In a dice game, if you roll 1-5, you get money for the number of points you've rolled, and if you roll 6, you lose all the money you've accumulated, so you can roll any number of dice, so how much is a risk-neutral investor willing to pay for this game?
2026-04-06 03:16:30.1775445390
Dice Problem, optimal stopping
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If we interpret te question literally, then a risk-neutral investor should be willing to pay any finite amount $M$ to play this game. Indeed, the investor can set a target of $M+1$, say, and keep playing until his fortune exceeds that target, then stop. With enough patience, this will definitely happen (with probability 1) although along the way, the fortune is likely to go down to zero several times. Indeed, each time the gambler starts at 0, there is a chance greater than $(5/6)^{M+1}$ of exceeding the target without rolling a 6.