Definitely yours and yours alone. You shouldn't be made to feel uncomfortable or obligated just because you won and he/she didn't.
If I went to the casino with my buddy and he drove me there and while we were walkign around suggested that I throw $10 on the roulette and I won, I might buy him a drink or dinner, but I sure wouldn't split the winnings with him. And I don't think that a good and conscientious friend would ask.
Sheesh.
peace,
~Ben~