Poker variance: how big normal downswings really are
Variance is the gap between your win rate and your results over any sample you actually play. Here are the real numbers: what a winning player can lose over ten thousand hands, and how long it takes results to mean anything.
Variance in poker is the spread between your true win rate and the results that any actual stretch of play hands you. It exists because the edge in this game is thin and the noise is loud: a strong winner earns perhaps 5 big blinds per 100 hands, while the standard deviation of those same 100 hands runs 80 to 100 big blinds. The signal is a whisper under a jet engine. Every practical truth about handling the game's swings, and most of the ways players deceive themselves, follow from that ratio.
The numbers, honestly
Take a genuine 5bb/100 winner with a standard deviation of 90bb/100, standard figures for no-limit cash, and project results over growing samples at 95 percent confidence:
| Sample | Expected profit | Realistic range (95%) | In 100bb buy-ins |
|---|---|---|---|
| 1,000 hands | +50bb | -510 to +610bb | -5 to +6 |
| 10,000 hands | +500bb | -1,260 to +2,260bb | -13 to +23 |
| 100,000 hands | +5,000bb | -580 to +10,580bb | -6 to +106 |
Read the middle row twice, because it is the one that reprices intuition: across ten thousand hands, months of live play or a solid month online, a true winner's ordinary outcomes include losing thirteen buy-ins. Nothing broken, nothing unfair, no leak to find; that is what a 90bb standard deviation does to a 5bb edge at that distance. And the bottom row's left edge says something stranger: even at a hundred thousand hands, the unlucky tail of a genuine winner is still slightly under water.
The flip side deserves equal honesty: the same table generates false winners. A breakeven player runs at plus 20 buy-ins across 10,000 hands just often enough to fund a lasting delusion, which is the polite explanation for a fraction of every stakes' regulars.
Why your win rate is a rumour
Turn the same arithmetic onto measurement. The uncertainty in a measured win rate shrinks with the square root of the sample, and at 100,000 hands it is still about plus or minus 5.6bb/100 at 95 percent confidence. A player who has recorded 4bb/100 over that sample is, statistically speaking, somewhere between a strong winner and a slight loser. Six figures of hands to get a blurry answer; a live player at 25 hands an hour needs 4,000 hours for the same blur.
The practical conclusion is not despair; it is a change of instrument. Results cannot certify skill on human timescales, but decisions can be graded immediately. A hand replayed against a solver baseline tells you tonight whether the line was right, which is the entire design premise behind reviewing hands properly and this site's daily trainer: the grade tracks the choice, never the runout. Judge yourself on the input the cards cannot vote on.
What variance is not
- Not a malfunction. Downswings are not evidence the game is rigged or that your opponents' calls "always" get there. Their bad calls losing on average and winning sometimes is exactly the deal you signed.
- Not reducible for free. You can shrink swings by nitting down, but a tighter, more passive game usually shrinks the win rate along with the variance and the trade is rarely worth it. Variance is the price of the edge, not a fee you can negotiate away at the table.
- Not an excuse, either. "Just variance" is also how leaks hide. The test is outcome-blind review: if the decisions grade well, it was the deck; if they do not, the downswing has co-authors. Coolers covers the single-hand version of that audit.
Living with it
The tools are structural, and they are the same three every time. A bankroll sized off the real numbers above, so that a 13 buy-in stretch is an entry in a ledger rather than an emergency. Tilt control built on the expectation of these swings, because most tilt is variance misread as injustice. And review that grades decisions, so improvement continues straight through the stretches when results say nothing. Get those three in place and variance is reduced to what it actually is: noise, with your edge compounding quietly underneath it.
Bottom line
Variance is the spread around your win rate, and in no-limit hold'em the honest numbers are humbling: a 90bb/100 standard deviation against a 5bb/100 edge means double-digit buy-in downswings inside ordinary luck for a genuine winner, and win rates that stay blurry past a hundred thousand hands. You cannot shrink it without shrinking your edge; you can only build for it, with a bankroll that absorbs it, a temperament that expects it, and a review habit that measures what you control. The players variance ruins are the ones who took results personally; the ones it merely delays graded their decisions and kept playing.
Frequently asked questions
- What is variance in poker?
- Variance is the natural spread between your true win rate and the results you record over any finite sample. It exists because the outcome of each hand is mostly luck even when each decision is skill, and it is the reason good players have losing weeks and bad players have winning ones.
- How big is a normal downswing?
- Bigger than intuition allows. With a standard deviation near 90bb per 100 hands, a genuine winner should expect stretches of 10,000 hands that lose more than ten 100-blind buy-ins to occur as part of ordinary play, and multi-week breakeven stretches are unremarkable for even strong players.
- How many hands until my win rate is reliable?
- More than almost anyone wants to hear. At 100,000 hands the 95 percent confidence interval on a measured win rate is still roughly plus or minus 5.6bb/100, wide enough to blur a solid winner into a breakeven player. Treat any figure from under six figures of hands as an estimate, not an identity.
- How do you handle variance?
- Structurally, not emotionally: carry a bankroll sized for the real swing sizes, grade your play by decision quality against a solver baseline rather than by results, and treat downswings as scheduled weather. Variance cannot be reduced at the table without also reducing your edge; it can only be survived and priced in.