The probabilities for the dealer’s final totals vary considerably based on what kind of upcard she’s showing. The probability of most interest to most players is how likely it is for the dealer to bust. If the dealer has an excellent chance of busting her hand, it makes it a lot easier to stand in certain situations.
Dealer probabilities also make a considerable difference to blackjack tournament players. Basic strategy varies in tournament situations because the player has to weigh the odds of losing the tournament when making the right strategy decision. One of your main goals in a tournament, especially in the early levels, is to stay alive until you need to start taking risks. Weighing the various probabilities for the dealer’s final hand can make that decision a lot more accurate.
If the dealer hits on a total of soft 17, the casino gains 0.22% on their edge. This change in the rules also affects the probabilities of various totals for the dealer, but those changes are generally pretty minor. A tenth of a percentage here or there on whether or not the dealer will bust doesn’t have a major effect on your basic strategy decisions, which is why most basic strategy charts will work on most blackjack games.
If the casino is using multiple decks, then the house edge increases. The more decks in use, the better the odds are for the casino. A single deck game is the best situation for the player, as it increases the player’s edge against the house by 0.48%. The worst case scenario is to play against 8 decks or more.
Of course, having multiple decks in play also changes the various probabilities of outcomes for the dealer, too. But just like the soft 17 rule, the changes are largely minor on individual totals, and they don’t result in very many or very major changes in the correct strategy decisions.
The ideal situation for a blackjack player is for the dealer to bust. The odds of the dealer busting on a hand go up dramatically with some cards, while it goes down dramatically with other cards. The numbers below are based on a single deck game where the dealer stands on all 17s, including soft totals of 17.
The dealer is most likely to bust when she has a 5 showing as her upcard. In that situation, she has a 42.89% chance of busting. The 4 and the 6 are also cards in which the dealer is apt to bust, with a 40.28% chance and a 42.08% chance, respectively.
Any upcard between 2 and 6 represents a good chance for the dealer to bust , in fact. Even a total of 2 or 3 will bust the dealer more than once every 3 hands. The odds are 35.3% and 37.56% respectively.
On the other hand, if the dealer has a 7 or higher showing, her chances of busting fall dramatically, especially when she has an ace showing. (That shouldn’t be a surprirse, as an ace can count as 1 or 11, so it’s harder to bust with an ace.) The odds of busting with a 7 showing are 25.99%, and the odds of busting with an 8, 9, or 10 are almost identical: 23.8%, 23.34%, and 23.25%, respectively. The dealer only has a 16.98% chance of busting when she has an A showing.
What does that mean for the player? It means that the player has to make riskier and more aggressive plays when the dealer is showing a 7 or higher.
Standing on a hard total of 13, 14, or 15 versus a dealer 2 through 6 makes a lot of sense when you realize that the dealer has at least a 35% chance of going bust in that situation. You can decide to stop taking cards, but the dealer has to take a hit on any total of 16 or less, which means you can just hope for the dealer to bust rather than trying to improve your hand. Since your odds of the dealer busting in those situations is better than the chance of improving your hand, you stand on that total and hope.
On the other hand, if the dealer has a 7 or higher showing, she usually has a less than 25% chance of busting, which means that if you have a hard 13, 14, or 15 showing, you’re usually better off trying to take another card and improving your hand.
Looking at some of the other probabilities facing the dealer can also help explain some of the other basic strategy decisions you might make. For example, you’ll stand on a total of 20 versus a dealer 8. One of the reasons you do that is because the dealer only has a 6.83% chance of also getting a 20 (which would result in a tie in that situation) and a 6.98% chance of getting a 21, which is the only way the dealer could beat your 20. That’s a great situation to be in, but it’s also great to understand the math behind why.
All of these probabilities, of course, assume that the dealer has already looked at her hole card and determined that she doesn’t have a blackjack. Of course, if she already has a blackjack, the game is over before it’s even begun, and there are no probabilities to calculate. She’s already won (or at least tied).
The probability of the dealer going bust in that situation is 0%.