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In this game you roll six dice. After each roll you must take at least one die but you can take more than one as well. After you take a die you have the ability to roll again. In order to score you must have the qualifying die rolls of (4) and (1). The four other spots compromise your scoring dice. Ties are effectively losses and the highest score wins.

In this scenario you have the ability to roll, which means that you can take any number of dice before rolling again. Do you take the (5) before rolling again? Math would be awesome.

I have a vague goal of finding a "perfect" strategy for this kind of game, is this possible?