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Interview prep / Probability

Paying 1.50 dollars to spin a five-slot wheel

Question

A wheel is split into five equal sectors. Four sectors pay $1 and the fifth pays $5. Each spin costs $1.50. Would you play this game many times? Would you play it just once?

Short answer

Yes to both, if you are close to risk-neutral. The expected payout is 4⋅1+55=$1.80\tfrac{4\cdot1+5}{5}=\text{\char36}1.80, a profit of $0.30 per spin, so repeated play wins on average and the law of large numbers makes that profit reliable. A single spin has the same positive expectation but you lose $0.50 with probability 80%80\%; with such small stakes it is still worth taking.

Adapted from Crack, Heard on the Street, Q4.18, p.41; question and answer rewritten by SelfMadeQuant.com.

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