Roll three times, keep the best, price it
Asked at Jane Street, DRW
You roll a fair six-sided die three times and get paid the highest face among the three rolls, in dollars. Unlike the keep-the-last game, a good early roll is never thrown away: you always end up with the maximum.
What is the fair value of this game?
Show a hint
Since you keep the best, there is no stopping decision at all, just roll all three. You need of three independent dice. It is easiest to compute via .