How about each ticket has an equal winning chance? So that if a player wants to increase his/her chances of winning, he/she will buy more tickets. It is going to be his/her option based on how much he/she really needs to win or how much he/she is willing to shell out for the game. As to the odds, isn't it just a jackpot, 1st prize, and so on?
...the winner will be decided by the players itself.
What exactly do you mean by this? How would you do this?