Why an unfavorable edge empties the bankroll first
The gambler ruin problem describes betting the same amount each round until the bankroll reaches a goal or falls to zero. Enter the starting bankroll i, the goal N, and the win rate p per round, and this calculator returns the chance of reaching the goal and the chance of going broke. At exactly 50% the chance of reaching the goal is i / N; otherwise it uses r = (1 − p) / p in (1 − r^i) / (1 − r^N).
The model assumes a flat 1-unit bet, independent rounds, and that play never stops early. One point of disadvantage is enough: at a 49% win rate, moving from 10 units to a 100-unit goal succeeds 0.9173% of the time and ends in ruin 99.0827% of the time, against 10% in a fair game. The expected loss compounds over rounds, so ruin becomes all but certain.
This is study material for a probability model. It does not cover variable bet sizes or games with several prize tiers and payout odds, and no ordering of bets converts an expected loss into a profit. Written as of October 2026.
Frequently asked questions
No. The chance of reaching it is the bankroll share i / N, and the rest of the probability ends in ruin.
Yes. At a 49% win rate, going from 10 units to 100 units succeeds only 0.9173% of the time.
This calculator only covers a flat 1-unit bet. No betting pattern turns a negative expected value into a positive one.