On October 13, 2012, one of the major sports books in Las Vegas said that there was a 108.8% chance of one of the four teams left in the baseball postseason would win the World Series. Of course it didn’t actually say there was a 108.8% chance of this happening, but the odds that they released to bettors did and helped ensure that over the long run, Vegas wins and we, as a whole, lose.

If you haven’t already, check out Part 1 for a review of AND vs OR probability. Now let’s imagine that instead of betting on outcomes, like we did in the previous article, you’ve wised up and decided to open your own sports book, gMATH. You decide to start simple and offer bettors a chance to bet on which number, 1-4, randomly rolls out of a bingo cage. You realize that the probability of each number being selected is 25%, but you need a way to translate this for paying bettors. In a scenario where four different people each put down $1 on each of the four numbers, one person would win $3 ($4 total – $1 they bet). So you place the very first odds at gMATH’s number guessing game at 3 to 1.

In the long run, gMATH’s inaugural betting event may attract a clientele of people who enjoy watching ping pong balls with painted numbers roll around, but it won’t be bringing you the fortunes that you passed up on business school for. You realize that you need a new betting game that will attract more than just the bingo-loving crowd, involves a small amount of luck, and allow you to make a profit no matter which team wins. As there are exactly four teams left in the postseason, you decide that baseball would make a perfect switch.
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