You might like Arimaa. It's playable on a chessboard and has no draws. I find it more fun than chess, mostly because at my low level of chess play, the game is mostly decided by blunders. In Arimaa, it's harder to evaluate who's winning, and it's harder to make big gains or losses in a single turn. It feels like you need more long term planning to win, which makes winning more satisfying IMO.