When studying the Gambler’s Ruin problem, we often encounter the recurrence relation where: A natural question is: How do we solve this recurrence? A Common First Attempt Many students initially try a solution of the form because powers of are familiar from algebra and calculus. Substituting this into the recurrence gives Unfortunately, this expression is … Continue reading Understanding Why We Assume P_i = r^i When Solving the Gambler’s Ruin Recurrence