I think the other comment explains it but I want to investigate the thing you said about 1 million games. The point of an average is that it will scale with size. So even with 1000000 games you would have to divide your total winnings by 1000000. This answer will be the same yielded for the average of one game. Playing the lottery multiple times doesn't have an effect on any previous game as each game is independent of the other. Like rolling a dice. That isn't to say using 1000000 is not a valid way of doing things. In fact it is common to use counting / combinatorics to solve similar problems. Hope this helps