calculate expected payoff when risk is involved

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Suppose you have quite a standard question about throwing a die up to three times

You have the option to throw a die up to three times. You will earn the face value of the die. You have the option to stop after each throw and walk away with the money earned. The earnings are not additive. What is the expected payoff of this game?

How to calculate expected payoff if some level of risk is involved?
 
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