I am trying to figure out how to get the highest score in a dice rolling game. Every roll adds to your score. The player has has 3 dice. Rolling a one on any of the dice resets the score to zero and ends the game. They can be rolled in any order. They are rolled in groups/turns meaning that once all three are rolled, then they can be re-rolled, (this will be relevant later). This can be repeated any number of times and the player can end the game at any time. For example, if there are three dice, dice a, dice b and dice c, here are some examples of valid rolls:
$abc$ (can be rolled in order)
$acb$ (out of order)
$cab, cba$ (can be rolled multiple times)
$bca,b$ (you can stop at any number of rolls)
But $abb,c$ is not possible because every dice can only be rolled once in a turn.
With that established, you use one regular six-sided dice which is mandatory, but the other two dice are special and are picked from three options:
- a dice that rolls 2-6
- a dice that rolls 1-6 but doubles the value of the roll (rolling a one still resets the score)
- a dice that rolls 1-3 and multiplies the score of that turn by that amount (rolling a one in this case does not reset the score)
So my question is which combination of dice and how many rolls would result in the highest average score?