What does the law of large numbers tell us about what will, Ask an Expert

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A roulette wheel has 38 slots, of which 18 are black, 18 are red, and 2 are green. When the wheel is spun, the ball is equally likely to come to rest in any of the slots. One of the simplest wagers chooses red or black. A bet of $1 on red returns $2 if the ball lands in a red slot. Otherwise, the player loses his dollar. When gamblers bet on red or black, the two green slots belong to the house. Because the probability of winning $2 is 18/38, the mean payoff from a $1 bet is twice 18/38, or 94.7 cents.

What does the law of large numbers tell us about what will happen if a gambler makes very many bets on red?

A. If the gambler keeps on playing forever he must win.

B. In the long run, the gambler earns an average of 94.7 cents per bet.

C. The player should change his bet to black if he wishes to win in the long run.

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