48.A Die With Two Optional Rerolls
★★★optimal stoppingBlackRock
You roll a fair six-sided die up to three times. After the first and second rolls you may either keep the value shown and stop, or discard it and roll again; after the third roll you must keep whatever it shows. Playing optimally, what is the expected payout?
Sign in to submit an answer and track it toward your stats.
Sign inHint
Work backwards. Solve the one-roll-left case, use that as the threshold for two rolls left, and repeat.
Want timed drills, mental math, and a market-making game too? Try the full practice suite →