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 odds from a race. The favorite at 6-2 was Pleasant Tap (P). The second choice was Thunder Rumble (T at 7-2, while the third choice was Strike the Gold (S) at 4-1. Suppose that just before the race, there has been frantic betting on Thunder Rumble, with the result that the odds have dropped to 4-5 for that horse. The odds on the other two horses remain unchanged. Assume you are making a $30 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 (N) of your horses to win.) Winner P N P You Bet T

Elementary Linear Algebra (MindTap Course List)
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Author:Ron Larson
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Chapter2: Matrices
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Betting Set up the payoff matrix.
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 odds from a race. The favorite at 6-2 was Pleasant Tap (P). The second choice was Thunder Rumble (T)
at 7-2, while the third choice was Strike the Gold (S) at 4-1. Suppose that just before the race, there has been frantic
betting on Thunder Rumble, with the result that the odds have dropped to 4-5 for that horse. The odds on the other two
horses remain unchanged. Assume you are making a $30 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 (N) of your horses to win.)
Winner
P
T
N
P
You Bet T
Transcribed Image Text:Betting Set up the payoff matrix. 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 odds from a race. The favorite at 6-2 was Pleasant Tap (P). The second choice was Thunder Rumble (T) at 7-2, while the third choice was Strike the Gold (S) at 4-1. Suppose that just before the race, there has been frantic betting on Thunder Rumble, with the result that the odds have dropped to 4-5 for that horse. The odds on the other two horses remain unchanged. Assume you are making a $30 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 (N) of your horses to win.) Winner P T N P You Bet T
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