Blackjack
Hit, stand, double and split against a real shoe with a blocker card. Every value is solved over the cards actually left, so nothing here is sampled.
Twenty-one against the shoe
- exactsolver
- 1–8decks
- counton show
Manual
- Object.
- Beat the dealer’s total without passing 21. A two-card 21 is a blackjack.
- Dealer
- draws to 17 and then stops, and peeks for blackjack under an ace or a ten.
- You may
- hit, stand, double for one card, or split a pair. Split aces receive a single card each.
- Every figure at the table is exact.
- The shoe is tracked rank by rank and the values are solved by recursion over what is actually left, not sampled — so there is no ± anywhere in this game.
The game and the decisions
Beat the dealer’s total without passing 21. Cards count face value, pictures count ten, and the ace is eleven until eleven would bust — a hand still counting an ace as eleven is soft, one that cannot is hard. A two-card 21 on the original deal is a blackjack and pays 3:2.
On your turn the choices are: hit (draw a card), stand (keep the total), double (twice the stake for exactly one more card), split (turn a pair into two hands for a second stake), and, where the house offers it, surrender (give the hand up for half the stake back). Every one of those choices has a number on it, and this app shows the numbers.
The dealer’s book
The dealer has no choices. They draw to 17 and stop, and at this table the house default is to hit a soft 17 — the common shoe-game rule, worth about 0.2% to the house. With an ace or a ten showing, the dealer peeks for blackjack before you act, so you never double or split into a natural.
That fixed book is what makes the game solvable: from any upcard, the dealer’s final totals follow from the shoe alone, and every value at this table is computed by recursion over the cards actually left.
The numbers
Measured by the engine, matched against published figures:
| Dealer busts showing 6 · stands all 17 | 42.3% |
| Dealer busts showing 6 · hits soft 17 | 43.9% |
| You are dealt blackjack | ~4.55% |
| House edge, playing the exact solver | ~0.5–0.7% |
Basic strategy, the highlights
A handful of lines carry most of the lesson:
| Hard 11 v 6 | double |
| Hard 12 v 6 | stand |
| Hard 16 v 10 | hit — borderline |
| Hard 20 | always stand |
| Soft 18 v 9, 10 or A | hit |
Counting
Hi-Lo assigns +1 to every 2–6 that leaves the shoe, −1 to every ten and ace, and divides the running count by the decks remaining to get the true count. A positive true count means the shoe is rich in tens and aces — more blackjacks for you, more dealer busts, doubles that pay better.
The whole story fits in one table. Dealer showing 6, solved exactly:
| Full shoe · dealer busts | 43.9% |
| Full shoe · double on 11 is worth | +0.665 |
| Forty tens gone · dealer busts | 38.3% |
| Forty tens gone · double on 11 | +0.380 |
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The cheat that demonstrates this lives in Training: pull tens and aces out of the shoe by hand and watch those figures — and the house edge on the betting screen — move as you pull.