Hitting Time Calculator

About this calculator

In a one-dimensional random walk confined between two boundaries — 0 and N — the expected hitting time answers a classic probability question: starting from some position between the boundaries, how many steps, on average, does it take to first reach one of the boundaries? This is a version of the famous gambler's ruin problem, and the expected time depends on the starting position, the distance to each boundary, and the probability of stepping in each direction at every step.

This calculator takes the boundary values, a starting position, and the step probability, then computes the expected hitting time using the closed-form solution to the corresponding difference equation. Probability theory students working through Markov chain problem sets, and quantitative analysts modeling barrier-crossing scenarios in risk or options pricing use it to verify hand calculations or to explore how the expected time changes as the starting position or step bias shifts.