Suppose we have two stacks of cards on a table. On each turn, each of two players draws a card from the top of one of the stacks. The game ends when there are no cards left in either stack. The person with the greatest sum then wins. If this were a chess problem, for example, one could attempt to solve this game by starting from a winning final position, and then inducting backwards. However, in this game, the final card picked up has little bearing, as it is the overall sum that results in a winner. Is it possible to find a game plan for perfect play, assuming both players pursue this game plan?