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A non-bankroll related risk of ruin question
First of all, this has nothing to do with the often-asked risk of ruin bankroll question.
A friend and I are talking about a game where two players take turn rolling a die. (The actual game is "Pass the Pig", but that's not important.) Each player can roll repeatedly, adding points each time. One event, however, causes the player to lose all of his points. Let's say that rolling a 6 will cause a player to lose his points. At any point, the player can stop and "stand pat" with his current total. The goal of the game is to be the first to 100 points or have the highest total after 10 rounds. So the question is, what is the best point to stop on a given round? A lot depends on the player and his lead/deficit in relation to his opponent. The other component is how much is he willing to risk. With the game I have described, (roll a die repeatedly, stopping at any point, and a 6 leaves the player with no points for that round) the EV of any roll is 2.5, with a standard deviation of sqrt(2)~1.414. I really don't know where to go from here, though I feel I'm making it more difficult than it needs to be. Any thoughts? |
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