Hi, i'm an online poker player and i need some help modeling a promotion that the site where i play offers. I think it's rigged and intend to prove it but i'm short on skillz. The promotion is described here and i already made a model but can't solve it. It goes like this: Supose you have 72 distinguishable urns. every one of them exactly alike except for 18 of them, which are smaller. let's call them "rare" urns. A gun randomly fires undistinguishable balls towards this urns, and each ball thrown goes always to one of the urns (no missed shots). The urns allow infinite balls to fall on them (they don't get full) Suppose the odds of throwing the ball to one of the 18 smaller urns is 1 in 350. Lets say urns 1 thru 18 are the "rare" ones. let r= 1/350 (r stands for "rare" urn) then the probabilty "p" of the gun throwing to a regular urn must be so that 18r + 54p = 1 solving for "p" it stands that the odds of getting the ball to a normal urn is roughly 1 in 56.9 Now suppose firing the gun costs 10 points. The question goes like this: How many points on average do you have to spend in order to achieve a 95% probability of getting at least 1 ball in every urn? Poker site claims that the last winner spent 54,000 points and manage to hit every urn. I call horse***. Of course, they don't give away the exact odds of hitting a "rare" urn and they might be different kinds of "rares", but from a very small sample in a poker forum, people seem to be hitting "rare" urns spending an average of 3500 points, hence i estimated the odds of getting a ball into one of this urns to be 1 in 350. plz help, thanks in advance!