# Five Dollar Man

There is a test that psychologists can give to a person to determine how much of a gambler he is. It is quite simple. Would you bet a quarter for a quarter on a coin flip?—that is to say, if it comes up heads, I pay you a quarter and if it comes up tails, you pay me a quarter. A man who would take this bet is a gambling man. But if he will not take this bet, the psychologist ups the ante. Would you bet a quarter on two quarters? The plot thickens. If not that, three quarters. Then a dollar. Most people are not really interested until it reaches the dollar for a quarter level. I’m more a five dollar man.

Even though I’m not a betting man, I used to be a professional sports handicapper. Sports betting is interesting to me, because unlike most forms of betting, you can win if you are good at it. The problem is that almost no one is. The reason is that it is highly random. One year, I looked at all the NFL games and found a striking correlation between the team with the fewest turn-overs (lost fumbles and interceptions) and the team that covered the line. Thus, it didn’t matter how well the teams played otherwise (that’s all figured into the line anyway), what really mattered were the random and uncommon events (the turn-overs).

Nonetheless, it is striking that almost all sport bettors lose money, because you don’t have to do much better than random (50%) to win. But you do have to do better. In order to explain this, I first have to explain how the house (casinos and similar institutions) run their sports betting operations.

It should come as no shock that the house is not a charitable institution; they are in the business of making money so they take a percentage off the top of any bet. This percentage is called the vig. This amount is traditionally 5% of the entire bet. So bets are usually placed as “Betting \$55 to win \$50.” This means that if you win, you get a \$50 profit but if you lose, you get a \$55 loss.

In order for the house to make sure it doesn’t take a bath on any given game, it moves the line around so that there is roughly the same amount bet on both teams. The house doesn’t care who wins, they just want that 10% of the loser’s money; the rest goes to pay the winner. The house always wins. Always.

To compensate for losing more when you lose than you win when you win, you must win more than 50% of the time just to break even. How much more? Well, not that much. A little algebra will help to explain. Assume that you are making \$50 bets. If x is the fraction of wins then the total amount of money you get from wins will be (\$50)*x. But the total amount of money you lose would be (\$55)*(1-x). For you to break even, these must be equal. So…

\$50*x = \$55*(1-x)
x = .5238 = 52.38%

You need to win roughly 52.4% of the time to break even. This may not seem like too much to ask for but most bettors lose money year after year after year. So I recommend not betting. But then, I would: I’m a five dollar man.

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