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  • 1 Post By HallsofIvy

Math Help - I need to know how to get this %

  1. #1
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    Dec 2012
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    lebanon
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    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.
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  2. #2
    MHF Contributor

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    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 \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 \sum_{m=0}^\infty \begin{pmatrix} 2m \\ m- 5\end{pmatrix}(.65)^{m- 5}(.35)^{m+5}.
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  3. #3
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    Dec 2012
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    lebanon
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    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%
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  4. #4
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    Dec 2012
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    lebanon
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    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
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