Poker Bankroll Calculator: Risk of Ruin, Formula and Buy-In Tables

A poker bankroll calculator estimates the probability that a player’s funds reach zero at some point over an indefinite playing horizon, based on a fixed win rate, standard deviation, and starting balance. Under the classic fixed-stakes model used here, a player with a win rate of 5 big blinds per 100 hands, a standard deviation of 90 big blinds per 100 hands, and a balance of 20 buy-ins faces a risk of ruin of about 8.5 percent. Increasing the balance to 25 buy-ins reduces this theoretical probability to about 4.6 percent. This model assumes that stakes remain fixed, no additional funds are deposited or withdrawn, and performance parameters stay constant over an indefinite timeline.

What this calculator does

The interactive tool evaluates long-term variance and sustainability for cash game players using statistical parameters. By processing your win rate, win-rate variability, and starting account size, it calculates the statistical chance of running your account balance to zero. Understanding this likelihood is essential for fundamental poker bankroll management, as even highly profitable players experience significant downswings due to short-term luck.

The calculations run exclusively in units of big blinds and standard 100-big-blind buy-ins. This unit-based approach ensures that the mathematical principles remain universally applicable regardless of the specific stakes played. The tool does not provide session-by-session predictions, nor does it guarantee future win rates. Instead, it provides a mathematical baseline showing how variance affects capital retention under idealized model assumptions. Players interested in analyzing individual hand equities or drawing chances alongside bankroll concepts can utilize our odds calculator for hand-level statistical breakdowns.

The risk of ruin formula

The equation used in fixed-stakes bankroll calculations is a Brownian-motion approximation to eventual ruin at fixed stakes. It assumes a positive constant win rate, constant variance, and no deposits or withdrawals. For actual discrete poker results, treat it as a useful planning approximation, not an exact prediction of real-world risk.

The model’s equation is written as:

$$\text{Risk of Ruin} = e^{\left( \frac{-2 \times W \times B}{SD^2} \right)}$$

Where the variables are defined as:

• $e$: Euler’s number, the mathematical constant approximately equal to 2.71828.
• $W$: Your long-term win rate expressed in big blinds per 100 hands (bb/100).
• $B$: Your total available bankroll expressed in big blinds (bb).
• $SD$: Your observed standard deviation expressed in big blinds per 100 hands (bb/100).

This formula models downswings using continuous distribution math. It shows that risk of ruin decreases exponentially as your bankroll grows in equal increments. Consequently, adding a small amount of extra capital to a modest bankroll significantly lowers the probability of running cold and going broke, whereas adding the same amount to an already large bankroll produces a smaller drop in overall percentage risk.

Worked example

To observe the formula in action, consider a standard cash game scenario featuring a player in a medium-variance environment. Assume the player holds an established win rate ($W$) of 5 bb/100 and experiences a standard deviation ($SD$) of 90 bb/100.

If the player sets their starting bankroll ($B$) at 20 full buy-ins, which equals 2,000 big blinds:

1. Multiply $2 \times W \times B$: $2 \times 5 \times 2000 = 20{,}000$.
2. Calculate the square of the standard deviation ($SD^2$): $90^2 = 8{,}100$.
3. Divide the numerator by the denominator: $-20{,}000 / 8{,}100 = -2.469135$.
4. Calculate $e^{-2.469135}$: $e^{-2.469135} \approx 0.08466$.

Under these parameters, the risk of ruin is about 8.5 percent.

If the player expands their capital allocation to 25 full buy-ins (2,500 big blinds) while maintaining identical win rate and variability metrics:

1. Multiply $2 \times W \times B$: $2 \times 5 \times 2500 = 25{,}000$.
2. Divide by $SD^2$: $-25{,}000 / 8{,}100 = -3.08642$.
3. Calculate $e^{-3.08642}$: $e^{-3.08642} \approx 0.04566$.

With 25 buy-ins, the risk of ruin drops to about 4.6 percent.

If a player sets a specific target risk threshold, the formula can be rearranged to calculate the precise required bankroll in buy-ins (where 1 buy-in equals 100 big blinds). Using the same parameters ($W = 5$ bb/100 and $SD = 90$ bb/100):

The rounded targets always round up, because 37 buy-ins still corresponds to about 1.04 percent risk, slightly above the 1 percent goal. As demonstrated by the target table, securing a 1 percent risk tolerance requires nearly 50 percent more capital than achieving a 5 percent target under the same win rate and variance profile.

Typical standard deviations by game

Standard deviation measures the statistical dispersion of your sample results around your mean win rate. Higher game aggression, wider preflop ranges, and multi-way pots lead to larger swings, which increases standard deviation.

When tracking data is limited, players typically rely on standard benchmark figures established across millions of simulated and tracked hands. You should substitute your own tracked figures from personal software databases whenever credible sample sizes are available.

Because games like Pot-Limit Omaha 6-max feature a standard deviation of about 140 bb/100 compared to about 70 bb/100 in full ring No-Limit Hold’em, PLO players require significantly larger bankroll cushions to achieve the same low risk of ruin target at equivalent win rates. Players wishing to explore how swing sizes impact confidence intervals can read more about poker variance in our math guides.

How to read your result

Interpreting your calculated risk of ruin correctly requires understanding what the underlying formula assumes:

• Zero Adjustments: The calculated risk metric assumes you will never change stakes, regardless of downswings. It models a player who continues at the exact same blind level until their balance reaches zero.
• No Capital Injections or Cashouts: The output assumes you never deposit emergency funds during a downswing and never withdraw winnings during an upswing.
• Indefinite Timeline: The theoretical risk percentage applies to an infinite sample size, not over a limited block of 10,000 or 50,000 hands.

A higher win rate, a lower standard deviation, or a larger total bankroll each directly lower your risk of ruin. Because the bankroll size sits in the exponent of the equation, increasing your reserve fund yields exponential safety benefits rather than simple linear improvements.

When the math breaks down

While the mathematical formula is internally consistent, its real-world accuracy relies on fixed variables. In actual play, several practical factors cause the model assumptions to break down:

1. Changing Stakes: Flexible cash game strategies involve moving down in stakes when downswings occur and moving up when bankrolls grow. A well-executed policy of moving down can reduce real-world risk of ruin compared to the fixed-stakes model, though the size of the reduction depends on how and when the moves are made.
2. Processing Withdrawals: Removing capital from your balance interrupts the compounding protection of a growing bankroll, keeping your actual risk of ruin higher than predicted by a static model.
3. Small Sample Sizes: Inputting an unproven win rate derived from a small sample size (e.g., under 100,000 hands) introduces severe estimation error. If your true win rate is lower than your small sample suggests, your true risk of ruin will be substantially higher.
4. Psychological Factors and Tilt: Extended downswings often lead to tilt, sub-optimal tactical decisions, or game selection degradation. These behavioral shifts lower your true win rate and raise your standard deviation mid-sample.
5. Shifting Game Quality: Player pools change over time. As games become more competitive or table dynamics change, your true win rate degrades, rendering past tracking metrics obsolete.

The standard calculator formula assumes the numbers entered remain static indefinitely; in real-world poker environments, those parameters fluctuate constantly.

FAQ

What is a good risk of ruin target for poker cash games?

A risk of ruin target between 1 percent and 5 percent is a common planning choice for serious players using a static bankroll model. Highly conservative players or professionals without alternative income streams often aim for a risk of ruin under 1 percent.

Why is standard deviation higher in 6-max than full ring?

In 6-max games, players play a wider percentage of starting hands and enter pots in looser positional setups compared to full ring formats. This broader range interaction creates larger pot sizes on average, which increases sample variance and results in higher standard deviations.

Does the calculator apply to multi-table tournaments?

No. The risk of ruin formula featured here uses a continuous approximation calibrated strictly for cash games with steady per-hand results. Tournament bankroll analysis requires a model of entry costs and payout distributions, including ROI uncertainty and re-entry behavior. The Independent Chip Model (ICM) addresses tournament chip value at a point in time and does not by itself estimate long-run bankroll risk.

How many hands do I need to accurately measure my win rate?

There is no universal hand-count threshold for a reliable win rate estimate. Precision improves gradually with sample size: under a simple model with a 90 bb/100 standard deviation, a 95 percent uncertainty interval still spans roughly ±5.6 bb/100 at 100,000 hands and ±3.2 bb/100 at 300,000 hands. Smaller samples carry wider intervals, and an overestimated win rate input leads to an underestimated risk of ruin output.

Data Used

• Model assumptions: fixed stakes, constant win rate, constant standard deviation, zero deposits, zero withdrawals, indefinite horizon.
• Formula: Risk of Ruin ≈ $e^{\left(-2 \cdot W \cdot B / SD^2\right)}$, a Brownian-motion approximation for eventual ruin at fixed stakes, not an exact discrete-game prediction.
• Worked example inputs: $W = 5$ bb/100, $SD = 90$ bb/100, Bankroll = 20 buy-ins (2,000 bb) yields about 8.5 percent risk; 25 buy-ins (2,500 bb) yields about 4.6 percent risk.
• Target bankroll thresholds ($W = 5$, $SD = 90$): 5% risk requires about 24.3 buy-ins (rounded up to 25); 2% risk requires about 31.7 (rounded up to 32); 1% risk requires about 37.3 (rounded up to 38, since 37 buy-ins still exceeds 1 percent).
• Standard deviation baselines: No-Limit Hold’em Full Ring about 70 bb/100; No-Limit Hold’em 6-Max about 90 bb/100; No-Limit Hold’em Heads-Up about 125 bb/100; PLO 6-Max about 140 bb/100. These are commonly referenced ballparks, not measured constants.
• All calculations operate strictly in big blinds and 100-bb buy-in units without referencing monetary currency values.

Educational content for poker study. 18+.