easy Probability

Ten Ten

A release-checked easy problem for training Games, Expected Value.

Question

Adam is rolling a fair 10-sided die. He gets to roll repeatedly and may decide when to stop at any time. If he obtains a value that is not $10$ on each roll, he adds the upface to his total monetary sum. If he rolls a 10, he loses all of his money. If Adam plays optimally, he should stop once he has at least $\$k$ total. Find $k$.

Practice focus

This Probability problem is tagged Games, Expected Value. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.