We can win (in) a game, a race, a battle, an argument etc, and We can win a prize, money etc.

But

We can beat a person that we are playing/arguing/fighting etc against.
üMy girlfriend usually wins when we play poker.
üMy girlfriend beat me at poker the first time we played.

(NOT My girlfriend win me at poker...)


Both verbs are irregular:

beat-beat-beaten

win-won-won
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