Two dice, one re-roll of both, price the sum
Asked at Optiver, SIG
You roll two fair six-sided dice and get paid their sum in dollars. After seeing the sum you may re-roll both dice once and must keep that second sum. A re-roll discards the first sum entirely.
Find the optimal strategy and the fair value of the game.
Show a hint
The continuation value (re-rolling) is just the expected sum of two dice. Keep your first sum only when it beats that. You will need .