The most coveted hand in blackjack is the fames ace-10 “natural” blackjack. Unless the dealer has a blackjack, too, then this hand always pays up 1.5 to 1. At worst, what could happen is a push, if the dealer also has a blackjack. And, of course, against ace-up, risk-averse players can wimp-out with insurance and win 1-to-1 regardless of the dealer's hand. This said, considering the importance of this hand, it is amazing how few people know what their chances of garnering a natural really are.
For most practical purposes, the probability of landing a natural can be estimated by assuming the cards come out of an infinite shoe. On this basis, the chance of your garnering a blackjack on any hand, wither yours or the dealer’s is 4.73 %. This means that you can expect a blackjack once in every 21 hands. The chances that both you and the dealer will get a blackjack at the same time are 0.22, or about one in 450 hands. In an infinite shoe, the chance a dealer's 10-up will mature into a blackjack is 7.69 percent. The chance an ace-up will become a blackjack is 30.77 percent.
Some games pay bonuses for selected blackjacks. The chance of a blackjack with two cards of the same color is 2.37 percent. The chance with both being a particular color, say red, or with both of the same suit is 1.18 percent. The chance of a blackjack in a certain suit, say spades, is 0.30 percent. And the chance of a blackjack comprising a specified two-card set, for instance the ace and king of diamonds, is 0.07 percent.
Players shopping for games might also want to be aware that the likelihood of a blackjack varies with the number of decks in a shoe. At eight decks, now standard in many casinos, the chance of any blackjack is 4.745 percent. Dropping to six decks, which most casinos offer their higher-rollers, the chance improves to 4.749 percent. Four decks raises this to 4.756 percent, two boosts it to 4.78 percent, and one deck advances it to 4.83 percent.
Shoe size also affects the probability that a dealer starting with ace-up will have a blackjack, but in the opposite direction. Ignoring what's in your own and other hands you can see on the table, here are the chances an ace-up will yield a blackjack in games with different-size shoes. Eight decks: 30.84 percent, six decks: 30.87 percent, four decks: 30.92 percent, two decks: 31.07 percent, and one deck: 31.37 percent.
What you see on the table also affects the probabilities of the dealer having a blackjack with an ace-up. The reason is that the more 10s you know have already been dealt, the less the chance the dealer will have one in the hole.
Say you're playing head-to-head with and the dealer has ace-up. In eight-deck games, if you have no 10s, one 10, or two 10s in your hand, the chance of a dealer blackjack is 30.99, 30.75, or 30.51 percent, respectively. In six-deck games, zero, one, or two 10s in your hand give the dealer 31.07, 30.74, or 30.42 percent chance of a blackjack, respectively.
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