Game theory: which two-player games solved analytically

[Gerenuk]

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)

 

[exk]

checkers?

 

[Gerenuk]

checkers?

You're right.

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