I was answering a question on Reddit and could only answer by simulation via code rather than figure out the math.
https://www.reddit.com/r/gambling/comments/15jualm/gambling_math_question/
If you are playing a martingale strategy where you double when you lose, but if you lose the doubled bet, you go back down to your original bet, what's your expected value over 10 rounds if you have a 70% chance of winning any given bet?
I know the answer is 4, but I couldn't figure out how to get their statistically without enumerating every outcome.