Nneetquant
Get started

Fair price for the higher of two dice

EasyExpected ValueMarket Making & Betting Games~3m

A game rolls two fair dice and pays you, in dollars, the larger of the two values (a tie pays that common value). What is the fair value of the game (in dollars, to four places)?

Show hints (2)+
  1. Build the pmf of the max from P(max⁡≤k)=(k/6)2P(\max\le k)=(k/6)^2, giving P(max⁡=k)=(2k−1)/36P(\max=k)=(2k-1)/36.
  2. Then E[max⁡]=∑kk(2k−1)/36=161/36E[\max]=\sum_k k(2k-1)/36 = 161/36.

Answer

Reveal answer →

4.4722 (± 0.001)

Want the full step-by-step worked solution? It's part of Premium - along with a worked solution for every question in the bank.

Practise freeUnlock solutions

Asked at: Game-Based Aptitude, ETF Market-Making

Related questions