# Question: Have you ever watched the odds at a horse race

Have you ever watched the odds at a horse race? You might hear that the odds against a given horse winning are 9 to 1, meaning that the horse has a probability 1/(1 + 9) = 1/10 of winning. However, these odds, after being converted to probabilities, typically add to something greater than one. Why is this? Suppose you place a bet of $10 on this horse. It seems that it is a fair bet if you lose your $10 if the horse loses, but you win $90 if the horse wins. However, argue why this isn’t really fair to you, that is, argue why your expected winnings are negative.

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