Poker Bankroll Management: Risk of Ruin Calculator and Practical Risk Management Model

Tool Purpose

Risk of Ruin (RoR) measures the probability that a player with a given win rate and bankroll will lose all their funds due to a downswing over an indefinite period of play. It is a core quantitative tool in Bankroll Management, helping players determine the minimum safe bankroll size to avoid going broke from short-term variance.

The value of calculating RoR lies in:

• Setting a rational buy-in threshold to avoid excessive risk
• Checking whether your current bankroll can withstand normal variance
• Guiding decisions on moving up or down in stakes

Formula Principles

The most commonly used risk of ruin formula is based on the Gambler's Ruin model, assuming known expected value and variance per hand or per session. The simplified formula is:

$$ \text{RoR} = e^{-2 \times \text{Win Rate} \times \text{Bankroll} / \text{Variance}} $$

Where:

• Win Rate (WR): Expected profit per 100 hands (or per 100 big blinds), with units consistent with variance.
• Bankroll (B): Total current funds, in the same unit as profit.
• Variance (Var): Variance of profit per 100 hands. If standard deviation is SD, then Var = SD².

The derivation assumes:

• A stable (long-term positive) win rate
• Independent and identically distributed outcomes per hand
• Fixed bet sizes (no self-adjustment)

In practice, we usually replace variance with Standard Deviation (Std Dev), rewriting the formula as:

$$ \text{RoR} = e^{-\frac{2 \times \text{WR} \times \text{B}}{\text{SD}^2}} $$

How to Use

1. Obtain your personal data: Extract your Win Rate (usually in bb/100) and Standard Deviation (bb/100) from tracking software like Hold'em Manager or PokerTracker.
2. Choose a target risk of ruin: Typically 5% or lower (conservative players use 1%).
3. Calculate the required bankroll: Rearrange the formula to solve for Bankroll: $$ B = \frac{-\ln(\text{RoR}) \times \text{SD}^2}{2 \times \text{WR}} $$
4. Add a buffer: The theoretical value only covers statistical variance; it is recommended to keep an extra 20–50% as a safety cushion.

Practical Example

Suppose you are a cash game player with the following stats:

• Win Rate WR = 5 bb/100
• Standard Deviation SD = 100 bb/100
• Acceptable risk of ruin RoR = 1% (0.01)

Calculate the required minimum bankroll:

$$ B = \frac{-\ln(0.01) \times 100^2}{2 \times 5} = \frac{4.60517 \times 10000}{10} = 4605.17 \text{ bb} $$

If you play NL200 (blinds $1/$2), the big blind is $2, so the required bankroll in dollars is: 4605 bb × $2/bb = $9,210.34.

Tiered recommendations:

• Conservative (RoR=1%): about 46 buy-ins (assuming 100bb buy-in)
• Aggressive (RoR=5%): only about 30 buy-ins (calculation omitted)

FAQ

Q: Do I need a positive win rate? Can I use it if I'm currently losing?

A: No. The formula requires a long-term positive expectation; otherwise, the risk of ruin is 100%. Losing players should first improve their skills before calculating bankroll.

Q: The formula assumes fixed bets, but I adjust in practice. Is it still applicable?

A: The formula gives a conservative lower bound. If you can move down during downswings, your actual risk of ruin will be lower than the calculated value.

Q: What if my standard deviation is very high?

A: The higher the standard deviation, the larger the bankroll required. For example, if SD=140, the same conditions would require about $18,000.

Q: Is the calculated bankroll "safe"?

A: It is only a mathematical expectation. You must also consider living expenses, rake, platform risk, etc. It's recommended to add a 20% buffer.

Further Study

• Kelly Criterion: Guides optimal bet sizing for maximum long-term growth. The risk of ruin formula is derived from it.
• Bankroll Management Strategies: Tiered bankrolls (e.g., 20 buy-ins for micro stakes, 50 for mid stakes), moving down rules.
• Simulation Methods: Monte Carlo simulations for more realistic evaluations of complex scenarios (e.g., rake, variable standard deviation).
• Related Tools: Online risk of ruin calculators (e.g., PokerBankrollManager.com), Excel templates.

Remember, the risk of ruin formula is a theoretical model; actual variance can be more severe. Always keep a separate life bankroll and never let your poker bankroll represent your entire net worth.