The Mathematics of Roulette I Understanding Casino Games

A roulette wheel has 38 numbers 18 of these numbers are red 18 of these, numbers. 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 simplest bet in roulette is to bet on one of the main. colors let's say 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 here let's. give it a try here 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 read then the probability that you win is 18 over 38 which is a little less than 50, percent, 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 probability 18 over 38 or you'll lose a dollar or you could say, win negative one dollars with, probability 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 negative 0.0526 what this means is that on average you'll lose about. 5.3 cents for every dollar that you bet. 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 here. 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 okay so, let's calculate our expected value here, so when you bet a dollar you're going to win, win two dollars with probability what 12 numbers out of 38, and you're going to lose a dollar with probability 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 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.. all right here the casino pays 35 to 1 odds. thus when you make this bet then you. either win 35 with probability 1 over 38 just one winning number out of. all 38 or you lose one dollar with probability 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 exact same expected value of, negative 5.3 cents. per dollar bet . you,