You would want to go first. You can lay down a pattern of cups that always leaves room for one more in the center. Doing so will allow your opponent to put a cup in that space, but since you will have placed two for their one, they will be left with the difficult choice, and you win!
Did that make any sense, or am I completely off?
I don't think you are completely off, but the valid solution would need to very clearly explain exactly what you'd play on each turn and why it is guaranteed to win. So I'd say that answer is incomplete :)
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