So I learned something from the binomial stock price model.
Namely, my Tim's calculation is ok, but has nothing to do with Poisson. In fact, the binomial distribution is only ok because I am using a probability of success given by the uber-wise marketing folk that is supposedly constant for the duration of the game.
Well no, I am not ripping off the tabs and mailing them back to head office for re-use into those ubiquitous red-and-yellow cups. But while the pool is not limitless, the apparent success rate is.
Quite the assumption, I agree...