I have built a game for my child's school festival, and I need to figure out the probability of winning. The game is a 3x3 grid in which a player tosses three balls to try to get 3 in-a-row, like tic-tac-toe, except without the 2nd player to confound the game. There is a fair amount of randomness, since wiffle balls bounce erratically unless they hit the hole dead center, but it isn't completely random. I suppose for simplicity, we can assume it is random.
Using three balls, there are 8 ways to win, but I'm not sure how many ways to lose. If I were to use 4 balls, odds of winning increase a lot, but again, I'm not sure by how much. 5 balls seem like a gimme.
Obviously, there is a happy medium- too many winners and the kids will bankrupt our prize bank, too few winners and people won't want to play.