Everyone is calculating the expected winnings of powerball incorrectly because no one includes that you'll probably have to share the prize since people pick the roughly the same numbers (birthdays, odd, prime numbers) making a collision likely.<p>So:<p>- what is the expected value of a random ticket, given that certain combinations are likely to be shared?<p>- Given deep pockets, what are the numbers to play and when is the time to play them?
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.<p>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 ;)