Dice Game

You are offered to play a dice game. You start with a balance of zero dollars, and you can roll a fair six-sided die as many times as you like until a 6 appears. On each roll:

• If you roll 1–5, you add that many dollars to your balance.
• If you roll a 6, your entire balance becomes 0 and the game ends. After each roll, you can decide whether to stop and keep your balance, or continue rolling. You must pay an entry fee to play. What is the maximum fee you’d be willing to pay if you are risk-neutral and play optimally?

Answer format: round to 2 decimal places.