Blackjack math
Blackjack Odds: The Working Numbers Every Player Should Know
You do not need a simulator at the table. You need about a dozen numbers: how often the dealer busts, how often you bust when you hit, how often the natural arrives, and what a hand actually wins. Here they are.
Published Wednesday, May 20, 2026 · 10 min read
Blackjack odds have a reputation for being a specialist’s subject, something you need software and a weekend to understand. The working set is actually about a dozen numbers, and they fit on an index card. How often the dealer busts. How often you bust when you take a card. How often the natural shows up, what a hand really wins, and what the payout line does to all of it.
This page is that index card, with the reasoning attached.
The blackjack odds that do the work
Start with the four numbers that carry the rest of the article. The dealer busts about 28% of the time. Your chance of busting when you hit a stiff runs from 31% at 12 to 62% at 16. A blackjack arrives about 4.75% of the time, one hand in twenty-one. And a played hand wins 42.4%, pushes 8.5%, loses 49.1%, per Wizard of Odds’ ten-billion-hand simulation.
Everything strategic in the game is an argument between those figures. Basic strategy is not a table of folk wisdom; it is the ledger of which risk is smaller in each spot, your bust chance against the dealer’s, computed once and memorized forever.
Your bust chance when you hit
Count a full deck’s mix and the one-card bust chances fall out directly. Sixteen of 52 cards are worth ten, so a hard 12 breaks on the next card about 31% of the time. Each step up the stiff ladder adds another rank of fatal cards:
| Your hard total | Cards that bust you | Chance the next card busts you |
|---|---|---|
| 12 | any ten-value | ≈ 31% |
| 13 | ten-value or 9 | ≈ 39% |
| 14 | ten-value, 9 or 8 | ≈ 46% |
| 15 | ten-value, 9, 8 or 7 | ≈ 54% |
| 16 | anything above a 5 | ≈ 62% |
The dealer, remember, climbs the same ladder with no say in the matter: house rules force a hit on every total through 16. That is the symmetry the whole game balances on. When the dealer shows a 6, the likeliest hole cards leave a stiff that must take a 54% or 62% gamble whether the dealer likes it or not, and your correct response is to stand back and let the rulebook do the busting.
Two readings matter. First, hitting a 12 is far safer than it feels; more than two-thirds of the time the card helps or at least doesn’t kill you. Second, even the 62% on a 16 can be the right price, because the alternative is standing on a total that only wins when the dealer busts. Against a dealer 7 or higher, that bust arrives too rarely to save you, so you hit anyway and accept the ugly math. Soft hands, for completeness, cannot bust on one card at all, which is why the ace is the engine of aggressive doubling.
How the dealer’s hand finishes
The dealer has no decisions, so their outcome distribution is a fixed piece of arithmetic. On the standard multi-deck game where the dealer stands on soft 17, the finishing line looks like this:
| Dealer final result | Frequency |
|---|---|
| 17 | ≈ 14.6% |
| 18 | ≈ 13.8% |
| 19 | ≈ 13.5% |
| 20 | ≈ 17.6% |
| 21 (multi-card) | ≈ 7.4% |
| Blackjack | ≈ 4.8% |
| Bust | ≈ 28.4% |
The two spikes tell the story. Bust is the single most common outcome, which is why letting the dealer break is a legitimate plan against weak upcards. And 20 is the most common standing total, which is why your 18 and 19 win less often than intuition suggests. The overall 28.4% bust figure hides enormous swings by upcard, from the low teens against an ace to the low forties against a 5 or 6; the full per-upcard breakdown lives on our dealer bust odds page and is worth ten minutes of anyone’s time. It is also the raw material for the entire dealer-bust wagering family graded on the side-bet board.
The natural: one hand in twenty-one
The probability of being dealt a blackjack on a six-deck game is about 4.75%. One hand in twenty-one, in the game of twenty-one. Nobody planned that; the ranks did.
The dealer draws naturals at the same 4.75% rate, of course, and this is one of the few places the rules tilt your way. When the dealer’s blackjack beats you, it collects exactly one bet. When yours beats the dealer, it collects one and a half. Same frequency, unequal consequences, and that half-bet difference on a one-in-twenty-one event is a meaningful slice of why the game is as close to fair as it is.
Rarity is exactly why the payout line dominates the game’s economics. At 3:2, the natural is a small, regular bonus that offsets the fact that you lose more hands than you win. At 6:5 the bonus is cut by 40 cents on the dollar, and because it lands on nearly one hand in twenty, the damage compounds to 1.39% of total action, per Wizard of Odds’ rule tables. In odds terms: the difference between a 3:2 and a 6:5 felt is bigger than the difference between playing perfectly and playing sloppily. The full accounting of what each printed rule costs sits in the house edge guide, but the one-line version travels well. Read the payout line before you read anything else.
Win, push, lose: the per-hand ledger
Now the number that surprises people. With sound play you win 42.4% of hands, push 8.5%, and lose 49.1%. Those figures come from Wizard of Odds’ simulation of roughly ten billion hands under liberal six-deck rules, and they hold steady enough across common rule sets to treat as the game’s resting pulse. The house wins the hand-count contest outright, every shoe, every night. Blackjack odds still land within half a percent of even because the wins are heavier than the losses: naturals pay 3:2, and doubling puts extra money out precisely in the spots where you are the favorite, while the dealer can never double back.
That asymmetry is the entire game. Protect it and you keep the 0.5% price; squander it and you don’t. Declining a double to “stay safe” trades your best-priced moments away, and buying insurance bolts a separate 7.4% leak onto a 0.5% game. The felt is full of invitations to trade heavy wins for frequent ones. All of them are priced against you.
One consequence deserves its own sentence: losing sessions are normal, common, and predicted by the math, at every skill level.
Streaks, variance, and what the odds don’t promise
Per-hand blackjack odds say nothing about the shape of a night, and the shape is where bankrolls go to die. Ignoring pushes, a resolved hand loses about 53.6% of the time, so five losses in a row show up about once every 23 stretches. Across a three-hour session you should expect several such runs, plus a streak or two the other way. The standard deviation on a hand is a bit over one bet, so a 100-hand session at $15 swings a few hundred dollars either side of expectation as a matter of routine.
Put a full session in those terms. Three hundred hands at $25 puts $7,500 through the game; at a 0.5% edge the expected cost is about $38, roughly a nice dinner. The standard deviation on that session is around $500, which means finishing anywhere from $500 up to $550 down is thoroughly ordinary, and a genuinely hot or cold night lands well outside even that. Anyone judging their skill, their system or their luck on one evening’s result is reading noise and calling it a signal.
None of it carries information. The shoe holds no memory of your last hand, only a composition of remaining cards, and unless you are tracking that composition the next hand is priced like the last one. Progressive betting systems, Martingale first among them, rearrange when the variance hits you without moving the average a cent. The blackjack odds on the next hand are the blackjack odds on the last one, indifferent to everything you have felt about either.
So carry the index card and let it set expectations: 28% dealer busts, 62% on your hit-16, one natural per twenty-one hands, 42.4% wins. The casino’s whole business model is knowing those numbers while you play on vibes. Knowing them back is free, and it is the only edge the house will hand you at the door.