Bankroll Calculator

What this bankroll calculator does

It answers one question: how much money you need set aside so that, at your win rate and your variance, the chance of losing all of it is as small as you are willing to accept. The answer comes from the risk of ruin formula, not from a rule of thumb, which is why two players at the same stakes can get very different numbers. A $1/$2 player winning 5 big blinds per hundred hands needs about 19 buy-ins for a 5% risk of ruin; a player winning 2 big blinds per hundred with slightly higher variance needs about 61.

The risk of ruin formula

For a game with a steady edge, the probability of ever losing a bankroll of size B is approximately

Risk of ruin = e^{−2 × WR × B / SD²}

Turn that round to solve for the bankroll and you get the figure this page computes:

Bankroll = (SD² ÷ (2 × WR)) × ln(1 ÷ RoR)

where WR is your win rate, SD is your standard deviation measured over the same unit (per 100 hands for cash, per tournament for tournaments), and RoR is the risk of ruin you accept as a fraction, so 5% is 0.05. Two things follow from the shape of the formula. Variance enters squared, so a game with 25% more variance needs about 56% more bankroll. Win rate enters in the denominator, so halving your edge doubles the bankroll you need, and a player with no edge needs an infinite one: no bankroll is big enough for a losing player.

Cash games: a worked example

Take a $1/$2 game with a $200 buy-in (100 big blinds), a win rate of 5 bb/100, a standard deviation of 80 bb/100 and a 5% risk of ruin:

• SD² = 80 × 80 = 6,400
• 2 × WR = 10, so SD² ÷ 2WR = 640 big blinds
• ln(1 ÷ 0.05) = ln(20) = 2.996
• Bankroll = 640 × 2.996 = about 1,917 big blinds, or $3,835 at $2 a blind

That is 19.2 buy-ins. Drop the acceptable risk to 1% and the same player needs 29.5 buy-ins, because ln(100) is 4.6 rather than 3.0. Cut the win rate to 2 bb/100 with a standard deviation of 90 and the requirement climbs to 61 buy-ins. The common advice of "20 to 30 buy-ins for cash" is the answer for a solid winner at ordinary variance and nothing else.

Buy-ins needed for cash games at 5% risk of ruin

Buy-ins of 100 big blinds. Rows are win rate, columns are standard deviation in bb/100.

Typical tracker figures for no-limit hold'em are 60 to 80 bb/100 at full-ring tables and 80 to 100 bb/100 at 6-max; heads-up and pot-limit Omaha run higher still. Read your own number from your tracking software over at least 50,000 hands before trusting it.

Tournaments: different inputs, same formula

Tournament results are not measured in big blinds per hundred hands, so the calculator's tournament mode takes return on investment (ROI, as a percentage of the buy-in) and standard deviation in buy-ins per tournament, and returns the bankroll in buy-ins. The formula is the same; only the units change.

A $109 player with a 20% ROI and a standard deviation of 7 buy-ins per tournament, accepting a 5% risk of ruin, needs about 367 buy-ins, roughly $40,001. At 1% risk it is 564 buy-ins. A 30% ROI player in smaller fields, with a standard deviation of 5 buy-ins, needs about 125.

Buy-ins needed for tournaments at 5% risk of ruin

Rows are ROI, columns are standard deviation in buy-ins per tournament.

Standard deviation per tournament rises with field size and with how top-heavy the payouts are. Small fields and flatter structures sit near 5 buy-ins; mid-sized fields near 7; large-field events with a thousand or more entries, and anything with a big jackpot-style first prize, reach 10 or more. Progressive knockout events sit a little lower than their field size suggests because bounties pay out along the way. As with cash games, your tracker's figure beats any typical value.

To see what a stretch at your numbers can look like before the bankroll question even arises, the variance calculator simulates sample run-outs and gives the chance of being down after a set number of hands or tournaments.

Reading the result

The number is a floor, not a target. Three things the formula leaves out all argue for keeping more than it says:

• Your win rate is an estimate. Over 100,000 hands the true win rate of a 5 bb/100 player is plausibly anywhere from 3 to 7, and at 3 the required bankroll is nearly double. Treat the result as the answer for an optimistic reading of your edge.
• The formula assumes you never move down. In practice a player who drops stakes when the roll shrinks has a far lower real risk of ruin than the formula states, which is the strongest argument for a moving-down rule: it lets you play with less than the formula demands.
• Games change. A win rate earned in soft games does not transfer to tougher ones, and the formula has no term for that.

A practical reading: use the 5% figure as the minimum to play a stake, move down if the roll falls below the 10% figure for that stake, and move up only when the roll clears the 1% figure for the next one.

Why variance, not skill, sets the number

Players are surprised that a 10 bb/100 crusher at 6-max with a standard deviation of 100 needs about the same bankroll as a 5 bb/100 winner at a quiet full-ring table with a standard deviation of 70. The squared term is why. Anything that raises variance, such as deeper stacks, more aggressive opponents, more multiway pots, or short-handed play, raises the bankroll you need faster than a better win rate lowers it. The same logic says a tournament specialist needs hundreds of buy-ins while a cash player needs tens, even at the same hourly rate.

Questions

How many buy-ins do I need for cash games? It depends on your win rate and variance. At 5 bb/100 with a standard deviation of 80 bb/100 and a 5% risk of ruin, about 19 buy-ins of 100 big blinds. At 2 bb/100 with a standard deviation of 90, about 61. Use the calculator with your own tracker figures rather than a blanket number.

How many buy-ins do I need for tournaments? Far more than for cash, because per-tournament variance is large relative to the edge. A 20% ROI player with a standard deviation of 7 buy-ins needs about 367 buy-ins at 5% risk of ruin; a 30% ROI player in small fields with a standard deviation of 5 needs about 125.

What is risk of ruin? The probability that you lose your entire bankroll at some point if you keep playing the same stakes with the same edge and variance. The formula is e to the power of minus 2 times win rate times bankroll divided by variance. Most serious players choose 1% to 5%.

What standard deviation should I use? The figure from your tracking software, measured in bb/100 for cash or in buy-ins per tournament. Without one, 70 bb/100 for full-ring no-limit hold'em, 85 to 100 for 6-max, and 5 to 10 buy-ins per tournament depending on field size are reasonable starting points.

Why does the calculator say I need an infinite bankroll? Because the win rate you entered is zero or negative. The formula only applies to winning players; no bankroll makes a losing game safe.

Does moving down in stakes change the answer? Yes, a lot. The formula assumes you play the same stakes until you are broke. A player who moves down when the bankroll shrinks has a much lower true risk of ruin, so a strict moving-down rule lets you play with fewer buy-ins than the formula requires.

Is 20 buy-ins enough for cash games? Only for a clear winner at ordinary variance: the formula gives about 19 buy-ins for 5 bb/100 at a standard deviation of 80 and 5% risk. For a marginal winner, or at 6-max variance, it is not enough.