Your question is Optimal Strategy With Limited Rolls. Take a moment with it on the right.
Talk me through your thinking if you like. When you're confident, submit your answer and I'll grade it like a real screen (7/10 or better passes).
You are offered a game where you roll a fair six-sided die. You can either take the dollar amount of the roll, or pay $1 to roll again, up to a maximum of three rolls total. What is your optimal strategy, and what is the expected value of this game?
Assume the $1 reroll fee is deducted from the final payout and that you may choose separately after each roll. Show your reasoning using backward induction, including the decision rule at each roll and the resulting expected net payout.
