If you assume numbers are picked uniformly, and you know the distribution of the numbers people pick, you can just apply the double expectation theorem to find

If you assume numbers are picked uniformly, and you know the distribution of the numbers people pick, you can just apply the double expectation theorem to find the expected value of a random ticket. Without the latter distribution, it's hard to answer the second question, but I'm going to hazard a guess that the optimal strategy is to put the money in the bank instead ;)