The Mathematics of Roulette Game

A roulette wheel has 38 numbers. Eighteen of these numbers are red, 18 are black, and two of the numbers, zero and double zero, are green. By the way, I’m describing American roulette; the European version has just one green number.

The Mathematics of Roulette game

Mastering Roulette Strategy – The Art of Making Informed Bets

The simplest bet in a roulette game is to bet on one of the main colors, red. Okay, so I’m going to bet one dollar on red. It’s an even money bet, which means that if you bet a dollar, then you’ll either win or lose one dollar, depending on whether or not a red number appears.

The Mathematics of Roulette Games

Here, let’s give it a try. Red 27, I win. Now, what are your chances of winning? Since there are 38 numbers, each of which has the same chance of occurring, and 18 of these numbers are red, then the probability that you win is 18 over 38, which is a little less than 50 percent.

Quantifying Disadvantages – The Power of Expected Value in Roulette Game

Clearly, you have a disadvantage at this game. We can quantify this disadvantage using the very important concept of expected value. If you only remember one concept from this lecture, this is what I want you to remember. The expected value of a bet is a weighted average of how much you can win or lose.

When you bet on red in roulette, you’ll either win a dollar with a probability of 18 over 38, or you’ll lose a dollar (or you could say win negative one dollar) with a probability of 20 over 38. Right, because there are 18 red numbers and 20 numbers that aren’t. Hence, your expected value is 1 times 18 over 38 plus negative 1 times 20 over 38. That’s negative 2 over 38, or negative 0.0526. What this means is that, on average, you’ll lose about 5.3 cents for every dollar that you bet.

Strategic Insights – Calculating Expected Values in Roulette Betting

Now, in roulette, you can bet on other things besides color. For instance, you can bet that a number between 1 and 12 shows up here. Let me show you. So, let’s say we bet a dollar that one of the first 12 numbers shows up. The casino pays two to one odds for this bet, which means that if you bet a dollar and you win, then the casino pays you two dollars.

Optimizing Your Roulette Game play – Making Smart Bets for Long-Term Success

Okay, let’s calculate our expected value here. When you bet a dollar, you’re going to win two dollars with a probability of 12 numbers out of 38, and you’re going to lose a dollar with a probability of 26 over 38. Because if you win 12 times out of 38, you lose 26 times out of 38. Hence, the expected value of this bet is 2 (that’s what you win, 12 over 38 times) plus negative 1 (that’s for losing 1, 26 out of 38 times). When you do the math, that’s negative 2 over 38, or negative 0.0526, which is the same number as before.

Or, suppose you bet on a single number. Let’s say I like lucky number 17. Alright, here the casino pays 35 to 1 odds. Thus, when you make this bet, you either win 35 with a probability of 1 over 38 (just one winning number out of all 38), or you lose one dollar with a probability of 37 over 38. So when you calculate the expected value, 35 times 1 over 38 plus negative 1 times 37 over 38, once again, you get negative 2 over 38. We still get negative 5.3 cents. Interestingly, when you play roulette, practically every bet has the same expected value of negative 5.3 cents per dollar bet.

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