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# How Often Do Blackjacks Occur?

18 October 1999

Blackjack buffs covet those ace-10 "naturals." Unless the dealer has blackjack too, these hands automatically win 1.5-to-1. The worse that can happen is a push if the dealer does get 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.

Considering the importance of blackjacks, few solid citizens know much about the associated chances, either in garden-variety games or when special premiums are paid for some or all naturals.

For most practical purposes, probabilities of procuring blackjacks can be adequately estimated by assuming that cards come from an infinite shoe. On this basis, the chance of a blackjack on any hand, yours or the dealer's, is 4.73 percent. This means you can expect a blackjack once in slightly over 21 hands. The likelihood of you and the dealer having blackjacks simultaneously is 0.22 percent, or roughly one out of 450. In an infinite shoe, the chance a dealer's 10-up will mature into a blackjack is 7.69 percent -- one out of 13; the chance an ace-up will become a blackjack is 30.77 percent -- four out of 13.

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.

Now picture an eight-deck table with seven spots covered. You see 14 cards plus the dealer's ace. If no players have 10s showing, the dealer has a 31.92 percent chance of a blackjack. If each player gets one 10 and one low card, the dealer has 30.17 percent chance of a blackjack. If all players get two 10s the dealer has 28.43 chance of a blackjack. I shouldn't have tell you in which of these situations the most people take insurance. It's when everyone thinks they're strong with two 10s, precisely when the dealer is least apt to have the blackjack. The poet, Sumner A Ingmark, described this phenomenon thusly:

Though reason loudly says "eschew it,"
Emotion urges us to do it.
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Best of Alan Krigman
Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.