Poker Variance Calculator: How Bad Can It Get?

This poker variance calculator is a simulator for your own cash game: it plays out your next 50,000 hands 2,000 times from your win rate, your standard deviation and your bankroll. A 5 bb/100 winner at a standard deviation of 90 loses money over those 50,000 hands roughly one time in nine. Nothing has gone wrong when that happens: at that length the swings are simply bigger than the edge.

What is variance in poker?

Variance is the spread of results around your true win rate. Your win rate is what you earn on average per hundred hands. Variance is how far a real hundred hands, or a real fifty thousand, can land from that average through card distribution alone.

Poker has a lot of it. A single 100-hand session at 6-max no-limit swings by about 90 big blinds in a typical case, and a player who wins 5 bb/100 on average is winning 5 while the session moves 90. The signal is small and the noise is large. That ratio is the whole reason a losing month proves almost nothing and a losing year proves quite a bit. The calculator exists to put numbers on “almost nothing” and “quite a bit”.

What do the four inputs mean?

The calculator asks for four things. Two you know, one you can look up, and one you should not guess at. All four are cash game units. Tournament variance is far larger, is not normally distributed over short samples, and needs its own model; this calculator understates it badly, so do not feed it an MTT win rate.

Win rate, in big blinds per 100 hands. Take it from your tracking software over your largest recent sample, not your best month. Live players rarely have that software at the table; a free session logger like Poker Bankroll Tracker records each session’s result and builds the sample for you. If you have no records, use the calculator to test assumptions rather than to confirm them: try 2, then 5, then 8, and watch what changes. Online mid-stakes winners typically sit in the low single digits; a live game with weak players can run much higher.

Standard deviation, in big blinds per 100 hands. This is the noise term, and your tracker reports it directly (PokerTracker and Hold’em Manager both show “Std Dev bb/100”). If you cannot look it up, the presets under the slider cover the usual cases. Primedope’s published guide puts full-ring no-limit at 60 to 80, 6-max at 75 to 120, and pot-limit Omaha at 100 to 160. The defaults here use 90, a middle value for a normal 6-max game. Aggressive players and deep stacks push it up.

Hands. The length of the stretch you are asking about. 50,000 hands is roughly six months for a serious online regular playing a couple of tables, or several years of live play. Drag it down to 10,000 and watch every range widen; that is the arithmetic of small samples.

Bankroll, in buy-ins. A buy-in here means 100 big blinds, so 30 buy-ins at $1/$2 is $6,000. This number only feeds the risk-of-ruin line, which is the one that decides whether you can survive the swings the other lines describe.

How do you read the results?

Each result answers one question, and they build on each other. With the default inputs (5 bb/100, standard deviation 90, 50,000 hands, 30 buy-ins) the calculator shows six numbers. Here is what each one is saying.

1. Expected result: +25 buy-ins. Win rate times hands, divided by 100. Five big blinds per hundred, over 50,000 hands, is 2,500 big blinds. This is the centre of the distribution, not a prediction. You will almost never finish exactly here.

2. Likely range: +4 to +46 buy-ins, seven times in ten. The spread of the sample is the standard deviation scaled by the square root of the number of hundred-hand blocks: 90 times the square root of 500, which is about 2,000 big blinds, or 20 buy-ins. Seven times in ten you land within one spread of the centre. The wider band (95% of the time) runs from a 14 buy-in loss to a 64 buy-in win. Both are ordinary outcomes for the same player.

3. Chance you lose over the sample: 10.7%. This is the single most useful number on the page. A winning player at 5 bb/100 finishes 50,000 hands in the red about one time in nine. Not because anything went wrong, but because the noise is four times the size of the signal at this length. Cut the win rate to 2 bb/100 and the same stretch loses 31% of the time. Over 10,000 hands, even the 5 bb/100 player loses 29% of the time.

4. Risk of ruin: 2.5% with 30 buy-ins. The probability that, playing at these numbers forever without ever moving down, you eventually lose the whole roll. The formula behind it is e to the power of minus (2 times win rate times bankroll, divided by standard deviation squared). Read that as: bankroll and win rate both push ruin down, and standard deviation pushes it up fast because it is squared. The line under the number tells you what roll would hold ruin under 5% and under 1%.

5. Worst stretch inside the sample. Everything above is about where you finish. This is about the trip. The calculator simulates 2,000 versions of your 50,000 hands and counts how many contain a fall of at least 10, 20 or 30 buy-ins from a peak. At the defaults, a 20 buy-in downswing happens somewhere in the sample about one time in four. A 10 buy-in downswing happens nearly every time. If a 10 buy-in dip feels like a crisis, the crisis is the expectation, not the cards.

6. How sure the win rate is: ±7.9 bb/100. Your observed win rate is itself a noisy estimate, and this is its 95% margin after this many hands. At 50,000 hands, a player showing 5 bb/100 has a true rate somewhere between about -3 and +13. That is uncomfortable, and it is the honest answer to “am I a winning player” at that sample.

How big a downswing is normal?

Bigger than most players budget for, and it depends heavily on win rate. The table runs the same simulation as the calculator with 20,000 paths at a standard deviation of 90 over 50,000 hands, and asks how often the run contains a peak-to-trough fall of at least the stated size.

Win rate	10+ buy-ins	20+ buy-ins	30+ buy-ins
2 bb/100	96%	44%	13%
5 bb/100	88%	23%	4.4%
8 bb/100	76%	10%	1.0%

Two things stand out. The 10 buy-in downswing is close to certain for everyone, which is why “I’m down 10 buy-ins” carries no information about your game. And the size of the rare downswing is mostly a win rate story: the 2 bb/100 player sees a 30 buy-in fall three times as often as the 5 bb/100 player, from identical cards. Stretch the sample to 100,000 hands and the 5 bb/100 player’s chance of a 20 buy-in downswing roughly doubles to 45%, because there is simply more road for it to happen on.

How many hands until you know your win rate?

More than you have, in almost every case. The margin of error on an observed win rate shrinks with the square root of the sample, which means quadrupling the hands only halves the uncertainty. At a standard deviation of 90:

Hands	95% margin on your win rate
10,000	±17.6 bb/100
50,000	±7.9 bb/100
100,000	±5.6 bb/100
500,000	±2.5 bb/100

So a player who has “been crushing at 8 bb/100” over 10,000 hands is, statistically, somewhere between a large loser and a huge winner. This is not a reason to ignore results. It is a reason to weigh them against the quality of your decisions, which you can assess on a far smaller sample than your win rate. One hundred hands is enough to know whether you are opening the right hands from each seat. Fifty thousand is not enough to know your win rate to within a buy-in per hundred.

How much bankroll do you need?

It depends on your win rate far more than on anything else. Hold the standard deviation at 90 and set an acceptable risk of ruin, and the formula gives a required roll:

Win rate	Roll for 5% risk of ruin	Roll for 1%
2 bb/100	61 buy-ins	93 buy-ins
5 bb/100	25 buy-ins	38 buy-ins
8 bb/100	15 buy-ins	23 buy-ins

The common advice of 20 to 30 buy-ins for cash games is fine for a clear winner and badly short for a marginal one. That is the point most bankroll articles skip. If your rate is 2 bb/100, the answer is not a bigger roll; a 60 buy-in roll at 2 bb/100 is a lot of money guarding a small edge. Most low-stakes downswings are a win rate problem wearing a variance costume, and the fix is the leak, not the bankroll.

Two practical notes on the formula: it assumes you never move down, which real players do, so the true risk is lower than it prints; and it assumes your win rate estimate is right, which result six says it probably isn’t, so the true risk is also higher. The two roughly cancel for a player who moves down promptly.

What actually shrinks variance?

Nothing shrinks the noise. Standard deviation is a property of the game and your style, and the only lever that moves it is playing tighter or smaller, both of which also cut the win. What you can move is the signal.

Every table on this page shows the same pattern: raising the win rate does more for the downswings, the risk of ruin and the required roll than any bankroll decision does. That is why the calculator carries a comparison toggle. It adds +6.1 bb/100 to whatever win rate you entered, which is the average EV gain intermediate players showed after 30 days of preflop drilling in the PlusEV trainer, measured across 1M+ recorded hands as +0.061 BB per training decision and applied here as if every hand you play were a trained decision, which makes it an upper bound. At the default inputs, that one change takes the chance of a losing 50,000 hands from 10.7% to 0.3%, and the bankroll needed for 5% risk of ruin from 25 buy-ins to 11.

Treat the figure as what it is: a measured gain in training play, in a cohort, over a month. It is not a promise about your table. But it makes the point the whole page is building to. The swings you are budgeting for are a function of how good you are, and below high stakes the cheapest place to get better is preflop, because that is where the same mistake repeats a hundred times a session. The blinds alone account for a large share of most players’ leaks, and every one of those decisions is also a pot odds problem you can drill until it is automatic.

Quick answers

How do you calculate your win rate in poker?

Divide the big blinds you have won by the hands you have played, and multiply by 100. Winning 1,500 big blinds over 30,000 hands is 5 bb/100.

Is a standard deviation of 90 bb/100 normal?

For 6-max no-limit, yes. Full ring runs lower (60 to 80), aggressive or deep games run higher, and PLO is higher again.

Is higher variance better?

Not in itself. Higher variance means bigger swings around the same win rate, so it needs a bigger bankroll to survive. It is only worth accepting when the style or game that causes it also raises your win rate.

Can a winning player lose over 100,000 hands?

Yes. At 5 bb/100 with a standard deviation of 90, it happens about 3.9% of the time. At 2 bb/100, about 24%.

What is the risk of ruin formula?

RoR = e^(-2 × win rate × bankroll ÷ SD²), with all three in big blinds per 100 hands or big blinds. It assumes you never move down.

What is a poker downswing calculator?

The same tool. A downswing is the biggest peak-to-trough fall inside a sample, which this calculator finds by simulation because there is no clean formula for it.

Does the calculator work for tournaments?

No. It is a cash game model, and it understates tournament swings badly.