... indeed, with an house edge of 1% and betting 2x, you have 19.33% of chances to encounter an 8 losing streak in your first 100 bets. 1/5, not so hard...
The math behind this is really hard, I struggled a bit to find it out and I definitely can't understand it, but for people who can here's the link:
http://www.askamathematician.com/2010/07/q-whats-the-chance-of-getting-a-run-of-k-successes-in-n-bernoulli-trials-why-use-approximations-when-the-exact-answer-is-known/
And, for lazy people like me, here you can find a calculator:
http://maxgriffin.net/CalcStreaks.shtml
I'm just sharing, because I was asking thiis question myself for a time, and now I found the answer
The math behind this is really hard, I struggled a bit to find it out and I definitely can't understand it, but for people who can here's the link:
http://www.askamathematician.com/2010/07/q-whats-the-chance-of-getting-a-run-of-k-successes-in-n-bernoulli-trials-why-use-approximations-when-the-exact-answer-is-known/
And, for lazy people like me, here you can find a calculator:
http://maxgriffin.net/CalcStreaks.shtml
I'm just sharing, because I was asking thiis question myself for a time, and now I found the answer
The number 19.33% you get is close enough, but it is not correct. With a house edge of 1%, you actually have 50.5% chance to lose a 2x bet, and hence the actual chance for you to get 8 losses in a row in 100 bets is 18.15141%. It seems you have used 51% in your calculation which would implies a 2% house edge instead of 1%.
