Variance: Why You Cannot Tell If You Are Winning

Updated 24 August 2026

The standard deviation of a single blackjack hand is about 1.13 bets — roughly 250 times the house edge on that hand. That ratio is the whole reason a session, a weekend, or often a month tells you nothing at all about whether you are playing well.

The short version

One hand: standard deviation 1.13 bets, expected loss 0.0046.
After 1,000 hands the swing is about 36 units, the expected loss only 4.6.
Swings grow with the square root of hands; the edge grows linearly.
That is why the edge eventually wins, and why it takes so absurdly long.

Every figure here is computed with our own solver and checked against an independent reference. The calculator applies the same numbers to your table.

What normal looks like

Flat-betting one unit with correct basic strategy on a six-deck game:

Hands played	Expected result	Standard deviation	Two thirds of results fall between
100	-0.5 units	11.3 units	-12 and +11
500	-2.3 units	25.3 units	-28 and +23
1000	-4.6 units	35.8 units	-40 and +31
10000	-45.6 units	113.2 units	-159 and +68

Read the 1,000-hand row. You expect to lose about 4.6 units, and two thirds of the time you will finish somewhere between -40 and +31. Finishing up 30 units after 1,000 hands is completely ordinary and means nothing.

The swing is the bar. The edge is the small number beside it. They only cross after tens of thousands of hands.

Why the edge eventually wins

The expected loss grows in proportion to the number of hands. The swing grows with the square root of it. Play a hundred times as many hands and your expected loss is a hundred times larger while the swing is only ten times larger.

That is the entire mechanism by which a casino makes money, and the entire mechanism by which a counter does. Neither works in an evening. Both work over a year.

How we computed the standard deviation

Most sites quote 1.14 or 1.15 from a textbook. We carried the second moment through the same recursion that produces our expected values: for every possible pair of player cards against every dealer upcard, both the average result and the average squared result.

That gives 1.1322 for six decks. It is slightly below the usual published figure, and we know why: our split calculation treats the two hands as independent when they in fact share the dealer’s card, which understates the variance a little. Splits are about 2% of hands, so the effect is small — but it is there, and we would rather say so than round to the number everyone else prints.

Keep reading

Risk of ruinwhat the swing can do Bankrollhow much to bring Losing streakshow normal they are

By Martin Kosek · every number on this site is computed by us, not copied.

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