Poker variance, standard deviation and risk

What variance actually is

Every session result is your true win rate plus noise. The edge is small: a strong live win rate is a handful of big blinds per hour. The noise is enormous: a single hour routinely swings fifty big blinds either way. Variance is that noise, the spread of outcomes around your long-run rate. It is not the deck punishing you and it is not a slump you can outplay in one night. It is the arithmetic of a game where whole stacks move on single cards.

Many live players are defenceless against it because they cannot see it. A buy-in and cash-out log proves a swing happened. It cannot tell you whether the swing was normal, because normal is defined by two numbers a basic log does not hold: win rate and standard deviation.

Standard deviation sets the size of the swings

Standard deviation measures the typical spread of your results and is quoted in BB/100 hands. Live full-ring cash usually runs at roughly 80 to 120 BB/100. That is lower per hand than short-handed or online pools, because nine-handed live play is tighter, but it is still an order of magnitude bigger than the edge you are trying to measure.

To think in session terms, convert to BB/hr. Standard deviation scales with the square root of hands, and live you see roughly 25 to 30 hands per hour. Take an SD of 100 BB/100 at 25 hands per hour: 100 × √(25/100) = 100 × 0.5 = 50 BB per hour. So a player whose true rate is 5 BB/hr has single-hour results that routinely land anywhere inside ±50 BB of that, and about one hour in twenty finishes more than 100 BB from expectation. The edge is real. It is just invisible at the scale of an evening.

Live samples are brutally small

Online databases settle arguments with volume. Live you cannot. At 25 to 30 hands per hour, 10,000 hands takes 330 to 400 table hours. At 15 hours a week, that is five to six months of solid play for a sample an online grinder clears in a fortnight of multi-tabling. A busy 60-hour live month is roughly 1,500 to 1,800 hands, which is not a sample, it is an anecdote.

This is why live variance feels crueller than the equivalent online swing. The per-hand maths is identical, but the calendar time is stretched by a factor of ten or more, so a routine downswing can occupy an entire season of your life. It also means memory becomes the default tracker for anyone not logging properly, and memory is precisely the instrument variance fools best. A basic spreadsheet records results but does not know what your standard deviation is.

The confidence band, worked through

Here is the calculation the win-rate confidence calculator runs, worked by hand. Inputs: a measured win rate of 5 BB/hr and an hourly standard deviation of 50 BB (that is an SD of 100 BB/100 at 25 hands per hour). The standard error of your win rate is SD divided by the square root of your hours, and the 95% confidence band is the measured rate plus or minus 1.96 standard errors.

At 100 hours: SE = 50 ÷ √100 = 5 BB/hr. Band = 5 ± 9.8, so -4.8 to +14.8 BB/hr. At 300 hours: SE = 50 ÷ 17.3 = 2.9 BB/hr. Band = 5 ± 5.7, so -0.7 to +10.7 BB/hr. At 1,000 hours: SE = 50 ÷ 31.6 = 1.6 BB/hr. Band = 5 ± 3.1, so +1.9 to +8.1 BB/hr.

Read that honestly. After 100 hours, a measured 5 BB/hr is statistically indistinguishable from a losing rate. After 300 hours the band still brushes zero. Only around 1,000 hours does it clear zero and become a measured edge rather than a hopeful one. The poker variance calculator shows the same spread from the results side: expected winnings over a given number of hands, with the 95% band around them.

Bankroll, downswings and risk of ruin

The same two numbers set your bankroll. The standard risk-of-ruin model says RoR = e^(-2 × WR × bankroll ÷ SD²), with win rate and SD in BB/100 and the bankroll in big blinds. Worked example: WR 5 BB/100, SD 100 BB/100, bankroll 2,000 BB (20 buy-ins of 100 BB). Exponent = -2 × 5 × 2,000 ÷ 10,000 = -2, so RoR = e^-2, about 13.5%. Add ten buy-ins to make it 3,000 BB and the exponent becomes -3, so RoR drops to about 5%. That is the maths behind the site's bankroll and risk of ruin calculators.

Expected deepest downswing follows the same shape: roughly SD² ÷ (2 × WR). For the 5 BB/100 player above, that is 10,000 ÷ 10 = 1,000 BB, ten full buy-ins, inside a perfectly normal career. The table shows how hard the numbers punish a thin edge.

What variance does and does not excuse

Variance explains a losing month with a winning game. It explains a 10 buy-in hole with sound decisions in it. What it does not do is cover for you indefinitely: if the confidence band around your rate still sits below zero after a thousand hours, that is not variance, that is the game telling you something.

It does not excuse skipping the log. Stopping during a downswing destroys the evidence at exactly the moment it is worth most: a downswing with a complete session log is diagnosable, one without is just a bad memory. It does not excuse poor game selection, since no bankroll makes a negative-EV seat pay. And it does not excuse refusing to review. Tagged hands separate coolers, which are variance, from repeated mistakes, which are leaks. The test is always decisions, not results.

Plan around it, do not argue with it

You cannot meaningfully reduce variance without also cutting into your edge. Game selection and positional discipline trim it at the margins; the bankroll absorbs the rest. So the plan is not to fight the swings, it is to make them survivable and legible: know your win rate and standard deviation, set a move-down threshold in buy-ins before the downswing starts, and judge sessions on decision quality rather than the money line.

All of that requires a session log that captures more than buy-in and cash-out: stakes, hours, venue, result, and the hands worth reviewing. That is the job Overshove is built for, a live-cash session tracker and study system with a free core. Variance never goes away. Measured, it becomes a range you plan around instead of a story you tell yourself.

Running bad vs playing bad

It is the question behind every losing stretch: am I running bad, or am I just bad? Your gut cannot answer it, but your hands and your sample can.

Why your gut fails

Losing feels like playing badly even when you are not, and winning hides leaks. Emotion is the worst possible instrument for this measurement. The only reliable answers come from your decisions (hand review) and your sample (the confidence band on your win rate).

The two-part test

First, review your tagged hands from the stretch: are the losses coolers and bad beats, or repeated mistakes? Second, check whether your overall sample still supports a winning rate within its confidence band. Variance looks like good decisions plus bad outcomes over a sample too small to be sure.

Acting on the answer

If it is variance, change nothing about your strategy, only your bankroll management if needed. If it is a leak, you have something concrete to study. Either way you have replaced a spiral of doubt with a decision.

Poker standard deviation

Standard deviation measures how far your results typically stray from your win rate. It is the key input to almost every variance and bankroll calculation, and the reason two players with the same edge can have very different months.

What it actually measures

Standard deviation, usually quoted in BB/100, is the typical size of your swings around your true win rate. A bigger figure means wider results for the same long-run edge, which is why a thin-edge, high-variance game feels so streaky.

Typical live numbers

Live full-ring cash often runs lower, roughly in the 70 to 100 BB/100 range, while short-handed and online play run higher. Knowing your own figure, rather than a textbook one, makes every downstream estimate more honest.

Why it matters for bankroll

Standard deviation feeds directly into expected downswing depth and risk of ruin. The larger it is relative to your win rate, the more buy-ins you need and the deeper a perfectly normal downswing runs.

EV vs actual results

Your actual graph is what happened. Your EV-adjusted graph is what your decisions were worth before the river decided. The gap between them is variance, made visible, and reading it honestly keeps you from misjudging your own game.

What EV-adjusted means

When the money goes in, your equity has a value regardless of the card that lands. EV-adjusted results bank that value rather than the single outcome, so over a sample they strip out some of the luck of the river and show what your decisions deserved.

Above or below

Running below EV means you played better than your graph shows; running above means you ran lucky. Neither changes what to do next, but both stop you from over-correcting on results that variance, not skill, produced.

Do not over-read it

EV adjustment only covers spots where equity is well defined, mostly all-ins. It is a useful sanity check on a downswing, not a full account of your edge. Pair it with a hand review for the spots it cannot measure.

Risk of ruin, explained

Risk of ruin is the probability you lose your whole bankroll before your long-run edge takes over. It is the single number that tells you whether a roll is genuinely safe for a stake, and it falls fast as you add buy-ins or raise your win rate.

What drives it

Three things: your win rate, your standard deviation, and how many buy-ins deep you are. A bigger edge and more buy-ins push it down; bigger swings push it up. Two players with the same bankroll can have very different risk of ruin if their edges differ.

What counts as safe

Most serious players want risk of ruin in the low single digits for a stake they intend to play regularly. There is no magic threshold, but a number you can state, and accept, beats a vague sense that the roll feels fine.

How to lower it

Add buy-ins, improve the win rate, or drop to a stake where your edge is larger. A stop-loss and move-down rule keep a normal downswing from ever reaching the tail where ruin lives.