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I guess there's a third outcome
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if you get into a cycle you could tie.
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So checkers fits all these descriptions and
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what this theorem tells us is that checkers has a solution.
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I'm not sure I know what that solution is,
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or I think actually somebody did compute it quite recently,
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even in the last few months,
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I just forgot to Google it this morning to remind myself.
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But what this theorem tells us even before
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those people that computed it: checkers has a solution.
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Let's be a bit more ambitious. What about chess?
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So chess meets this description.