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A release-checked easy problem for training Expected Value/LOTUS, Dice.

Question

You repeatedly roll two fair 6-sided dice. If both dice show values larger than $1$, add them to your running cumulative sum; otherwise, the game ends and you receive no payout. You can decide to stop rolling at any time. Under the optimal strategy, what is the minimum number of points at which you want to stop?

Practice focus

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