Money Cards Puzzle

To solve this, I find it's easiest to consider all the "losing pairs":

1+8
2+7
3+6
4+5

In the best case scenario, you will start by picking one card from each losing pair. After that, you have no choice but to pick another card from one of the pairs. Then it's game over.

This means the maximum number of cards you can pick is 5 and the most you can win is $500.

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