A Two-Player Game

Let's play a game.  I'll be the computer, and you be the human, OK?  I'll hand you a slip of paper on which will be printed two numbers -- all numbers are nonnegative integers.  Then you can reduce one or both of the two numbers by any positive integer amount, but you can't make either number negative, and then you can hand me back the slip of paper.  We take turns reducing one or both of the numbers until one of us reduces both numbers to 0, winning the game.

What is a good strategy for winning the game?

Let's play while you think about your strategy.  I'm handing you this card:

The webmaster and author of the Math Help site is Graeme McRae.
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