A mathematician might say that an average exists for the amount you can win for n games for the second game, but it doesn't converge to a limit as n goes to infinity.
> it doesn't converge to a limit as n goes to infinity.
Yes, I think this is more precise way to describe what is happening. I should update the article. But, average that doesn't converge is not a really average in normal sense, so the statement of "average doesn't exist" is not totally wrong?
