World Series Gamble
The winner of the World Series is the first team to win four games, so the maximum number of games that could be played is 7. You want to place a $100 bet (even money) on your team to win the whole series. A bookie says he will not take bets on the whole series, but would be willing to let you bet on each individual game. Is there a betting strategy you could put in place to replicate your $100 bet?
HintThink back from game 7
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Answer
On games 1 and 2, bet $31.25. On game 3, bet $25.00 if your team is 20 or 02, and $37.50 if the record is 11. On game 4, bet $12.50 if the record is 30 or 03, and bet $37.50 if the record is 21 or 12. For game 5 (if you get to it), bet $25 if the record is 31 or 13, or $50 if the record is 22. If there is a game 6, bet $50 on it. If you get to a game 7 (so the record is 33), bet $100.
Here is why this works. At game 7, you need to have had $0 profit or loss from the previous games, so you want to bet $100 to replicate your winnertake all bet. Taking a step back, this means that if your team was 32, you would have had to lose enough money to get to $0 profit, and win $100 if they won, so your bet would have had to be $50. (Same on the losing side, so you would lose $100 if your team lost and they were 23 coming in to the game, or gotten back to $0 if they won to get to 33.) The reverse induction works all the way back to the initial bet of $31.25.
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