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Imagine a situation where you and a friend both have 5 dollars, and you play him in a 50/50 coin flip "duel" where if it flips heads you receive a dollar from them otherwise you lose a dollar to the other person. You stop playing when you lose all your money.

What's the probability of having any arbitrary amount above or equal to zero after n flips? As an example, how likely is it that I'd have $6 after 10 flips.

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Let say you make $n$ flips and desire amount $x$ at the end. In the $n$ flips, consider $k$ times you loose one dollar and $n-k$ times you win a dollar.

Therefore, $5 + n - 2k = x \implies k = \lceil{(5+n-x)/2}\rceil$.

This reduces to finding the probability of k "tails" which can be modelled by binomial distribution. ${n \choose k} 0.5^n$.

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  • $\begingroup$ @JacobTorba could you give a feedback on my solution? $\endgroup$ – Pratik Soni Nov 11 '14 at 2:55

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