Bust Probability Calculator
Calculate your probability of going bust (ruin) based on bankroll, bet size, and game odds. Understand the math behind gambling risk before you play.
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How Bust Probability Works
The Gambler's Ruin Problem
The Gambler's Ruin is a classic problem in probability theory. It models a gambler who starts with a finite bankroll and repeatedly makes fixed-size bets on a game with known odds. The central question: what is the probability that the gambler eventually loses everything?
When the game has a negative expected value (as most casino games do), the probability of eventual ruin approaches 100% given enough bets. Even with a slight house edge, the longer you play, the more certain it becomes that you will go bust.
Risk of Ruin Formula
For a simple win/loss game with fixed bet size, the classic Risk of Ruin (RoR) formula is derived from the Gambler's Ruin theorem:
If p != q:
RoR = (q / p) ^ B
If p == q (fair game):
RoR = 1 (certain ruin)
Where:
p = win probability
q = 1 - p
B = bankroll / bet_size The Kelly Criterion
The Kelly Criterion is a formula for determining the optimal bet size to maximize the long-term growth rate of your bankroll:
Kelly % = edge / (multiplier - 1)
Where:
edge = p * (multiplier - 1) - (1 - p)
p = win probability
multiplier = payout multiplier Why Bankroll Management Matters
Even with a positive expected value, poor bankroll management can still lead to ruin. Overbetting relative to your bankroll dramatically increases the chance of hitting a losing streak that wipes you out before the edge has time to materialize.
Discipline in bet sizing is the single most important factor in long-term survival. A player risking 1% per bet with a 2% edge has near-zero probability of ruin. The same player risking 20% per bet has significant bust risk.
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