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The Mathematics of Roulette I Understanding Casino Games - YouTube
Channel: Wondrium
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a roulette wheel has 38 numbers
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18 of these numbers are red 18 of these
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numbers
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are black and two of the numbers
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zero and double zero are green
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by the way i'm describing american
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roulette the european version has just
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one green number the simplest bet in
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roulette is to bet on one of the main
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colors let's say red
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okay so i'm going to bet one dollar on
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red it's an
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even money bet which means that if you
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bet a dollar then you'll either win
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or lose one dollar depending on whether
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or not a red number appears here let's
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give it a try here
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red 27 i win
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now what are your chances of winning
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since there are 38 numbers
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each of which has the same chance of
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occurring
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and 18 of these numbers are read
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then the probability that you win is 18
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over 38 which is a little less than 50
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percent
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clearly you have a disadvantage at this
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game
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we can quantify this disadvantage using
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the very important
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concept of expected value
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if you only remember one concept from
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this lecture
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this is what i want you to remember the
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expected value
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of a bet is a weighted average
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of how much you can win or lose
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when you bet on red in roulette you'll
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either
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win a dollar with probability 18 over 38
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or you'll lose a dollar or you could say
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win negative one dollars with
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probability
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20 over 38 right because there are 18
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red numbers
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and 20 numbers that aren't hence your
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expected value is 1
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times 18 over 38 plus negative 1
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times 20 over 38 that's negative 2
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over 38 negative 0.0526
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what this means is that on average
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you'll lose about
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5.3 cents for every dollar that you bet
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now in roulette you can bet on other
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things besides color
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for instance you can bet that a number
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between 1 and 12 shows up here let me
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show you here
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so let's say we bet a dollar that one of
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the first 12
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numbers shows up the casino pays
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two to one odds for this bet which means
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that if you bet a dollar
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and you win then the casino pays you
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two dollars okay so
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let's calculate our expected value here
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so when you bet a dollar you're going to
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win
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win two dollars with probability
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what 12 numbers out of 38
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and you're going to lose a dollar
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with probability 26
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over 38 because if you win 12 times out
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of 38 you lose
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26 times out of 38. hence the expected
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value of this bet
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is 2 that's what you win
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12 over 38 times plus negative 1
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that's for losing 1 26 out of 38 times
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when you do the math that's negative 2
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over 38
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negative 0.0526 which is the same number
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as before or suppose you bet on a single
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number let's say i like lucky number 17.
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all right here the casino pays 35 to 1
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odds
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thus when you make this bet then you
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either
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win 35 with probability
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1 over 38 just one winning number out of
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all 38
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or you lose one dollar with probability
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37 over 38. so when you calculate the
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expected value
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35 times 1 over 38 plus negative 1
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times 37 over 38 once again
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you get negative 2 over 38. we still get
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negative
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5.3 cents interestingly
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when you play roulette practically every
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bet
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has the exact same expected value of
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negative 5.3 cents
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per dollar bet
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[Music]
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