When You Bet on a Racehorse with Odds of M-N

Essay

When you bet on a racehorse with odds of m-n, you stand to win m dollars for every bet of n dollars if your horse wins; for instance, if the horse you bet is running at 5-2 and wins, you will win $5 for every $2 you bet. (Thus a $2 bet will return $7.). Here are some actual odds from a 1992 race at Belmont Park, NY. The favorite at 4-1 was Pleasant Tap. The second choice was Thunder Rumble at 7-2, while the third choice was Strike the Gold at 7-2. Assume you are making a $20 bet on one of these horses. The payoffs are your winnings. (If your horse does not win, you lose your entire bet. Of course, it is possible for none of your horses to win.) Suppose that just before the race, there has been frantic betting on Thunder Rumble, with the result that the odds have dropped to 1-5. The odds on the other two horses remain unchanged. Set up the payoff matrix with your bet as the row player and winner as the column player.
​
Let the first column correspond to Pleasant Tap, the second one to Thunder Rumble, the third one to Strike the Gold and the first row correspond to Pleasant Tap, the second one to Thunder Rumble, the third one to Strike the Gold .