Imagine a game in which you have the integers from 1 to 12 written on slips of paper. You roll 2 dice and take their sum. You can then flip over any combination of pieces of paper with a sum equal to the sum of the dice. (For example, if you roll a 5 and a 2, you could flip over the 7; the 6 and 1; the 5 and 2; the 4 and 3; or the 4, 2, and 1.) Once a piece of paper is flipped over, you cannot use that number anymore. You win if you flip over all 12 pieces of paper.
What is the best strategy? (I believe you should always avoid flipping small numbers and try to flip the single number equal to the sum you rolled, if possible. I base this on the fact that if you roll a 12, you’d be foolish to flip anything other than the 12, and so on.)
Is there an easy way to calculate the probability of winning the game? (This seems to me to be a situation with way too many branches to really evaluate, but maybe there’s some trick to think about it from the right perspective.)
This isn’t a homework problem.