beat and win

You can win (in) a game, a race, a battle, an argument, etc, and you can win a prize, money, etc. You can beat a person that you are playing/arguing/fighting, etc against. Compare:

• My girlfriend usually wins when we play poker.
• My girlfriend beat me at poker the first time we played. (not My girlfriend won me at poker …)

Both verbs are irregular:

• beat – beat – beaten
• win – won – won