Risk of Ruin

Context: Term article: Risk of Ruin

Overview

Risk of Ruin (RoR) is a core concept in poker bankroll management, measuring the likelihood that a player will exhaust their entire bankroll due to downswings or variance over the long run. It is typically expressed as a percentage; for example, a 5% risk of ruin means that if the game were repeated infinitely, there is a 5% probability of eventually losing all funds.

Influencing Factors

Risk of ruin primarily depends on three variables:

• Win Rate: Expected profit per hand or per hour, usually measured in BB/100 (big blinds per 100 hands). The higher the win rate, the lower the risk of ruin.
• Standard Deviation: Measures the volatility of profits. The larger the standard deviation, the higher the risk of ruin. Texas Hold'em typically has a high standard deviation, around 80–100 BB/100 hands.
• Bankroll Size: Total available funds. The larger the bankroll, the lower the risk of ruin.

Formula

Under a simplified model (assuming profits follow a normal distribution), risk of ruin can be approximated by:

RoR = e^(-2 * WR * B / SD^2)

Where:

• WR is the win rate (in BB per hand)
• B is the bankroll (in BB)
• SD is the standard deviation (in BB per hand)

For example, if the win rate is 2 BB/100 hands (i.e., 0.02 BB/hand), standard deviation is 10 BB/hand, and bankroll is 100 BB, then RoR ≈ e^(-20.02100/100) = e^(-0.04) ≈ 96%. This means ruin is almost certain. If the bankroll increases to 1000 BB, then RoR ≈ e^(-0.4) ≈ 67%, still high. In practice, professional players usually aim to keep risk of ruin below 1%, requiring a much larger bankroll.

Bankroll Management Recommendations

• Cash games: It is generally recommended to have 20–40 buy-ins (each buy-in being 100 BB), corresponding to a risk of ruin of about 1–5%.
• Tournaments: Due to higher variance, it is recommended to have 100 or more buy-ins.
• Multi-tabling: Playing multiple tables simultaneously reduces standard deviation (due to independent and identically distributed outcomes), thereby lowering risk of ruin.

Limitations

The risk of ruin model assumes that the player's win rate and standard deviation are constant and that the game continues indefinitely. In reality, players can reduce risk through skill improvement, adding funds to their bankroll, or moving down in stakes. Additionally, the model does not account for factors such as rake or emotional tilt. Therefore, risk of ruin should be used as a reference rather than an absolute prediction.