I need to know how to get this %

Hello,

i have a problem calculating this:

I have a bankroll of : 100 $

i have 65% chance to win 10$

i have 35% chance to lose 10$

and i have unlimited tries.

what is the % of my bankroll to become 0

example: first hit 65% for my bankroll to become 110$ and 35% chance for my bankroll to become 90$

thanks.

Re: I need to know how to get this %

If you win i times then you must lose i+ 10 times, out of a total of n= 2i+ 10 times or i=(n-10)/2. It looks like it is a binomial distribution with p= .65, q= .35. That is, the probability of losing all your money in n turns is $\displaystyle \begin{pmatrix}n \\ (n-10)/2\end{pmatrix}(.65)^{(n-10)/2}(.35)^{(n+10)/2}$. For that to be possible n must be even, say n= 2m, so the probability of eventually losing all your money is $\displaystyle \sum_{m=0}^\infty \begin{pmatrix} 2m \\ m- 5\end{pmatrix}(.65)^{m- 5}(.35)^{m+5}$.

Re: I need to know how to get this %

can you calculate this for me, for only 100 runs and 1000 runs

cause it's not working with me

i m trying to calculate how much bankroll i need to move to bigger stakes. with a risk of 0.1%

Re: I need to know how to get this %

it's always so close to zero, i think i m doing it right.

thanks alot hallofivy