Blackjack Basic Strategy: The Chart, and the Arithmetic Under It
Basic strategy is not a system and it does not beat the game. It is the single cheapest way to play a hand, computed once and memorised.
· 10 min read
Basic strategy has a reputation it does not deserve. It is not a system, it does not beat the game, and it involves no judgement about what the dealer is holding. It is a lookup table: for every combination of your hand and the dealer’s upcard, the single action with the highest expected value, computed once, exhaustively, and then memorised.
Played perfectly under liberal Las Vegas Strip rules it leaves a house edge of 0.28%. Played badly, the same game can run several percent against you. The difference between those two numbers is the largest free improvement available anywhere on a casino floor, and it costs nothing but a few hours of memorisation.
0.28%
House edge on blackjack under liberal Las Vegas Strip rules with perfect basic strategy — the lowest priced game in the building
Wizard of Odds, house-edge comparison
Where the chart comes from: the dealer’s hand
Every decision in basic strategy is really a bet about what the dealer will end up with, and the dealer has no choices at all. They hit until they reach 17 and then stop. That makes their final hand a pure probability distribution given one visible card, and it can be computed exactly.
| Dealer upcard | One deck | Eight decks |
|---|---|---|
| 2 | 35.30% | 35.35% |
| 3 | 37.56% | 37.41% |
| 4 | 40.28% | 39.55% |
| 5 | 42.89% | 41.79% |
| 6 | 42.08% | 42.29% |
| 7 | 25.99% | 26.20% |
| 8 | 23.86% | 24.40% |
| 9 | 23.34% | 22.90% |
| 10 | 21.43% | 21.24% |
| Ace | 11.65% | 11.54% |
Dealer stands on soft 17, European rules (no hole-card peek). Figures from the Wizard of Odds blackjack appendix 2B.
The whole chart falls out of that column. Against a 4, 5 or 6 the dealer busts more than two times in five, so a hand that cannot improve should simply stand and let them break. Against a 9, 10 or Ace they bust roughly one time in five, so standing on 14 is choosing to lose four times out of five. That is the entire logic, and it explains why the chart has such a sharp boundary between the dealer’s 6 and their 7.
The rules that matter, compressed
The published chart runs to a few hundred cells, but almost all the value sits in a handful of lines. These are the ones the Wikipedia summary of basic strategy states, and they cover the overwhelming majority of hands you will actually be dealt:
- Hard 17 or more: always stand. There is no card that improves you and five that break you.
- Hard 12 to 16: stand against a dealer 2 through 6; hit against 7 through Ace. This is the bust-probability table applied directly.
- Hard 11: always double down. No dealer upcard is strong enough to make a single card at a two-unit stake the wrong play.
- Soft 17 (Ace-6): double against 2 through 6, hit against 7 or better. Never stand — a soft 17 cannot be improved by standing and cannot be broken by hitting.
- Always split Aces and 8s. Two aces played as one hand is a 12; played as two they are two hands starting at 11. Sixteen is the worst total in the game and two eights escape it.
- Never split 10s or 5s. Twenty is already close to the best hand available; a pair of fives is a 10 and should be doubled, not broken into two weak hands.
The rule changes that quietly reprice the game
A casino cannot change the arithmetic of the cards, so it changes the rules around them. These are the published effects on player return:
| Rule | Effect on player return |
|---|---|
| Single deck (versus six or eight) | +0.48% |
| Dealer hits soft 17 | −0.22% |
| No doubling after a split | −0.14% |
| Blackjack pays 6 to 5 | −1.39% |
| Blackjack pays 1 to 1 (even money) | −2.27% |
From the Wizard of Odds blackjack basics page. Figures are changes to the player’s expected return, so a negative number is a worse game.
The bottom two rows are the story of the last twenty years. A table paying 6 to 5 on a natural adds roughly 1.39% to the house edge — it takes a game priced at 0.28% and prices it near 1.7%, a sixfold increase, without altering a single card. Wikipedia describes 6:5 and 1:1 payouts as the most damaging change available to the player, and it is not close.
This is the one thing worth checking before sitting down, because it is printed on the felt and it costs nothing to read. A 3:2 table two steps away is a materially different product from a 6:5 table, and they look identical.
Insurance, and the other side bets
Insurance is offered when the dealer shows an Ace and is presented as protection. It is not protection; it is a separate bet that the dealer’s hole card is a ten, paying 2 to 1 when roughly four of every thirteen unseen cards qualify. At those proportions the bet loses money, and it loses it independently of the hand you are holding. Basic strategy declines insurance every time.
The same applies to the side bets that now ring most layouts — perfect pairs, 21+3, lucky ladies. They exist because they carry house edges several times the main game’s, and they are sold on the strength of an occasional large payout. None of them is covered by basic strategy, because basic strategy is a solution to blackjack and these are different games sharing a table.
What perfect play still does not buy you
A 0.28% edge is a very good price and it is still a price. Play a thousand hands at $25 with perfect strategy and your expected loss is about $70 — but the standard deviation is 1.142 betting units a hand, which over a thousand hands is roughly $900. The expectation is small, the noise is large, and the noise is what you will actually experience.
Basic strategy makes blackjack the cheapest entertainment on the floor. It does not make it an income, and any source that tells you otherwise is selling something.
