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Pricing the higher of two dice

MediumExpected ValueMarket Making & Betting Games~3m

A game rolls two fair dice and pays you the larger of the two faces, in dollars (a roll of 3 and 5 pays $5). What is the fair price to play - the expected payout, in dollars to four places?

Show hints (2)+
  1. E[max⁡]=∑kP(max⁡≥k)E[\max]=\sum_k P(\max\ge k).
  2. P(max⁡≥k)=1−((k−1)/6)2P(\max\ge k)=1-((k-1)/6)^2.

Answer

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4.4722 (± 0.001)

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Asked at: Timed Mental-Math & Sequences, Options Market-Making

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