What a basic strategy chart is actually doing

Every cell in a basic strategy chart answers one question: given your total and the dealer's upcard, which of hit, stand, double, split and surrender is worth the most? Not which one wins. Which one is worth the most. In a large share of the grid every option is bad, and the chart is telling you which flavour of bad to take.

People memorise the grid, play it cleanly for a year, and never learn that it is a ranking of losses computed against one specific set of rules. So they cannot tell when the grid they memorised is the wrong grid for the table they are sitting at.

What the grid looks like

Ten columns, one per dealer upcard: 2, 3, 4, 5, 6, 7, 8, 9, 10, ace. Tens and face cards share a column, because they are the same card to the arithmetic.

The rows come in three blocks.

• Hard totals, 5 through 19. No ace, or an ace that has to count as one.
• Soft totals, A,2 through A,9. Hands where the ace can still be eleven without busting, which is why they play differently from the same total hard.
• Pairs, 2,2 through A,A. Asked as pairs rather than as their totals, because 8,8 is a splitting decision and hard 16 is not.

Thirty-three rows, ten columns, 330 cells, one letter in each: H hit, S stand, D double, P split, R surrender. Two of those letters are conditional. Double and surrender are not always on offer, and when they are not the cell falls back to a second choice — which is not the same second choice everywhere, and is where most memorised charts go wrong.

The chart is downstream of the rules

Six decks, dealer stands on soft 17, double after split allowed, blackjack pays 3:2, 75% penetration. Perfect basic strategy on that game leaves the house 0.41%.

Change one line. Same game, except the dealer hits soft 17: 0.63%. You played correctly both times. The game got 0.22 percentage points more expensive while you did nothing.

Change a different line instead. Same game, dealer still standing on soft 17, but blackjack pays 6:5: 1.77%. The payout line costs 1.36% on its own, taking the game to more than four times the price of the same table with 3:2 intact — from a change most players read as decoration.

Change both, hits soft 17 and 6:5, and that six-deck game runs 1.99%. Two changes, not one. No single rule takes 0.41% to 1.99%.

So "the basic strategy chart" is a category error. There is a chart per rule set. The charts differ in surprisingly few cells; the cost of a rule is mostly in the rule, not in the cells. Take the 0.41% game and switch the dealer to hitting soft 17, and exactly three of the 330 decisions move:

• Soft 19 against a 6. Stand becomes double.
• Soft 18 against a 2. Stand becomes double.
• Hard 11 against an ace. Hit becomes double.

Three cells. Not "a handful", not "about half a dozen" — three, and they are the whole difference between the two grids. The rule charges you the 0.22 whether or not you ever find them, because the cost is in the dealer making 17s he would otherwise have stood on.

The engine underneath: whose bust is it

The dealer has no choices. The upcard is not a threat, it is a forecast, because everything the dealer does afterwards is fixed by the rule card.

How often the dealer breaks, by upcard — published Wizard of Odds dealer-outcome tables, six decks, dealer stands on soft 17. Change the deck count or the soft-17 rule and these move, which is why the number is worthless without the placard attached to it:

The cliff is between 6 and 7: 42.1% down to 26.0%. And 5 breaks more often than 6 does — 42.9% against 42.1% — which is the reverse of the folklore about the dealer's worst card.

The mechanism is visible in the row. A dealer showing 5 with a ten in the hole is on 15 and is required to draw, into a shoe where roughly 31% of the cards are ten-valued. A dealer showing 8 with a ten in the hole is done.

That is a race, and a race has two runners. The upcard alone does not decide the cell, which is where the "stand against the dealer's small cards" version of the rule breaks.

Worked hand: where the hard 12 line falls

Every stiff from 13 to 16 stands against 2 through 6, and hits against 7 through ace unless surrender is offered and takes the cell. Hard 12 does not follow that pattern. Hard 12 stands against 4, 5 and 6 only. Against a 2 and against a 3 it hits.

Those two cells are among the most-missed in the grid, and they fall out of the two bust rates put side by side.

Standing on 12 wins on exactly one branch: the dealer busts. Twelve beats nothing that stands. Seventeen through 21 all beat it. So standing is worth the dealer's bust rate and nothing more — 35.3% against a 2, 37.6% against a 3, 40.3% against a 4.

Hitting 12 loses the hand on the spot when the next card is ten-valued, and four of the thirteen ranks are: about 31%. That is the cheapest instant loss of any stiff. Hitting 13 breaks on 5 ranks in 13, 38%. Hitting 16 breaks on 8 in 13, 62%. (One card, thirteen equally weighted ranks, an ace counted as one wherever eleven would break the hand — not a shoe-composition figure.)

Two facts meet at 12: it is the one stiff cheap enough to hit, and 2 and 3 are the two weakest bust rates in the small-card family. Against a 2 you are handing over 31% to a dealer who breaks 35.3% of the time, and keeping the 69% of draws that improve a hand that beats nothing — and hitting wins, by a small margin. At a 4 the dealer's bust rate has climbed to 40.3%, enough to pay for giving up the draw, and standing takes over. That is where the line falls, and the margin on either side of it is thin. Thin enough that guessing gets these two cells right about half the time and teaches you nothing.

Now the same total against a 7. The dealer makes 17 or better three times in four; his bust rate is 26.0%. Standing on 12 is playing for that one branch and losing on all the others. You take the 31% because the alternative is a hand that wins almost never.

Most of the right-hand side of the hard-totals chart is this: not plays you expect to win, plays that lose less. Where late surrender is offered, 16 against a ten is a surrender — you pay half to stop playing, because half is cheaper than playing it out.

Aces and eights, for two different reasons

Both are always splits. The arithmetic is not the same arithmetic.

Aces. Played as one hand, A,A is a soft 12, and a ten does nothing for it. The ace's flexibility is wasted the moment it is stapled to another ace. Split, and each half begins on the strongest card in the deck: four of thirteen ranks make 21 immediately. Most six-deck games deal one card to each split ace and refuse a redraw or a resplit. Split anyway. You are converting one dead hand into two live ones.

Eights. Sixteen is the worst total in the game. Eight of the thirteen ranks break it, and standing loses to every made dealer hand. Split and each half starts at 8, which is live: a ten makes 18, a three makes 11 to double on.

Splitting 8,8 against a ten is not a winning play. Both halves are underdogs. It is in the chart because it is the cheapest of the available losses. If your model of the chart is "these are the plays that win", 8,8 against a ten will feel wrong for as long as you play. If your model is "these are the cheapest available losses", it is obvious.

Where DAS actually shows up

DAS is double after split. It is usually described as moving the double rows. It does not, really — it moves the split rows, because doubling is a thing that happens after a split.

Take 2,2 against a 3. Split it and each half is a 2 that might draw a 9 for 11. With DAS you double that 11. Without it you hit, and the split is worth less. Enough marginal splits sit right on that line — pairs of 2s and 3s against small upcards, 6s against a 2, 4s against 5 and 6 — that they flip from "don't" to "do" when the option exists. The pair section is the most rule-sensitive part of the whole grid and the part most players learn last.

The genuine double rows move with a different rule: a game that restricts doubling to hard 9, 10 and 11 deletes the soft doubles outright. The fallback is not one action, and this is where charts get misremembered. A,2 through A,6 against the dealer's small cards stop being doubles and become hits. A,7 does not. Soft 18 against 3, 4, 5 and 6 falls back to standing.

A reader who learns it as "the soft doubles become hits" will hit soft 18 against a 4. That is a real and expensive misplay, on a hand that was already good enough to stand. Soft 19 against a 6 — the H17 double — falls back to standing too. Nobody announces any of this at the table.

Worked hand: soft 18 against a 9

A,7 against a dealer 9. Basic strategy hits it. Everybody hates it.

Eighteen is a good-looking total and a bad hand here. Against a 9 the dealer's most likely made total is 19. Eighteen loses to 19, 20 and 21, ties 18, and beats only 17 and a bust — and a 9 breaks 23.3% of the time. Standing is not marginal, it is losing.

Hitting a soft 18 cannot bust. Worst case you land on a hard total and play it out. Best case an ace, a 2 or a 3 gives you 19, 20 or 21. It is a free re-roll on a hand that is behind. It feels wrong because hitting 18 feels like risking a good hand, and 18 against a 9 was never a good hand.

Worked hand: insurance, the one cell that says never

The dealer shows an ace and offers insurance at 2:1 that the hole card is ten-valued. A 2:1 bet needs the event to happen more than one time in three to break even: 33.33%.

Six decks, ace exposed: 96 ten-valued cards among 311 unseen. That is 30.87%.

30.87 against 33.33 required. It loses, every time, and it loses in the same way when the dealer offers you "even money" on your blackjack, which is the same bet wearing a different hat.

The chart does not say never because insurance is a sucker bet. It says never because 30.87 is smaller than 33.33 off the top of a six-deck shoe. Change the composition of the shoe and the answer changes. That is the only cell in the grid whose "never" has an expiry date, and it is the door that everything past basic strategy walks through.

What the chart cannot do

Play the 0.41% game perfectly and the house keeps 0.41%. Basic strategy is the floor. It is the price of admission on the best commonly available six-deck game and it is not an edge.

The floor moves with what is printed on the felt. Six decks, dealer stands on soft 17, DAS, 75% penetration, blackjack pays 6:5: perfect basic strategy leaves the house 1.77%. Correct play on a bad game is still a bad game, and the chart cannot tell you which one you are sitting at — the sign on the table can.

Those tables are the common ones now. On the Las Vegas Strip, 275 of 855 tables paid 3:2 in a September 2022 Vegas Advantage survey, down from 720 in 2010. No single-deck 3:2 game is left in Las Vegas at all; the last one closed at El Cortez on 28 April 2024.

The territory past the chart is smaller than people expect. Counting is legal in the United States; it is arithmetic done in your head, not a device and not cheating, though a casino is a private business and can bar you for it. And counting alone does nothing: perfect counting on that six-deck stand-on-soft-17 game with no bet spread is worth about -0.2%. Still negative. The edge lives in bet sizing, and the published realistic band for a skilled counter is 0.5% to 1.5%.

At that scale the variance is the story. Take a reference ramp — the Wizard of Odds six-deck Hi-Lo column: 1-to-10 spread, 4.5 of 6 decks dealt, Illustrious 18 plus Fab 4. It reports an advantage of 0.587%, an average bet of 1.68 units, and a standard deviation of 2.27 units per round. Their simulated game is more liberal than the 0.41% floor, so every figure taken from that ramp — including all of the ones in the rest of this section — is an upper bound on the game you will actually find.

Over one hour, about 70 hands at a six-deck table with four or five players, the swing is 27 times the expectation. Over 100 hands it is 23 times. The ratio is 230.2 divided by the square root of the number of rounds, so it improves with volume, at the speed of a square root. N₀, the point where expectation equals one standard deviation, sits at 52,960 hands: about 757 hours at 70 an hour. Standing there, the chance of still being behind is about 16%, which is the one-sigma tail doing what tails do. Sitting through it requires 782.5 minimum bets for a 5% risk of ruin on that ramp — $19,562 at a $25 table — and 1,202.9 units for 1%. None of that is a statement about what anyone takes home. It is the shape of the arithmetic.

What to do with all this

Ask five questions before you sit: how many decks, does the dealer hit soft 17, does blackjack pay 3:2, is double after split allowed, is surrender offered. Then learn the chart for that game, not a generic grid off an image search.

The Cut Card renders one free, no account, at thecutcard.com/chart. You set the placard; all 330 cells are computed from it rather than looked up, so the three cells the soft 17 rule moves actually move, and the double and surrender fallbacks are the ones your table would force on you.

Learn it as a bust race plus a small set of rules for turning dead hands into live ones, and most of the cells you cannot recall become derivable at the table. Then drill the ones you get wrong instead of the ones you already know: the misses cluster in the pair rows, the soft doubles, and hard 12 against a 2 and a 3 — which is exactly where the rule set and the fallbacks move things. That is the argument for the drill on the same site, which builds the chart from the rules you set, tracks the cells you actually miss, and prints the rule set beside every edge figure it shows.