Six decks, dealer stands on 17, blackjack pays 3:2. Play with basic-strategy hints and the exact value of every option, then see the exact house edge of each rule and strategy.
Blackjack’s odds depend on your decisions, so the question is “what is each play worth?”. For an infinite deck — every card drawn with the same chance, 1 in 13 per rank — that can be computed exactly: the dealer’s final total by recursion, then the value of standing, hitting, doubling and splitting for every hand. Nothing on this tab is simulated.
Per unit of the first bet in each round, for an infinite deck under this table’s rules. Real shoes come out slightly better for the player: with a finite number of cards, removal effects — blackjacks come a little more often, for one — tilt toward you.
The dealer has no choices, so the final total follows from the up card alone. A 5 or 6 busts the dealer about 42% of the time — the reason basic strategy stands on stiff hands against them.
| Up card | 17 | 18 | 19 | 20 | 21 | Blackjack | Bust |
|---|---|---|---|---|---|---|---|
| 2 | 14.0% | 13.5% | 13.0% | 12.4% | 11.8% | — | 35.4% |
| 3 | 13.5% | 13.0% | 12.6% | 12.0% | 11.5% | — | 37.4% |
| 4 | 13.0% | 12.6% | 12.1% | 11.6% | 11.1% | — | 39.4% |
| 5 | 12.2% | 12.2% | 11.8% | 11.3% | 10.8% | — | 41.6% |
| 6 | 16.5% | 10.6% | 10.6% | 10.2% | 9.7% | — | 42.3% |
| 7 | 36.9% | 13.8% | 7.9% | 7.9% | 7.4% | — | 26.2% |
| 8 | 12.9% | 35.9% | 12.9% | 6.9% | 6.9% | — | 24.5% |
| 9 | 12.0% | 12.0% | 35.1% | 12.0% | 6.1% | — | 22.8% |
| 10 | 11.1% | 11.1% | 11.1% | 34.2% | 3.5% | 7.7% | 21.2% |
| A | 13.1% | 13.1% | 13.1% | 13.1% | 5.4% | 30.8% | 11.5% |
Each cell is the play with the highest expected value, computed for that hand against that up card. Click a cell to see what every option is worth.
H = hitS = standD = doubleP = split
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | A | |
|---|---|---|---|---|---|---|---|---|---|---|
| 5 | ||||||||||
| 6 | ||||||||||
| 7 | ||||||||||
| 8 | ||||||||||
| 9 | ||||||||||
| 10 | ||||||||||
| 11 | ||||||||||
| 12 | ||||||||||
| 13 | ||||||||||
| 14 | ||||||||||
| 15 | ||||||||||
| 16 | ||||||||||
| 17 | ||||||||||
| 18 | ||||||||||
| 19 | ||||||||||
| 20 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | A | |
|---|---|---|---|---|---|---|---|---|---|---|
| A,2 | ||||||||||
| A,3 | ||||||||||
| A,4 | ||||||||||
| A,5 | ||||||||||
| A,6 | ||||||||||
| A,7 | ||||||||||
| A,8 | ||||||||||
| A,9 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | A | |
|---|---|---|---|---|---|---|---|---|---|---|
| 2,2 | ||||||||||
| 3,3 | ||||||||||
| 4,4 | ||||||||||
| 5,5 | ||||||||||
| 6,6 | ||||||||||
| 7,7 | ||||||||||
| 8,8 | ||||||||||
| 9,9 | ||||||||||
| 10,10 | ||||||||||
| A,A |
Hit beats Stand by 0.0006 per unit bet.
* The standard six-deck chart (the table’s hint) doubles here instead. These are close calls — within a fraction of a cent — that the removal of the cards in play tips the other way in a real shoe.
The same calculation with one rule changed at a time. Small print on the felt matters more than it looks.
| Rule | House edge | vs this table |
|---|---|---|
| This table (S17, 3:2, double after split, split to 4) | 0.512% | — |
| Late surrender allowed | 0.426% | −0.086% |
| Split once only (2 hands) | 0.570% | +0.059% |
| No double after split | 0.653% | +0.141% |
| Dealer hits soft 17 | 0.731% | +0.219% |
| Blackjack pays 6:5 | 1.865% | +1.353% |
Exact edges for simple ways of playing, never doubling or splitting. Playing like the dealer loses because you bust first — and lose even when the dealer then busts too.
| Perfect basic strategy | 0.512% |
| Play like the dealer (hit to 17) | 5.675% |
| Never bust (stand on 12+) | 6.079% |
Deals real six-deck shoes to the cut card and plays each strategy one unit a round. Every strategy gets the same shuffles. The dashed lines are the exact infinite-deck edges.
A Hi-Lo counter plays basic strategy through the same kind of shoes and reads the true count before every round. Each round is scored twice: with a flat one-unit bet, and with a 1–8 spread (1 unit up to a true count of +1, then 2, 4 and 8 units at +2, +3 and +4 or more). Only the bet changes.