🛟 Bankroll Calculator — Gambler's Ruin, Solved

What the Gambler's-Ruin Formula Actually Says

Enter your bankroll, bet size and target, and the gambler's-ruin formula tells you the true probability of getting there before the edge gets you.

The setup is the oldest problem in probability: you have a bankroll, you make even-money bets of a fixed size, and you stop either at a target or at zero. We model your bet as an even-money wager where the house edge shaves the win probability to p = (1 − edge) / 2 — at a 1% edge, you win 49.5% of bets instead of 50%. Measured in betting units of k = bankroll ÷ bet size and N = target ÷ bet size, the probability of reaching the target before ruin is:

P = (1 − (q/p)k) / (1 − (q/p)N), where q = 1 − p

In plain language: in a perfectly fair game, your chance of doubling $100 with $2 bets before busting would be exactly 50% — bankroll divided by target, no matter the bet size. The house edge breaks that symmetry, and it breaks it harder the more bets you make. Because q/p is slightly above 1, every extra unit between you and the target multiplies your disadvantage. That produces the single most useful, least intuitive fact in gambling: small bets are more dangerous than big ones when you are chasing a target. Trying to double $100 in one $100 flip succeeds 49.5% of the time. Trying to do it with $2 bets — fifty units of grinding — succeeds only about 27% of the time, because you hand the edge fifty times more turnover to work on. Slow and careful feels safe; mathematically it is the expensive route.

The expected-bets line comes from the companion formula E = (k − N·P) / (q − p) and is usually a surprise in the other direction: sessions last longer than intuition says, which is exactly how the edge earns. The calculator converts it to a session length at a typical ten bets per minute so you can see the grind in hours as well as wagers.

How to use this honestly: the calculator is descriptive, not a strategy engine. No bet sizing changes the sign of the expected value — bigger bets raise your chance of hitting the target and your variance, while the average outcome stays −edge × turnover regardless. What the formula genuinely teaches is to pick modest targets (doubling is far harder than a 20% win), to stop at them, and to treat the ruin column as the real price of the attempt. Try the same numbers on our free dice simulator and watch the formula come true at fake-money prices. If the ruin probability on your own numbers is uncomfortable, believe it — and see our responsible gambling page before testing it with rent money.