A roulette wheel has 38 slots, of which 18 are black, 18 are red,and 2 are green

Question

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 likelyto come to rest in any of the slots. One of the simplest wagerschooses red or black. A bet of $1 on red returns $2 if the balllands in a red slot. Otherwise, the player loses his dollar. Whengamblers bet on red or black, the 2 green slots belong to thehouse. B/c the probability of winning $2 is 18/38, the mean payofffrom a $1 bet is twice 18/38, or 94.7 cents. Explain what the lawof large #s tells us about what will happen if a gambler makes verymany bets on red.

Explanation / Answer

The law of large numbers gives that as the gambler makes many bets,they will have an average payoff of .947. Thus, if the gambler makes n bets of $1, as n grows large, theywill have only $.947*n out of the original $n. Moregenerally, as the gambler makes a large number of bets on red, theywill lose money.

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