How to Use the Risk of Ruin Calculator

A risk of ruin calculator estimates the probability of a specified critical event conditional on your inputs and over the model’s horizon. That event might be losing the entire bankroll or falling to a chosen remaining balance. Start by selecting the event and horizon in the ToolsGambling calculator: four analytical modes have no fixed limit on the number of bets, while Monte Carlo covers a specified series.

The result does not establish that you have an edge. It answers a conditional question: what happens if the probability of winning, stake size and other assumptions accurately describe the game?

What counts as ruin, and over what period?

Define ruin as reaching zero, crossing a fixed threshold relative to the starting bankroll, or suffering a drawdown from a previous peak. These are different events, so their probabilities are not directly interchangeable.

• Zero bankroll: In the classic gambler’s ruin model, each fixed-stake bet adds or subtracts one bankroll unit until the balance reaches zero or a target.
• Fixed starting-bankroll threshold: Starting with 1,000 and choosing 20% remaining sets the critical level at 200, regardless of any subsequent growth.
• Peak drawdown: A bankroll that rises from 1,000 to 2,000 and then falls to 1,000 has a 50% drawdown, even though the starting balance remains intact.

The horizon matters too. The probability of ever reaching zero is not the probability of losing the bankroll during today’s session. Monte Carlo can model 500 bets; the analytical modes do not impose that time limit.

With proportional staking below 100% of a positive current balance, ordinary losses do not reach exact zero in a finite number of bets. A critical threshold is therefore needed. A minimum permitted stake can create a practical floor, but the calculator does not model minimum stakes or account restrictions.

Which of the five modes should you choose?

Choose the mode that matches your event, staking method and available inputs—not the one displaying the lowest risk.

The table uses the actual English tab names.

In Gambler's ruin, target 0 means eventual ruin without an upper boundary—not ruin within a particular session. Across all modes, stable parameters are assumptions rather than established facts about your play.

How should you prepare bankroll, stake and edge inputs?

Use a separate bankroll, consistent units and a defensible edge estimate. Fixed staking needs bankroll units; proportional staking needs a fraction of the current balance.

Your bankroll is money separately allocated to gambling, not your total savings. For starting bankroll B and fixed stake S:

n = B / S

For example, 1000 / 20 = 50 bankroll units. The stake remains 20 as the balance changes. By contrast, staking 2% of the current bankroll changes the stake after every result; it is not a permanent 50-unit fixed-stake setup.

For a binary bet with no push, decimal odds d and probability of winning p, the expected net return per amount staked—the edge—is:

e = p × d − 1

Use a fraction for p: 51% is 0.51. Decimal odds include the returned stake in the payout. The break-even probability is 1 / d.

At d = 2, an edge of 2% corresponds to p = 0.51, because 0.51 × 2 − 1 = 0.02. Do not derive a supposed probability from an edge you would like to have: you first need a justified estimate of p.

For poker, win rate means expected net profit in big blinds per 100 hands, not the percentage of hands won. Standard deviation must describe results over the same 100-hand block. The bankroll itself is a balance in big blinds, not big blinds per 100 hands.

How can you test uncertainty in the edge?

Recalculate with a lower edge: a small error in the assumed advantage can substantially change the modeled risk.

For 100 bankroll units, Advantage betting gives:

This is sensitivity analysis for one model, not an estimate of your actual risk. The 100% result at zero edge applies to an unlimited horizon, not the next 100 bets.

How do you calculate risk with a fixed stake?

Select Advantage betting, enter a 2% edge, 50 bankroll units and a 1% target risk. The example returns 13.53% current risk and 116 units required for the target.

1. Open the Advantage betting tab.
2. Set the Your edge per bet slider to 2.
3. Set the Bankroll in units slider to 50.
4. Enter 1 in Target risk of ruin.
5. Compare the current 13.53% risk with the calculated requirement of 116 units.

Advantage betting with a 2% edge, 50 bankroll units, 13.53% risk of ruin and 116 required units

Local English calculator interface showing the fixed-stake example; the screenshot does not verify an edge in real play.

The implemented formula is:

R = ((1 − e) / (1 + e))^n

Here, e is the edge as a fraction and n is the bankroll in fixed-stake units. At decimal odds 2, e = 2p − 1, with loss probability q = 1 − p. The formula can therefore be written:

R = (q / p)^n

This is the exact probability of ever reaching zero for independent, constant-probability steps of +1 or −1 unit, with integer n, a fixed stake, no upper target and p > 0.5. For p ≤ 0.5, eventual ruin in that model has probability 100%.

At e = 0.02 and n = 50, the implemented ratio formula gives 13.53%, rounded to two decimal places. The expression R ≈ exp(−2 × e × n) is a small-edge approximation, not the calculator’s implemented formula.

For unequal wins and losses, edge alone is insufficient to determine risk of ruin. This mode uses the equal-sized win/loss model as an approximation. See MIT’s gambler’s ruin material for the fixed-step model.

With a bankroll of 1,000 and a fixed stake of 20, you have the same 50 units. Halving the fixed stake to 10 gives 100 units and a conditional risk of 1.83%.

For the hypothetical 1% target, 116 units produce a displayed risk of 0.97%. With a bankroll of 1,000, that corresponds to a maximum fixed stake of approximately 1000 / 116 ≈ 8.62. This is a rounded unit conversion, not a staking recommendation; it assumes the 2% edge remains unchanged.

How do you calculate ruin before reaching a goal?

For a fair game with a 50% probability of winning, a starting balance of 20 units and a target of 40 units, the probability of ruin before the target is 50%. The probability of reaching the target is also 50%.

1. Open Gambler's ruin.
2. Set the probability-of-winning slider to 50%.
3. Enter 20 in the starting-bankroll input.
4. Enter 40 in the target input.
5. Read the probabilities of reaching zero and reaching the target.

Gambler's ruin with a 50% probability of winning, 20 starting units, a 40-unit target and 50% risk of ruin

Local English interface showing the gambler’s ruin model with two finite boundaries.

Each bet wins or loses one unit. Let p be the probability of winning, q = 1 − p, n the starting bankroll, T the target and r = q / p.

For 0 < p < 1, p ≠ 0.5 and integer values 0 < n < T:

P(target before zero) = (1 − r^n) / (1 − r^T)

P(ruin before target) = 1 − P(target before zero)

When p = 0.5, the target probability is n / T, and the ruin probability is 1 − n / T. With 20 / 40, both are 50%.

Setting the target to 0 selects the model without an upper boundary. At a 50% probability of winning, eventual ruin is 100%. That does not mean 100% ruin within one session. For a finite-goal scenario, enter a target above the starting bankroll; an equal or lower target does not define the intended scenario.

These formulas assume independent, constant-sized steps and have no bet-count limit. The derivation is covered in MIT’s gambler’s ruin notes.

How should you read the Kelly result?

A Kelly fraction of 0.5 and a 50% drop from the starting bankroll give a modeled threshold probability of 12.5%. A fraction of 0.5 means half of full Kelly—not staking half your bankroll.

1. Open Kelly drawdown.
2. Set the Kelly-fraction slider to 0.5.
3. Set the bankroll-drop slider to 50%.
4. Enter 5% in the target-risk input.
5. Compare the current 12.5% with the target. For this target, the interface displays a rounded Kelly fraction of 0.38.

Kelly drawdown with half Kelly, a 50% drop from the starting bankroll and a 12.5% threshold probability

Local English Kelly interface. Despite the tab name, the calculation uses a fixed threshold relative to the starting bankroll.

Let f be the fraction of full Kelly and a the remaining fraction of the starting bankroll. A 50% drop means a = 0.5. The approximation is:

R ≈ a^(2 / f − 1)

For the same threshold:

This is a small-stakes diffusion approximation, not an exact answer for every discrete betting game. Its barrier is fixed relative to the starting bankroll, not a later peak. The model is discussed in William Chin’s paper.

The separate Kelly calculator calculates stake sizing from your probability and odds inputs; it does not guarantee low risk. The interface’s guidance about professional players is not a verified population statistic or a personal recommendation.

How do you calculate poker risk of ruin?

A win rate of 5 big blinds per 100 hands, standard deviation of 100 big blinds over a 100-hand block and bankroll of 1,000 big blinds produce a modeled risk of 36.79%.

1. Open Win rate + variance.
2. Enter 5 in the win-rate input.
3. Enter 100 in the standard-deviation input.
4. Enter 1000 in the bankroll input.
5. Check the units: win rate and standard deviation describe the same 100-hand block; bankroll is a balance in big blinds.

Poker risk calculation with a win rate of 5 big blinds per 100 hands, standard deviation of 100 over 100 hands, a 1000-big-blind bankroll and 36.79% risk

Local English poker interface; bankroll is measured in big blinds, not big blinds per 100 hands.

Let μ be expected profit per block, sigma the standard deviation over that same block and B the bankroll. With a positive, constant win rate:

R ≈ exp(−2 × μ × B / sigma²)

Variance is sigma². The expression is exact for the corresponding continuous positive-drift model but approximates discrete poker results. The underlying model appears in Columbia University’s Brownian motion notes.

Changing only the bankroll to 2,000 big blinds gives 13.53%.

You can calculate the bankroll for a hypothetical 1% target separately:

B = −sigma² × ln(R) / (2 × μ)

Using the same inputs and R = 0.01 gives 4,605.17 big blinds. Rounding upward gives 4,606 big blinds, or 47 whole 100-big-blind buy-ins. This is an external formula calculation: the poker tab does not offer an inverse-bankroll function. Its displayed 1.00% at 4,606 big blinds is also rounded.

How do you reproduce the Monte Carlo example?

Set a 55% probability of winning, decimal odds of 2, a stake of 5% of the current bankroll, 500 bets and a threshold of 20% remaining. In the verified example, 19 of 3,000 paths crossed the threshold, producing a displayed risk of 0.63%.

1. Open Monte Carlo.
2. Enter 55% in the probability-of-winning input.
3. Enter 2 in the decimal-odds input.
4. Set the stake-size slider to 5% of the current bankroll.
5. Enter 500 in the number-of-bets input.
6. Enter 20% in the ruin-threshold input. This means 20% of the starting bankroll remains—not a 20% loss.
7. Use the simulation run button. It runs 3,000 paths; the run count is not another input to set.

Monte Carlo example with a 55% probability of winning, decimal odds of 2, a 5% current-bankroll stake, 500 bets, 20% remaining threshold and 0.63% risk

Local English simulation interface showing final-balance distributions and equity bands.

The scenario returns:

The large modeled growth depends on a hypothetical, stable 55% probability of winning at decimal odds of 2. It is not an income forecast or evidence that this edge is available to you.

A threshold crossing remains flagged for the risk count, but the path continues afterward. Final percentiles therefore include paths that crossed the threshold and potentially recovered. They are not conditioned on staying above the threshold.

The chart’s equity bands show the 10th, 50th and 90th percentiles at each point in the series. They are cross-sectional summaries, not three predicted paths. Maximum drawdown measures a fall from a previous peak, unlike the starting-bankroll threshold used for the risk count.

Identical inputs use the same random seed. Repeating the run reproduces the result rather than adding independent evidence. Even zero crossings would not prove that the event has zero probability.

How can you adjust the scenario and limit real losses?

Change stake size or your loss limit first, then test less favorable inputs. Do not manufacture a low risk figure by assuming an unjustifiably high edge.

• For fixed stakes, reduce the amount represented by one unit. The 50-unit and 100-unit examples show the effect while holding edge constant.
• Plan when to move down in stakes. If the bankroll falls, apply a predefined step-down rule and recalculate for the new level. In poker, changing stakes can change both win rate and standard deviation.
• Stop when the allocated budget is exhausted. Household-expense funds are not an extension of the bankroll.
• If the edge is unknown, compare several scenarios, including no edge. A larger bankroll does not turn negative expected return into positive expected return.
• Check dependencies and game rules. Correlated bets, changing odds, pushes, fees and probability-estimation errors can make the selected model inappropriate.

The calculator does not model correlated outcomes, changing probabilities or odds, deposits, withdrawals or bookmaker restrictions. Results display two decimal places: 0.00% is rounding, not a promise of zero risk.

For separating gambling funds from other money, see the bankroll management guide. To distinguish an assumed player edge from the operator’s built-in advantage, read the house edge explanation. Neither replaces checking the inputs and assumptions of your calculation.