Exact figures for an infinite shoe (very close to 6 or 8 decks), dealer stands on soft 17. Dealer figures assume he has already checked for blackjack, as in most casinos.
Your chance of busting if you take a card
| Your hand (hard) | Cards that bust you | Bust chance |
|---|---|---|
| 11 or less | none | 0% |
| 12 | 10, J, Q, K | 31% |
| 13 | 9 to king | 38% |
| 14 | 8 to king | 46% |
| 15 | 7 to king | 54% |
| 16 | 6 to king | 62% |
| 17 | 5 to king | 69% |
| 18 | 4 to king | 77% |
| 19 | 3 to king | 85% |
| 20 | 2 to king | 92% |
A soft hand (with an ace counted as 11) can never bust with one card: the ace becomes 1.
How the dealer finishes, by up card
| Card | Bust | 17 | 18 | 19 | 20 | 21 |
|---|---|---|---|---|---|---|
| 2 | 35% | 14% | 13% | 13% | 12% | 12% |
| 3 | 37% | 13% | 13% | 13% | 12% | 11% |
| 4 | 39% | 13% | 13% | 12% | 12% | 11% |
| 5 | 42% | 12% | 12% | 12% | 11% | 11% |
| 6 | 42% | 17% | 11% | 11% | 10% | 10% |
| 7 | 26% | 37% | 14% | 8% | 8% | 7% |
| 8 | 24% | 13% | 36% | 13% | 7% | 7% |
| 9 | 23% | 12% | 12% | 35% | 12% | 6% |
| 10, J, Q, K | 23% | 12% | 12% | 12% | 37% | 4% |
| Ace | 17% | 19% | 19% | 19% | 19% | 8% |
This table explains all of basic strategy: against 2 to 6 the dealer busts often, so you stand on 12 to 16 and double more. Against 7 to ace he usually ends on 17 or more: a 16 only wins if he busts, so you hit.
16 against a 10: if you stand, you only win when the dealer busts (23%). If you hit, you bust 62% of the time, but when you don't you often have a real hand. Both lose; hitting (or surrendering if allowed) loses slightly less.
The chance of a blackjack
An ace plus a 10-value card on your first two cards: about 4.75%, roughly one hand in 21. The dealer has the same chance. Paid 3 to 2, blackjack is a big part of what the player wins back; paid 6 to 5, the house edge goes up by about 1.4 points. Avoid 6:5 tables.
The insurance math
The dealer shows an ace and offers insurance: you bet half your stake, paid 2 to 1 if he has a 10 underneath. In a 6-deck shoe, about 96 of the remaining 311 cards are 10s: roughly 31%. Insurance would need more than 33.3% to break even.
Result: insurance loses about 7% of the amount insured. Taking "even money" on a blackjack is the same bet. Only a card counter takes it, from a Hi-Lo true count of +3 (see card counting).
The house edge
| How you play | House edge |
|---|---|
| Perfect basic strategy (6 decks, 3:2, common rules) | about 0.5% |
| Same, but blackjack pays 6:5 | about 1.9% |
| Playing "by feel" | 2 to 4% |
| Mimic the dealer (hit to 17, never double) | about 5.5% |
| Card counter with a wide bet spread | -0.5% to -1.5% (player edge) |
The game's simulator plays hundreds of thousands of hands in seconds with your own rules: try the simulator.
You know the numbers. Would you have hit?
Take the quizFAQ
What are the odds of a blackjack?
About 4.75%, roughly one hand in 21 with 6 decks.
Which dealer card busts the most?
The 5 and 6 (about 42%), then the 4 (39%). With an ace, the dealer busts only about 17% of the time.
How often does the dealer bust overall?
About 28% of the time across all up cards. The player busts more often because he acts first: that is where the house edge comes from.
Do cards already dealt change the odds?
Yes, a little: that is the idea behind card counting. Many small cards gone = a shoe rich in 10s and aces, better for the player.