The only way he can win is if things get complicated like mutual attacks on the castled position or an otherwise wild position. He will try hard to unbalance the position and avoid trades giving you maximum chance to make an error. That and/or he'll go for an all out attack on your king. These are the ways for him to win.
The strategy for you is opposite. Keep the position as calm and solid as possible (passive is never good, in any type of game, you aim for active but solid) you will seek to exchange pieces whenever possible (so if you can pin his knights with your bishops and exchange them early then great).
Try to keep the lines around your king closed and watch for sacrifices. If he attacks your king sacrificing to displace a few pawns (open lines) is almost forced for him, so just be aware of that possibility so it doesn't catch you off guard.
like the subject says im playing somebody who is better and i got him to agree to him starting with no bishops for 50 bucks, he is white. any ideas on how i should play. im thinking he is starting with the kings pawn. should i get on the attack since im up 6 points from the start, should i try to trade peices, just put up a good defense. any suggestions would be loved.