No, you can receive more than you give away as well. So it's not binomial in two ways. :-) It's really cool though to have a skewed distribution at each time s

No, you can receive more than you give away as well. So it's not binomial in two ways. :-) It's really cool though to have a skewed distribution at each time step and a uniform distribution over the entire time series. It's not exactly the same as just being ergodic. The probability that the distribution is uniform at a particular time step is very small.