Who Wins?
Chomp belongs to the category of impartial two-player perfect information games.
It turns out that for any rectangular starting position bigger than 1×1 the first player can win. This can be shown using a strategy-stealing argument: assume that the second player has a winning strategy against any initial first-player move. Suppose then, that the first player takes only the bottom right hand square. By our assumption, the second player has a response to this which will force victory. But if such a winning response exists, the first player could have played it as his first move and thus forced victory. The second player therefore cannot have a winning strategy.
Computers can easily calculate winning moves for this game on two-dimensional boards of reasonable size.
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