Recreational Math

Sports Numbers

How does a person determine the odds in horse racing?

The track makes its money in a certain mathematical way: When the odds of the horse race are converted to probabilities, they usually add up to more than 1, giving the track the advantage. For example, say a race track has 12 races with four horses, and the odds of winning each race are as follows (note: race tracks don’t use the same horse in each race—this example is for illustrative purposes only):

  • Horse 1—1:1; probability = chances for (1) / total chances (1 + 1) = ½ or 6/12
  • Horse 2—2:1; 1 / (1 + 2) = 1/3 or 4/12
  • Horse 3—3:1; 1 / (1 + 3) = ¼ or 3/12
  • Horse 4—5:1; 1 / (1 + 5) = 1/6 or 2/12

If a person puts $1 bets on horse number 2, he or she would have to win 4 out of 12 races to break even. But note: All these numbers add up to 15/12, or 1.25, a higher number than 1, so as long as no horse wins more than its probability, the house wins.

There’s another way of looking at this type of betting. In order for the gambler to do “better” than the track, he or she has to win 15 times in 12 races—a physical and mathematical impossibility—which is why the track always makes money. Of course, a gambler may bet on certain low-probability horses that win more races than expected, earning a few more dollars along the way, but don’t bet on it.


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