Estimating weights in a game of chance.

There is this game of chance (part of a video game and not gambling strictly speaking) that i think can be modeled with the classic colored balls in a bag model.

However each time a ball is picked all balls of the same color are also removed.

I'm trying to estimate how many balls of each color there are from a set of outcomes.

My data set will have many first picks and fewer of each subsequent pick because those "cost" more.

I would go ahead and estimate based on only the first picks but some of the colors are rare enough that it may be hard ro get a good picture from just the first pick data.

However after a few picks the rarer balls are much more likley to come up but at that point the picks are happening with varied contents of the bag and im only going to get a few data points of each possible scenario.

Is/Are there (a) formula(s) that i could use to relate the sub-sets that would let me better estimate the underlying weights?


Ambassador to the humans
Can you provide some example data? I think it would easier to help and think about what is going on if we can see what you're seeing.