Roll or Bank

Free

A game offers you two fair dice: an 88-sided die and a 1212-sided die. You must first roll the d8d8 and look at the result. Then you decide: bank that number as your payout, or discard it and roll the d12d12 once — in which case the d12d12 result is your payout, with no going back. Playing optimally, what is your decision rule, and what is the game's expected payout?

Answer