Why you hit 16 against a 10 but stand against a 6 — the expected-value logic behind all 250 cells of the basic-strategy grid.
I. What "optimal" means here
Basic strategy is the set of decisions that maximises the player's expected value (EV) for each hand, assuming no knowledge of the cards still in the shoe beyond the composition of a freshly shuffled deck. For any hand you hold and any dealer up-card, you have up to five legal actions — stand, hit, double, split, surrender — and each has a computable expected return per unit staked. The rule is mechanical: choose the action with the highest EV. Apply that rule to all 250-odd combinations of player hand and dealer up-card and the familiar colour-coded chart falls out. There is no judgement in it.
action* = argmax over { stand, hit, double, split, surrender } of EV(action | player hand, dealer up-card)
Every cell of the basic-strategy chart is the argmax above, evaluated for one player-hand / dealer-up-card pair under a fixed rule set.The house's structural advantage comes from one rule: the player acts first. If you bust, you lose immediately — even if the dealer would have busted on the same round. That single ordering is worth roughly eight percentage points of raw edge to the house before any player options claw it back. Basic strategy is the art of clawing back as much of that eight points as the rules permit, and the lever it pulls hardest is knowing when the dealer is likely to bust.
II. The engine: dealer bust frequency by up-card
Because the dealer plays a fixed, non-optional strategy (hit until 17 or more, then stand), the probability that the dealer busts from each up-card is a fixed, computable number. It is the single most important table in the game — almost every basic-strategy decision is a comparison against it.
| Dealer up-card | Approx. bust probability | Reading |
|---|---|---|
| 2 | ≈ 35% | Dealer relatively safe — a "made hand" is likely |
| 3 | ≈ 37% | |
| 4 | ≈ 40% | Dealer's weakest cards — bust more than 4 times in 10 |
| 5 | ≈ 42% | |
| 6 | ≈ 42% | |
| 7 | ≈ 26% | Strong up-cards — dealer usually makes 17–21 |
| 8 | ≈ 24% | |
| 9 | ≈ 23% | |
| 10 / face | ≈ 21% | |
| Ace | ≈ 12% | Strongest up-card of all |
Premise. Figures are the standard computed bust frequencies for a multi-deck shoe with the dealer standing on soft 17 (S17). They shift by fractions of a percent under H17 and single-deck, but the shape — a trough at 5 and 6, a peak of safety at the ace — is invariant.
III. Stiff hands — the stand-or-hit decision
A "stiff" hand is a hard total of 12 to 16: high enough to bust if you draw a ten, low enough to lose if you stand into a made dealer hand. Every stiff-hand cell is the same comparison:
stand when EV(let the dealer draw) > EV(risk busting yourself)
Stand against the dealer's weak up-cards (4, 5, 6) where the bust column above is largest; hit against 7 through ace where it collapses.This is why the chart tells you to stand on 12 against a 4, 5 or 6 even though 12 is nowhere near 21. You are not trying to reach 21 — you are trying to beat the dealer, and against a 6 the dealer beats himself 42% of the time. Taking a card there risks a bust you do not need. Against a 7 or higher the dealer's bust frequency collapses to a quarter or less, so a made hand becomes likely and you must improve your total: hit 16 against a 10. The two decisions look opposite but come from one inequality read off the bust table.
IV. Doubling — why 11 is the marquee play
Doubling doubles your stake in exchange for exactly one more card. It is only correct when the extra card is likely to build a winning hand and the dealer is not too strong. The most powerful doubling total is 11: one card of value ten (there are sixteen of them in each 52-card set, the most common single value) makes 21, and no single card can bust an 11. That combination of high upside and zero bust risk makes doubling 11 correct against every dealer up-card from 2 through 10 under standard rules.
- Double 11 vs 2–10. Best doubling spot in the game — high ten-density, no bust risk.
- Double 10 vs 2–9. Strong, but back off against a dealer 10 or ace, which out-power your likely 20.
- Double soft 13–18 vs 5–6. Only where the dealer is at his weakest; the ace's dual value removes bust risk on the draw.
V. Splitting — the three anchor rules
Splitting a pair turns one hand into two, each taking a fresh second card, at the cost of a second matching bet. It is correct only when two separate hands have a higher combined EV than the single combined hand. Three cells anchor the whole splitting grid:
| Pair | Ruling | Why (EV logic) |
|---|---|---|
| A-A | Always split | Combined = 12 (weak). Split = two hands each starting at 11, the best total in the game. |
| 8-8 | Always split | Combined = 16 (worst hard hand). Split replaces it with two hands starting at 8, each with better prospects. |
| 10-10 | Never split | Combined = 20 wins ~92% of the time. Splitting trades a near-certain winner for two drawing hands. |
| 5-5 | Never split | Treat as a hard 10 and double where allowed — two 5s are a doubling hand, not a splitting one. |
VI. Soft hands — the free draw
A soft hand contains an ace counted as 11 (A-6 = "soft 17"). Its defining property: a single card can never bust it, because the ace silently reverts to 1 if the draw would exceed 21. That makes soft totals uniquely aggressive. You never stand passively on soft 17 — you hit it, or double it against a weak dealer up-card, because the downside of drawing is capped while the upside is not. Soft-hand cells are the clearest illustration that the goal is expected value, not a target number.
- The whole chart is one rule — pick the highest-EV action — evaluated for every hand-versus-up-card pair.
- The dealer bust table is the engine: weak up-cards (4–6) mean stand your stiffs; strong up-cards (7–A) mean improve them.
- 11 is the marquee double; aces and eights always split; tens and fives never do.
- Soft hands are hit or doubled aggressively because a single card cannot bust them.
- Perfect basic strategy makes the game as cheap as the rules allow — roughly 0.4% on a good six-deck game — but never negative for the house.
VII. When the chart changes
Basic strategy is rule-specific. A change to the rule set shifts both the house edge and, occasionally, a handful of cells. The naturals payout is the single biggest edge lever; the others move the number by tenths of a percent. Our companion derivation, how rule variants move the house edge, itemises each lever, and what the house edge actually is shows the formula those figures come from.
| Rule change (worse for the player) | Approx. edge added |
|---|---|
| Naturals pay 6:5 instead of 3:2 | ≈ +1.4 percentage points |
| Dealer hits soft 17 (H17) instead of standing | ≈ +0.2 pp |
| No double after split (no-DAS) | ≈ +0.14 pp |
| No surrender offered | ≈ +0.08 pp |