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Mathematics
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A field bet in craps occurs when a player places a bet on a single roll of the dice. The following can occur in a field bet: You win your bet if you roll a 3, 4, 9, 10, or 11. You win twice your bet if you roll a 2. You win three times your bet if you roll a 12. You lose your bet if you roll a 5, 6, 7, or 8. (Remember, for each roll you're rolling two dice, so "rolling a 7" means any combination of dice that adds to 7.) You make 100 consecutive field bets, and put two chips down for each bet. Your expected winnings by the end of these 100 bets is:
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