I'm playing Farkle a lot on Facebook. It's a mindless but somehow interesting game. The idea is that you throw 6 dice. If any of those dice make one of the scoring combinations, you can pick them up and roll the remaining dice again, hoping to score some more. If you run out of dice, you get to continue with 6 more. If you reach at least 300 points, you can "bank" the points you've made this turn and start with 6 fresh dice.
The trick is that if, at any time, you roll no scoring combination, you "Farkle". You lose all the points you made this turn. Farkle three times in a row, and you lose 500 points, to boot.
Being the mathematically inclined person I am, I've been trying to find the most advantageous method of picking up the dice.
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