> 
> Ram and Shyam have agreed to bet one dollar on each flip of a fair coin and to continue
>  playing until one of the them wins all of other’s money. Use a recurrence relation to find
>  the probability that Ram will win all of Shyam’s money if Ram starts with $a$ dollars and
>  Shyam starts with $b$ dollars.
> 
> 
> 

My attempt:
Probability of Ram winning at $b$-th try = $\frac{1}{2} \times \frac{1}{2} \times \dots
 = (\frac{1}{2})^b$

Probability of Ram winning at $(b + 1)$-th try = $(\frac{1}{2})^{b+1}$

.
.
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Summing up all probabilities till infinite tries, I get probability to be $\frac{\frac{1}{2}^b}{1-\frac{1}{2}}$ = $\frac{1}{2}^{b-1}$

Now I am pretty sure, my approach is incorrect. Can someone tell me how to solve this?