Calculate risk of ruin from win probability, total bankroll, and bet size to estimate the chance of losing your bankroll over repeated even-money bets.

Risk Of Ruin Calculator

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Risk Of Ruin Formula

The following equation is used to calculate the Risk Of Ruin.

ROR = (q/p)^{(B/S)}
  • Where ROR is the risk of ruin (probability ranging from 0 to 1)
  • p is the probability of a win (0 to 1)
  • q is the probability of a loss (0 to 1, where q = 1 – p)
  • B is the total bankroll or available capital ($)
  • S is the bet size or position size ($)

Important: This formula is the classic “even-money, fixed-bet” risk-of-ruin result (each bet changes the bankroll by exactly +S on a win and −S on a loss, with independent bets and constant win probability). It applies when p > 0.5. If p ≤ 0.5, the probability of eventual ruin under this model is 1 (100%). If your average win size differs from your average loss size, a different risk-of-ruin model is needed.

To calculate the risk of ruin (for p > 0.5 in this model), raise the ratio of loss probability to win probability to the power of the bankroll size divided by the bet size.

What is a Risk Of Ruin?

Definition:

Risk of ruin typically refers to the probability that a gambler, trader, or investor will lose all of their capital, reaching a point where they can no longer continue due to losses.

How to Calculate Risk Of Ruin?

Example Problem:

The following example outlines the steps and information needed to calculate the Risk Of Ruin.

First, determine the probability of winning (p). In this example, p = 0.55, so the probability of losing (q) = 0.45.

Next, determine the bankroll (B) and bet size (S). Assume the bankroll (B) is $10,000, and the bet (S) is $100.

Finally, calculate the risk of ruin using the formula above (note: this model assumes fixed, even-money bets and p > 0.5):

ROR = (q/p)^(B/S)

ROR = (0.45 / 0.55)^(10000 / 100)

ROR = (0.8181818)^(100)

ROR ≈ 1.93 × 10−9 (about 0.000000193%)

FAQ

How does bet size affect risk of ruin?

Larger bet sizes relative to your total bankroll typically increase the risk of ruin because you deplete available funds faster with each loss. Conversely, smaller bet sizes help preserve your bankroll and reduce the risk of ruin.

Can increasing the probability of winning reduce the risk of ruin?

Yes, improving win probability (p) generally lowers the risk of ruin, assuming bet size and bankroll remain constant (and under models where p represents a stable edge). A higher p indicates a more favorable trading or gambling edge which decreases the chance of depleting funds entirely.

How can I lower my risk of ruin?

You can lower your risk of ruin by reducing your bet size, increasing your bankroll, improving your probability of winning through better strategies or analysis, and diversifying your trades or bets to spread out risk.