinite capital, the casino reserves the right to... Another play, which is the following, the

[08:40] limit: normally there's a betting limit, meaning I allow you to bet on colors, for example, from €1 up to € to € 500. Look what would happen here if we continue:

[08:53] 128, 256, and on the next spin, 512. I've already gone over. 256, and on the next spin, 512. I've already gone over. And now, what have I had? Well, these And now, what have I had? Well, these were 8, 9, 10 spins, and I've already gone over. I can't reach it anymore; I can't

[09:08] bet the maximum that the table's V limit is 500. That is, my next bet doesn't recover the entire investment; I don't win any money. That is, it's entire investment; I don't win any money. That is, it's due to these two facts that

[09:21] this strategy doesn't work. If your capital were infinite betting limit, this would work, as long as the roulette wheel was balanced, which, a priori, it is. Having

[09:38] mathematically winning strategy in roulette doesn't exist. Why? Because mathematically, roulette is designed so that the probabilities, or in this case, the expected value, favor the casino. Now, you might ask, "Hey, how did

[09:50] the Pelayo family win?" Well... They did it in a very, very ingenious way, which is as follows: The roulette wheel, like any man-made object, cannot be manufactured perfectly. Ultimately, the probability of a number

[10:07] coming up is one in 37 times; that is, the probability of any number being equal to 1 divided by 37. This is somewhat theoretical. Why? Because when you manufacture something, a slot might be

[10:19] a little bigger, or a ramp might be a little steeper. So what they did was observe several thousand spins on the roulette wheel to detect these manufacturing anomalies. These anomalies resulted in

[10:37] certain numbers coming up more often than expected. Then, if you consistently bet on those numbers, you can

[10:49] reverse the expected value and make it positive. It's a super ingenious strategy, so much so that they were banned from world tour. While they were being

[11:03] from all casinos, they applied this method of observation: "I'm going to observe many spins, I'm going to collect data, and I'm going to see which numbers come up most often." These anomalies are probably unrealistic today. Why?

[11:19] constantly improving, process controls are becoming more stringent, and roulette wheels are likely being checked and calibrated. Casinos will probably have statistical controls in place to ensure these anomalies don't occur, and so on. In

[11:33] conclusion, if you want to make money, roulette is a very, very, very inadvisable way to do it. I hope you enjoyed this video, and I'll see you in enjoyed this video, and I'll see you in the next one. Goodbye!