Not So Useless Utilities

I was perusing through some of the less used programs in my Start Menu, and I came across the “Accessibility” folder under “Accessories”. Now, for most people out there, the programs in this folder will never see the light of day. But there is one program which can actually prove quite useful: the On-Screen Keyboard.
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Game Theory Proof

I read an interesting theorem the other day which states that every two-person, finite, zero-sum game of perfect information is strictly determined. In other words, one of the players has a winning strategy: a strategy that guarantees a win no matter what the opponent does. Note that this does not apply to games that can end in a draw, such as chess. We will only be concerned with games that end with a win for one player and a loss for the opponent. The proof goes something like this:
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