• Roulette Probability Cheat Sheet

    A roulette wheel has 38 numbers. 18 of these numbers are red, 18 of these numbers are black. And two of the numbers, 0 and 00, are green. This is basically the American roulette description, the European version has just one green number.

    The simplest bet in roulette is the bet on one of the main colors. Let's choose red. It's an even money bet which means that if you bet $1 then you'll either win or lose $1 depending on whether or not the red number rolls out. What are your winning chances? There are 38 numbers and each of them has the same chance of occurring and 18 of these numbers are red then the probability that you win is 18/38=47.3%.

    Obviously, you have a disadvantage at this game of chance. We can explain this disadvantage using a very important concept of Expected Value. This is what you need to remember each time you are to spin the roulette wheel. The Expected Value of a bet is a weighted average of how much you can win or lose.

    E.g. when you bet on red in roulette you'll either win a $1 with probability 47.3% or lose a $1 with probability 20/38. Easy! There is 18 red numbers and 20 numbers that aren't red. Hence, your expected value is

    EV=1(18/38)+(-1)(20/38)=- 2/38= -0.526.

    What it means is that on average you lose about 5.36 cents for every dollar that you bet.

    In roulette, you can bet on another spot besides color. You can bet that the number between 1 and 12 appears.

    The casino pays 2 to 1 odds for this bet which means that if you bet $1 and you win then the casino pays you $2. Let's calculate the Expected Value here. When you bet a dollar, you're gonna win $2 with probability 12/38, and you going to lose $1 with probability 26/38. Easy, when you win 12 times out of 38, you lose 26 times out of 38.

    Hence, the Expected Value of this bet is

    EV=2(2/38)+(-1)(26/38)=- 2/38= -0.526

    You see, this is the same number as before. Or let's say you bet on a single number. I like 20 black.

    Here the casino pays 35 to 1 odd. Thus, when you make this bet then you'll either win $35 with probability 1/38 (just one winning number out of 38 numbers) or you lose $1 with probability 37/38.

    When you calculate the Expected Value

    EV=35(1/38)+(-1)(37/38)= - 2/38= -0.526

    Remember, when you play roulette basically every bet has the exact same Expected Value of -5.36 cents for $1 bet.


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