Game theory: which two-player games solved analytically

Gerenuk
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I was wondering for which two-player/two-option games (symmetric, ...?) definite solutions for the best strategy can be found? (like a single equation for which probability for the choices to use)
 
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checkers?
 
exk said:
checkers?
You're right.

Sorry, I forgot to mention that I want to consider abstract two option games with a 2x2 payoff matrix.
 

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