Alice and Bob play a game with the following rules:
Question: Which player has a winning strategy?
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This is basically a spin on the classic "sum to 15" problem, except it's with exponents and products.
Notice that 3 2 7 6 8 = 2 1 5 and that the cards have numbers of the form 2 k , where 1 ≤ k ≤ 9 . When we multiply the values in any two of the cards, we are adding their exponents together.
Thus, Alice and Bob are trying to pick up cards such that the sum of their exponents equals 15. This can be shown to correspond to a game of Tic-Tac-Toe, with a grid of numbers from 1 to 9 such that the sum of each row, column, and long diagonal is equal to 15. Since Tic-Tac-Toe, when played optimally, is a draw, we conclude that neither Alice nor Bob has a winning strategy.