You'd probably need to provide some more information on the exact rules you play by. For example, if the rules are "Draw balls until someone wins" then each person has a roughly equal chance to win. If you are playing with N total people, that is 1/N. Play alone, and you're certain to win. Play with one other opponent and you will win 1/2 the time. And so on.

But your 20% win rate suggests that you're either playing with small crowds or by some other rules.