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Poker variance calculator

This poker variance calculator shows how far cash-game results swing around your win rate. Enter your win rate and in big blinds per 100 hands, and see the range your results can land in, how many hands it takes to prove you win, your and sample runs.

Lesson: Same decisions, different results (needs an invite). In the glossary: Standard deviation, Risk of ruin, bb/100. How the numbers are made.

Last updated

Expected result
5,000bb
95% of results land between -578bb and 10,578bb
-0.6 to 10.6
bb/100, measured over 100,000 hands
Hands to prove it
124,468
until the 95% range sits above zero
2.5%
with 3,000bb, playing forever
A 1,000bb downswing
99%
of runs fall that far from a high within 100,000 hands
Losing runs
4%
of runs are behind after 100,000 hands

A bankroll of 2,427bb keeps the risk of ruin at 5%; 3,730bb keeps it at 1%.

20 sample runs over 100,000 hands9,930bb to -4,672bb

Gold dashes: your expected result. Shaded: where 90% of runs end up at each point.

How to use it

Your tracking software shows your win rate and standard deviation in bb/100. Full-ring and six-max no-limit players usually sit between 70 and 110 bb/100 for standard deviation; looser games run higher. Set the number of hands, the bankroll you play with and a downswing size you want to know about. The sample runs come from a fixed seed, so a shared link draws the same lines.

A worked example

The page opens on a solid winner: 5 bb/100 with a standard deviation of 90. After 100,000 hands, the true win rate could be anywhere from −0.6 to 10.6 bb/100, so 100,000 hands are not enough to tell this player from a break-even one. It takes about 124,000 hands for the range to clear zero. With 3,000 big blinds, 30 buy-ins at 100 big blinds, the risk of going broke is 2.5%; about 2,430 big blinds keeps it at 5%.

The formulas

The 95% range of a win rate is the win rate plus or minus 1.96 × SD ÷ √(hands ÷ 100). Risk of ruin, playing forever, is exp(−2 × win rate × bankroll ÷ SD²). The downswing and losing-run figures come from simulating 100 hands at a time. For tournaments, where results come from rare deep runs, use the tournament variance calculator instead. Every formula is on the poker math page.