Date: 01/26/98 at 22:49:35 From: Humberto Castaneda Subject: Probability/Statistics and gambling Roulette Questions: 1. What is a safer bet: to bet on a number, or to bet on color? 2. Which bet maximizes your wins: betting on numbers, or betting on colors? Thank You.
Date: 01/27/98 at 20:32:13 From: Doctor Bill Subject: Re: Probability/Statistics and gambling Humberto, As to the question about the safety of betting, you're always going to lose in the long run, so no bet is "safe." As for which is the "better bet," it turns out they are about the same. If we are assuming you are playing roulette in America (in Europe the roulette wheel is different) then there are 36 numbers, half red and half black, and also a 0 and a 00, both green. (In Europe there is not a 00.) The payoff for a bet on a number is 35-1 (notice that if it were a "fair" game the payoff would be 38-1,because there are 38 different numbers, but that's how the house makes its money), and the payoff for red or black is 1-1 (notice here again the game is not quite fair since you will lose more often than you win because of the two green numbers, but you are paid off as if you win and lose an equal number of times). In statistics and probability there is something called "mathematical expectation," which is the AVERAGE amount you will expect to win on any given play, if you play for a LONG time. (If the expectation is negative you "win" a negative amount, or in other words you expect to lose each time you play.) To find the expectation for a game you multiply each payoff times the probability of getting that payoff, and then add all of those numbers together. That total then is your EXPECTION. You probably won't win (or lose) that particular amount on any given play, but if you play for a long time you can "expect" to win that amount, on the average, each time you play. If we now look at the roulette game, suppose you bet $1 on the number 5 each time you play. What are the payoffs? You can either win $35 or lose $1. The probability that you win $35 is 1/38 (only one winning number out of the total of 38). The probability that you lose $1 (that is you "win" $-1) is 37/38 (37 losing numbers out of the total of 38). To find the expectation of this game do the following calculation: 35(1/38)-1(37/38). What do you get here? If it is positive you win and if it is negative you lose. Suppose you bet $1 on RED each time you play. Here the payoffs are that you win $1 or lose $1. The probability of winning is 18/38 and the probability of losing is 20/38. (Do you see where these probabilities come from?) To find the expectation do the calculation: 1(18/38)-1(20/38). Notice that both of the calculations above came out negative, that is, you're going to lose in the long run. In these two cases I think they both came out the same, so it doesn't matter which way you bet your money, you're going to lose it at the same rate. If they had come out different, then the better bet would have been the bet with the highest expectation. -Doctor Bill, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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