How do you get "the total amount of bet result/number of bets = $100"? If your first bet wins, your next bet is $105, so the total amount of bet result/number of bets after two bets is $102.5, isn't it? Similarly, if your first bet loses, your second bet is $95, so the average is $97.5.
Charliepatrick explained it very well.
The EV is still zero. What you've stumbled on is the difference between the arithmetic and geometric mean. The linear growth is zero while the exponential growth rate is negative, and the latter is more relevant here because you're wagering percentages rather than fixed dollar amounts. This is where the Kelly Criterion comes in handy. It maximizes the exponential growth, in turn maximizing the median outcome. In this case, it would tell you not to play at all.Quote: ReyGarcia
it seems to imply "betting systems work", that I can steer a 0% EV game to become a negative EV game by varying the bet amount, which I don't understand.
If you're not familiar with the Kelly Criterion, here's a great paper on it - http://www.eecs.harvard.edu/cs286r/courses/fall12/papers/Thorpe_KellyCriterion2007.pdf