# Probability of coin flip betting

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 $6 after 10 flips. ## 1 Answer Let say you make$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\$.

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