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# In Blackjack, Choose Shoes to Avoid Hurting Defeat

18 July 1994

Here's a quick quiz for blackjack buffs:

1) Do the odds of getting a blackjack go up, stay put, or fall with an increase in the number of decks per shoe?

2) Since your chance of a blackjack is the same as the dealer's, is there a benefit to raising the likelihood of this hand?

More is better

Start with question 2. It's easier. The higher the likelihood of a blackjack, the better for you. Why? When the dealer gets blackjack, you lose your bet. When you hit, you win one and a half times your bet. Ties don't matter.

Say you're betting \$10 in a game where you and the dealer each get five non-tied blackjacks. The dealer's slammers cost you \$10x5 or \$50. Yours pay you \$15x5 or \$75. A nice \$25 profit. If you each had ten blackjacks, they'd cost \$10x10 or \$100 and pay \$15x10 or \$150 \$50 net win. More is better.

Less is more

Question 1 has a simple answer. As the number of decks per shoe goes up, the chance of getting a blackjack goes down. But, the reason is complex.

With one deck, over long periods of play, blackjacks will be dealt in 4.826 percent of all hands. Two decks drops this to 4.780 percent. In a four-deck shoe, it's 4.756 percent. At six decks, the figure is 4.749 percent. And in an eight-deck game, blackjack can be expected 4.745 percent of the time.

Say you're playing a one-deck game with no knowledge of anything previously drawn. The 52 cards include four aces and sixteen 10-values. The probability that your first card is an ace is 4 out of 52, or 4/52. The probability that your second card is a 10-value is 16 out of the 51 remaining cards, or 16/51. You'll also have blackjack if your first card is a 10-value (probability is 16/52) and your second card is an ace (probability is 4/51). Find the overall probability of a blackjack from the following formula, which works out to 0.04826 or 4.826 percent:

[(4/52)x(16/51)] + [(16/52)x(4/51)]

Here's the skinny for two decks; figure the rest yourself if you like. Out of 104 cards, eight are aces and thirty-two are 10-values. The probability of starting with an ace is 8 out of 104 or 8/104. The probability you'll then draw a 10-value is 32 out of the 103 remaining cards. Extending this to 10-A gives the following formula, which works out to 0.04780 or 4.780 percent:

[(8/104)x(32/103)] + [(32/104)x(8/103)]

How much more

Fewer decks offer more chances of blackjack. More blackjacks mean more profit. But, how much more?

Imagine you play 1000 statistically-correct \$10 hands. With one deck, you and the dealer each expect 48.26 blackjacks. If none tie, your theoretical win is \$5x48.26 or \$241.30. At two decks, you expect to make \$5x47.8 or \$239.00. Four decks lowers this to \$5x47.56 or \$237.80. Six decks drops probable profit to \$5x47.49 or \$237.45. And eight decks shrinks it to \$5x47.45 or \$237.25.

Differences predicated purely on probable blackjacks are real but not large. At \$10, going from one to six decks theoretically only costs \$3.85 per thousand hands. For eight decks, add another \$0.20. So, is it worth scouting out small shoes? Decide on your own, based on the odds of getting a blackjack and on other ways you think shoe size impacts your game. Still, as Sumner A Ingmark, the players' poet, prophetically penned:

Here a fraction, there a fraction,
Buttressing the betting action,
Sought amongst the expert faction.

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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.