Gambler ruin probability calculator
What is the chance of ruin starting 3 units from zero with a target of 10 units in a fair game?
With equal odds of winning or losing one unit per step, the probability of reaching zero before ten is 1 - 3/10 = 0.7. A small edge changes this through powers of the ratio of loss to win probabilities.
The model assumes unit-size wins and losses with constant odds and no time limit, which a trading account rarely satisfies.
Calculate exact eventual ruin probability in a finite fair-or-biased unit-step random walk. Two absorbing boundaries terminate the unit-step walk.
The fair three-to-ten walk
At p = 0.5, starting three units from ruin with an upper boundary at ten units, eventual ruin probability is exactly 1−3/10 = 0.7.
This classic first-passage result offers a transparent reference model for two absorbing barriers. Capital is an integer number of units. A winning step adds one, a losing step subtracts one, and the walk stops upon reaching either zero or the selected upper level. The fair case has a simple linear answer. With a biased step, the ratio of loss to win probabilities enters through powers; the implementation uses equivalent rearrangements to limit overflow when the bias is strong. At win probability zero the lower barrier is certain, and at one the upper barrier is certain. These boundary results are useful tests, but neither resembles a real strategy with varied trade sizes. The horizon is eventual absorption, so it can be much longer than a particular account evaluation. The challenge simulator includes daily limits and asymmetric payoffs; its process must be specified before comparing outputs.
Absorbing boundaries
Each step changes capital by exactly one unit. Win probability is constant, steps are independent, and the game stops at either zero or the upper boundary.
P(ruin) = (r^i−r^N)/(1−r^N), r=(1−p)/p; for p=0.5, P=1−i/NAn upper boundary turns the question into which barrier arrives first. The result is not the chance of ruin over a chosen number of trades, and changing the upper boundary changes the event.
Where this model stops
A trading account rarely has constant one-unit wins and losses. There is no time horizon, transaction cost, position sizing, gap risk or changing edge here. A probability of zero or one is handled as a deterministic walk.
Grinstead and Snell
Grinstead, C. M. and Snell, J. L. (1997), Introduction to Probability, second revised edition, American Mathematical Society, chapter 12, section 12.2 Gambler's Ruin. The result here has a finite upper barrier and unit-size steps. Original or institutional source.
Risk of ruin · All tools
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Stochastly (2026). Gambler ruin probability calculator [web calculator]. https://stochastly.com/tools/gambler-ruin-probability-calculatorThe method behind the gambler ruin probability calculator comes from the paper below: cite that paper for the method, and the reference above for the gambler ruin probability calculator itself.
Grinstead, C. M. and Snell, J. L. (1997). Introduction to Probability, 2nd edition, chapter 12. American Mathematical Society.