I wasn't sure what you meant by what you said regarding users picking outcomes - if it was something on the order of a lottery, that would probably be covered under betting laws. If it's something like a trivia quiz and whoever gets the most right answers wins, that would probably be covered under contest law, which is just as complex.
In the US at least, every state determines what is and isn't a contest and what rules apply, though most of them apply to any game where the reward is money or some sort of tangible item (even if players don't have to pay anything to play). That's why if you look closely, some of the fast food contests (like McDonalds Monopoly) say something in the fine print like "Not valid in New York or Rhode Island" or something to that effect. They've determined that their game won't meet the contest laws in those states so they simply say if you live there, you can't play.
If you are hosting your site in the US, this might fall under gambling statutes. Your options are probably: a) this is illegal just like other online casinos, or b) this isn't illegal but you may fall under contest regulations which are different from state to state. If you are hosting outside the US, you might fall under whatever gambling or contest statutes apply in that country.
In the US at least, every state determines what is and isn't a contest and what rules apply, though most of them apply to any game where the reward is money or some sort of tangible item (even if players don't have to pay anything to play). That's why if you look closely, some of the fast food contests (like McDonalds Monopoly) say something in the fine print like "Not valid in New York or Rhode Island" or something to that effect. They've determined that their game won't meet the contest laws in those states so they simply say if you live there, you can't play.