Interesting game Anders.
I would think it would depend on the sophistication of the game players.* The more sophisticated, the lower your guess, with a limit of the lowest possible number if you're playing against computers or game theoreticians (i.e., 1). The less sophisticated your opponents, the higher your guess, with a limit of 33 if you're playing against total dummies who generate random number guesses.
Playing against an average group of people, I'd assume the best guess would be in between those numbers somewhere, but I don't think there is any mathematical method of knowing where to guess in between 1 and 33. You'd need empirical data on what average people typically do in this situation.
Without any other data I'd just guess right in between 1 and 33 and say 17.
* It just occurred to me that it's not so much the sophistication of the players, but also their beliefs
about the sophistication of their opponents. If you're playing with a large group of game theoreticians, and they all know they're playing with other game theoreticians, 1 is obviously the dominating response. But if you're playing with a group of game theoreticians who believe they're playing against a group of random-number generating chimpanzees, they'd all guess 33. Then you could come in and guess 33*.67=22, and take all the money.