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Math

Variance

The natural gap between actual results and expected win

Definition

Variance is the statistical dispersion of your results around your expected value (EV). Poker is a game of thin edges repeated thousands of times: even playing perfectly, your short-term results swing violently around their average. Variance isn't a malfunction — it's the reason bad players keep playing (they sometimes win), and therefore the very source of good players' profit. It's measured by the standard deviation, expressed in bb/100 hands in cash games (typically 80-100 bb/100 in 6-max, more in heads-up). Concretely: a winner at 5bb/100 with an 80bb/100 standard deviation still has roughly a one-in-four chance of being down after 10,000 hands. Downswings of several dozen buy-ins are part of a winning player's normal trajectory. In tournaments, variance is multiplied by the payout structure, concentrated on the very top places: an excellent MTT player can string together hundreds of tournaments without a big score without their real ROI being in question. The two defenses: a bankroll sized to absorb the dips, and judgment based on decision quality rather than results. A variance simulator makes these orders of magnitude visible — and vaccinates against tilt.

Concrete example

Win rate 5bb/100, standard deviation 80bb/100. Over 10,000 hands your expected profit is 500bb, but the standard deviation of the cumulative result is 800bb: finishing anywhere between −300bb and +1,300bb is unremarkable, and you're a loser in about 27% of cases. Over 100,000 hands the probability of being down falls below 3%: variance dilutes, it never disappears.

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Variance in poker — Definition | Forge.poker