What is risk of ruin in poker?

Risk of ruin is the probability that a player will lose their entire bankroll before it grows to infinity. For a winning cash game player, it depends on three variables: win rate, standard deviation, and bankroll size. A higher win rate and larger bankroll reduce risk of ruin; a higher standard deviation increases it. The Malmuth formula provides an analytical solution: RoR = e^(-2 * winrate * bankroll / stddev^2).

How many buy-ins do I need for cash games?

It depends on your win rate, standard deviation, and risk tolerance. At 5% risk of ruin, a typical 5 bb/100 winner with 80 bb/100 standard deviation needs 25 to 30 buy-ins for 100bb games. Lower win rates or higher variance styles require significantly more. Use the calculator above to get the exact number for your parameters.

What is the Malmuth formula?

The Malmuth formula calculates the exact risk of ruin for a player with a known win rate and standard deviation: RoR = e^(-2 * WR * BR / SD^2), where WR is win rate in bb/100, BR is bankroll in bb, and SD is standard deviation in bb/100. It assumes a normal distribution of session results, which is a reasonable approximation for cash games over large samples. The formula comes from Mason Malmuth's Gambling Theory and Other Topics.

What is standard deviation in poker?

Standard deviation measures how much your results vary from hand to hand. In cash games, it is expressed in bb/100 (big blinds per 100 hands). A typical tight-aggressive player has a standard deviation of 60-80 bb/100. LAG players and those who play larger pots run 80-100+ bb/100. Higher standard deviation means wider swings and larger bankroll requirements for the same risk of ruin.

Cash Game Bankroll Simulator

Bankroll paths at your winrate and standard deviation.

Enter Cash Game Parameters

Win Rate (bb/100)

Std Deviation (bb/100)

Current Bankroll (bb)

Hands to Simulate

Running 10,000 simulations...

Risk of Ruin Analysis

Analytical RoRMalmuth formula	--
Monte Carlo RoR10,000 simulations	--
Probability of profit	--

Bankroll by Risk Level

Risk Level	Required Bankroll (BB)	Buy-ins (100bb)	Buy-ins (20bb)

Profit Distribution

Expected profit	--
Median profitp50 of simulations	--
Worst case (p5)5th percentile outcome	--

Percentile Table

Percentile	Profit (bb)

Maximum Drawdown

How Many Buy-ins Do I Need?

How This Calculator Works

The simulator runs 10,000 independent bankroll paths at your win rate and standard deviation. Each path plays out hand by hand, drawn from a normal distribution. Alongside the simulation, it computes the Malmuth analytical formula from Gambling Theory and Other Topics as a cross-check. When both methods agree, you can trust the number.

The Drawdown tab matters more than the Risk of Ruin number for most players. RoR tells you whether your bankroll can survive indefinitely at a given stake. Drawdowns describe what the ride feels like. A 5% RoR bankroll can still drop 40 or 50 buy-ins before recovering.

Win rate moves the results more than any other input, and it is the one you know least precisely. At 100,000 hands of 6-max and 80 bb/100 standard deviation, the 95% confidence interval still spans 5 bb/100 either side of your observed rate. A 6 bb/100 winner in your database could be a 1 bb/100 or an 11 bb/100 player. You need 200,000+ hands at a single stake before the number tightens enough to plan around. If your sample is smaller than that, use the lower bound of your confidence interval as the input here rather than the midpoint. With fewer than 50,000 hands, skip the formula and use a flat 30 to 40 buy-in rule while you build a real sample.

Your observed rate is also probably higher than your true rate. Table selection, soft player pools that have since dried up, and a few big pots that went your way all inflate the number. A common correction is to assume your true edge is 1 to 2 bb/100 lower than your tracker says.

Standard deviation for most cash games falls between 75 and 120 bb/100 depending on format and style. If you are not sure, 100 bb/100 is a reasonable default for 6-max NLH. PLO players should start closer to 130-150. The collapsible guide above the inputs has ranges by format.

The model assumes your win rate stays constant. In practice, it does not. Tilt, table selection, stake changes, and improving over time all shift the real number. Treat the output as a baseline for a player who shows up and plays their game every session. If your win rate drops when you are running bad, your actual ruin risk is higher than the number on screen.