Blackjack, six decks, H17, double after split, no surrender · main bet
Standard blackjack
the plain six-deck shoe game, priced the way the rest of the world plays it, with an alternate card that never divides
Blackjack is beatable and has been public knowledge since 1962. What this page adds is the true price of that fact on a real six-deck game, plus two results the folklore gets wrong: playing skill cannot rescue bad shoes, and the graduated ramp's middle is dead weight.
The primary system below is the one the books teach. Plain hi-lo, a true count, and a graduated 1-to-8 spread, played every round. At $25 units it clears about $16 per 100 rounds and wants a $64k bankroll at 5% risk of ruin. Those are the standard terms, stated in the standard configuration so you can compare them with everything else ever written about this game.
Two measured results then reshape the picture. Even perfect knowledge of the remaining shoe recovers 8 to 9% of what a negative count costs, so there is no skill route through bad shoes, only not having money on the table. And the bet rung at true count +1 is breakeven on its own, so the graduated middle of the classic spread buys nothing. The alternate card built on those two facts, in its own section below, makes more money on about half the bankroll and never divides.
1The rules, as data
The plainest game in the pit: six decks, dealer hits soft 17, double after split, no surrender, dealt to a cut card.
Nothing exotic here. Blackjack pays 3:2, the dealer hits soft 17, you can double after splitting, there is no surrender, and the shoe is dealt to a cut card placed at 75% in the standard scenario. Every one of those choices is a parameter in the engine's configuration, and this exact configuration is the one every number on the page was measured on.
This game is also the reference point for everything else on this site. The engine that plays the exotic side bets is the same engine playing this game, so the validation it earns here travels with it.
2The published-figure gate
The engine matches the published house edge, the published dealer outcome tables, and Griffin's effect-of-removal table before any new claim gets made.
against the published record
✓house edge 0.646% vs 0.62% published, agreeing at +0.31 standard errors, and 0.624% in continuous-shuffle modeWizard of Odds✓the effect-of-removal table reproduced in sign, rank order, and magnitudeGriffin, The Theory of BlackjackBasic strategy on this ruleset measured a 0.646% house edge against Michael Shackleford's published 0.62%. The gate scored that at +0.31 standard errors, which is agreement. Switch the engine to continuous-shuffle mode, where no cut card exists, and it lands on the published figure to a tenth of a standard error, and that's the cleaner of the two checks. Dealer outcome frequencies match the published tables too.
Dealing the same hands three ways brings the cut-card effect into view without pinning it down. Dealing to a cut card reads highest, dealing a fixed number of rounds sits below it, and continuous shuffling sits lowest and on the published number. That ordering is what theory calls for, since a cut card deals extra rounds out of the ten-poor shoes that produced them. The gaps between the three modes each run about one standard error at the sample sizes I used, so the direction is measured and the size isn't. Anyone comparing this page against a published calculator should expect a couple of hundredths of a point of slack for the same reason.
One more check matters for everything downstream: the per-rank effects of removal I derived had to reproduce the classic table in Peter Griffin's The Theory of Blackjack before I trusted the machinery to derive removal effects for any bet Griffin never analyzed. It did, and that same machinery later showed hi-lo is the best balanced single-level count for this game, so the standard system's tags are a measured optimum rather than a tradition.
3The oracle
Perfect knowledge of the remaining shoe recovers 8 to 9% of what a bad count costs. The camouflage dream dies here.
The oracle for blackjack is a composition-exact expected-value calculator: give it the exact remaining shoe and it prices every decision perfectly. The most useful thing it settles has nothing to do with making money in good shoes. It answers whether skill can save the bad ones, because a counter who could survive negative counts could bet flat forever, and flat betting is invisible.
The answer is no. Composition-perfect play, which is strictly better than any index card ever printed, recovers +0.06% per round at true count −1, +0.13% at −2, and +0.24% at −4, against deficits of −1.1%, −1.5%, and −2.7%. That's 8 to 9% of the hole, and it only reaches about 22% at true count −8. The mechanism is plain once you see it: every player advantage in blackjack (the 3:2 natural, the double, the split, the right to stand) is built on tens and aces, and a shoe poor in tens and aces shrinks the options themselves. Perfect knowledge of a bad shoe mostly tells you exactly how bad it is.
The consequence, priced: a flat bettor playing every round loses about $16 per 100 rounds at $25 units, and playing every hand with composition-perfect skill still loses about $12. There is no skill route out of negative counts. There is only not having money on the table when they happen.
4The state dataset
120 million rounds, binned by true count: frequency, expected value, variance, and insurance value per bin. Profit is linear in the bet, so any ramp prices from these bins by arithmetic.
One long pass recorded, for every true count, how often it occurs and what a round is worth there, in mean and in variance, with insurance accounted separately. Blackjack profit is exactly linear in the initial bet, so once the bins exist, any betting pattern anyone can dream up gets priced with arithmetic instead of a new simulation. A live replay of three chosen patterns over 10 million fresh rounds each matched the arithmetic, worst gap two standard errors.
What the bins say about betting patterns, at $25 units: everything that pays wears the same signature. The bets have to track the count, and the correlation between bet size and true count comes out at 0.7 or higher in every profitable pattern. The money is the correlation. What a player chooses is only where that correlation shows: in the bet spread, in leaving bad shoes, or in only sitting down for good ones.
| pattern | corr(bet, count) | per 100 rounds | bankroll (5% risk of ruin) |
|---|---|---|---|
| flat bet, play every round | 0.00 | −$15.6 | — |
| flat bet, leave at TC ≤ −1 | 0.71 | +$1.2 | $63k |
| 1-to-8 spread, play every round | 0.78 | +$15.9 | $64k |
| 1-to-8 spread plus leaving | 0.84 | +$32.7 | $30k |
| only sit at TC ≥ +2, 8 units | 0.68 | +$43.5 | $35k |
5The fit, and the count
Hi-lo is the measured best of its class, and the graduated spread is the standard way to turn its curve into bets.
The count is plain hi-lo: 2 through 6 count +1, 7 through 9 count nothing, tens, faces, and aces count −1. I didn't adopt it out of tradition. The same removal-effect machinery validated against Griffin shows hi-lo is the best balanced single-level count for this game, so the tags are a measured optimum. The card is in the next section.
A running count means different things at different depths of the shoe, and the standard fix is the true count, dividing the running count by decks remaining. The standard bet shape is a graduated spread that climbs with the count, roughly in step with the advantage. That configuration is the primary on this page because it is the version the literature prices, so its numbers are comparable with every book and forum thread ever written. This site's own measurements argue with the shape itself, and that argument gets its own section further down.
Higher-order terms were considered and aren't needed, since for pricing the next round's bet, blackjack's value moves linearly with the composition. Playing deviations (index plays) measured +$3.5 per 100 rounds ± 1.6 on the alternate card, and they need true-count division, so they appear nowhere on this page's cards.
♠How to play it
The standard system: hi-lo tags, a true count, and the classic graduated spread.
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10/face | A | |
|---|---|---|---|---|---|---|---|---|---|---|
| tag | +1 | +1 | +1 | +1 | +1 | 0 | 0 | 0 | −1 | −1 |
| when | action |
|---|---|
| every card you see | add its tag to the running count |
| before each bet | true count = running count divided by decks remaining, to the nearest half deck |
| true count 0 or less | bet $25 |
| true count +1 | bet $50 |
| true count +2 | bet $100 |
| true count +3 | bet $150, and take insurance from here up |
| true count +4 or more | bet $200 |
| every hand, every count | straight basic strategy |
6Certified live
The betting patterns were replayed live against the bin arithmetic, and two older measurements from independent code agree.
Three betting patterns were replayed on 10 million fresh rounds each, bet by bet, exactly as a person would play them. The replays matched the bin arithmetic with a worst gap of two standard errors, and the average bet, the per-round standard deviation, and the bet-to-count correlation each matched to three decimals.
Two numbers on this page were also measured twice by unrelated code paths before it existed: the 1-to-8 spread's return on money and the roughly +1.1% edge of only sitting down at good counts. Both reproduced here. The alternate card carries its own dedicated certification, described in its section below.
7The ledger
About $16 per 100 rounds on a $64k bankroll. The second number decides who can actually play this.
Blackjack's edge is small and its variance is enormous, and the ratio between them sets the bankroll. An edge that is real beyond argument still wants $64k behind it at a 5% risk of ruin in the standard configuration, and the road to the long run is about 269,000 rounds. The scenario is the site's standard one: shoe game, 0.75 penetration, 5% risk of ruin. The ramp is the classic graduated spread, and it is the primary here because it is the standard of comparison, with the site's preferred shape priced in the next section.
the scenario
Penetration sensitivity
Penetration moves this result more than every other input combined. Measured on the hi-lo version of the site's alternate shape, one row of cut-card depth swings the take from about $28 per 100 rounds at 0.70 penetration to $34 at 0.75 and $46 at 0.80, with the bankroll falling as the take rises. The direction and rough magnitude carry to any pattern, because the deep end of the shoe is where counts diverge from neutral. Before anything else about a table matters, this one number decides whether the game is worth sitting at.
8The verdict
Beatable, as everyone knows. What this page adds is the price tag.
The standard system's terms are about $16 per 100 rounds on a $64k bankroll, arriving over roughly 269,000 rounds. The alternate card below improves both numbers at once and removes the mental division. One structural fact belongs next to either version: every pattern that pays correlates bets with the count at 0.7 or better, and that correlation is the exact statistic a pit is trained to see. The edge is real and public. The price of collecting it is the bankroll, the patience, and the visibility.
§The crouch, and the card that never divides
The graduated middle of the standard spread is dead weight. Remove it, add one red tag, and the card gets simpler and better at the same time.
The bet rung at true count +1 prices at −0.07% per round, breakeven within noise, so the $50 bet in the standard ramp buys nothing and the $100 rung barely pays. The shape that wins sits at the table minimum everywhere below the money counts and then jumps straight to large bets. I call it the crouch. Against a graduated 1-to-20 ramp it makes more per hour on a smaller bankroll with a shorter road to the long run, while putting less total money on the felt.
The second improvement removes division. A running count means different things at different depths, which is why the standard system divides. An unbalanced count has one exception: a single running-count value that reads the same at every depth, called the pivot. Add one tag to hi-lo, red sevens count +1, and the pivot lands exactly on the crouch's jump threshold, so the one decision carrying nearly all the money fires at a depth-exact fixed number. That count is Red 7, published by Arnold Snyder in 1983, and an exhaustive search over every count of its class, run against this game's own removal effects, returns Red 7 itself as the optimum. The popular alternative KO keeps 88%, but its pivot sits four true counts away from the money decision, which is the wrong address. On the same card stream, this card keeps 93.5% of the divided hi-lo version's earnings, so about $4 per 100 rounds is the entire price of never doing mental division.
The card was certified on its own: the literal rules below, replayed on 12 million live rounds, matched the bin arithmetic (agreement z = +0.89, time at each bet rung matching to a tenth of a percent), and the insurance rule got its first measured value, +$2.3 per 100 rounds, 73% of what composition-exact insurance would pay. An independent re-measurement a month later read +$23.2 per 100 rounds against the original +$20 ± 1, agreement z = +1.4, with a measured per-round standard deviation of $72.6.
the scenario
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10/face | A | |
|---|---|---|---|---|---|---|---|---|---|---|
| tag | +1 | +1 | +1 | +1 | +1 | +1 red, 0 black | 0 | 0 | −1 | −1 |
| when | action |
|---|---|
| start of each shoe | running count starts at 6 |
| count below 18 | bet the $15 table minimum |
| count reaches 18 | bet $100 |
| count reaches 22 | bet $200 and take insurance while it stays there |
| every hand, every count | straight basic strategy, and never divide anything |
| count falls to 0 | nothing required. Walking to an adjacent fresh shoe is worth a few dollars an hour if one exists |
Why the thresholds are 18 and 22
The slid scale is cosmetic: start at 6 instead of −12 and every threshold moves up by 18, so no number on the card is ever negative. The jump threshold, 18, is the pivot, equal to true count +2 at every depth of the shoe, and that is the whole trick, since the bet that carries nearly all the money fires at a depth-exact number. The 22 threshold doubles as the insurance line because 74% of the insurance value on this shape arrives while the top bet is out. Nothing here is knife-edge, since moving a threshold by a point costs a few percent.
§What this verdict depends on
- Six decks, dealer hits soft 17, double after split, no surrender, blackjack pays 3:2. A stand-17 game shifts every expected value about +0.2% in the player's favor, and no verdict changes.
- Penetration 0.75 in the standard scenario. The sensitivity spoiler shows how hard this input swings the result.
- Cut-card shoes only. A continuous shuffling machine kills counting completely.
- Stakes are examples: $25 units for the standard system, a $15 table for the alternate card. Blackjack profit is linear in the bet, so both rescale.
- The simulator's tracker sees every dealt card including the dealer's hole card. For betting decisions this barely matters, since hole cards are revealed at settlement before the next bet, but it is a modeling convention worth stating.
- Rounds are treated as independent for variance, stakes are fixed with no resizing, and risk of ruin is computed at 5%.
- Nothing here models how long a card room tolerates the play. The betting pattern that earns the money is the pattern surveillance watches for, and that risk is real and unpriced.
Last updated 2026-08-10.