Blackjack Basic Strategy

♥♣

The chart computed for your table's rules · a trainer that drills it cell by cell · the exact house edge, and what each rule costs

How this works, and what "exact" means here

There is no chart in this page

There is a description of your table and a solver. Ten dials with two to five settings each is a few thousand distinct games, and a few thousand hand-typed charts is a few thousand chances to ship a wrong cell — so the grid is computed from the rules every time they change. A rule and its chart cannot disagree.

That is also why every cell holds one action instead of a footnote. A printed chart has to serve every rule set at once, so it carries "Ds — double if allowed, otherwise stand" and leaves you to work out which you are. This one knows whether your table allows doubling after a split, so the cell just tells you what to do.

The payout is the exception that proves the rule

A 6:5 blackjack does not move a single cell of the chart. You never make a decision holding a blackjack, so there is nothing for the payout to change — and it still moves the house edge by 1.36 points, more than every other rule on this page put together. Players who "adjust" for 6:5 by playing differently give up the edge twice. The Rules tab prices it next to everything else.

The cells nobody ever learns

Misplaying 16 against a ten costs about four thousandths of a bet. That is far too small to show up in a night's results, or a year's, so nothing at a table ever corrects it — which is exactly why those cells are the ones people carry wrong for decades. The chart marks them and the Trainer has a mode that deals nothing else.

What is exact, and what is not

The dealer's outcome distribution is a dynamic program over every hand they can reach — no simulation, no infinite-deck shortcut. It reproduces the standard published table to four decimal places in all seventy cells.

The four cards dealt face to face every hand — your two, the upcard, the dealer's hole card — are removed from the shoe exactly, so the chart is composition-dependent: T,6 and 9,7 really are solved as different 16s. Cards drawn after that come from the residual composition without further removal, which is the one approximation and the standard one. On six decks it moves an EV in the fourth decimal place.

The peek matters too, and it is easy to miss: behind a ten the dealer has looked and does not hold an ace, so the shoe you are about to draw from is short of everything except aces. Pricing a 12 against an ace without that is wrong by about 0.007 of a bet.

Why you should believe the house edge

Because it is checked against something that shares no code with it. test-blackjack.mjs shuffles a shoe, deals four cards, reads the chart the way a player does, splits into real hands under a real four-hand cap and settles against a dealer who actually drew. At 40 million hands per rule set the two land inside one standard error of each other — the six-deck S17 game at −0.8σ, H17 at +0.4σ, single deck at −0.5σ, and the European no-hole-card game at −0.5σ.

Where this engine and that simulation agree with each other but disagree with a published rule-effect figure, they win, and the harness records why. Two of them do.

What this is not

This is basic strategy — the best play knowing only your cards and the dealer's upcard. There is no card counting here, no running count and no bet spread. Basic strategy is what makes the rest possible and it is the only part that pays off from the first hand.

Built by Kevin Braner. If a number here is wrong, tell me: [email protected].

For entertainment & analysis only. No real-money gambling.