When it comes to the number of decks in a blackjack game, the fewer the better. Most players have heard this fact somewhere along the line, but many of them don’t know why fewer is better.
I often get this question by email, where players will note that the proportion of each rank of card is the same whether the casino uses a single deck or shuffles six decks together. Regardless of how many decks are in play, we start out with one thirteenth of the cards being Aces…
Despite the initial card proportions being equal, in games with fewer decks you will be dealt more blackjacks. You will also be more successful in your double downs. How can that be, when all the ranks are equally represented no matter how many decks are used? It is because removing cards has more impact in a game with fewer decks.
To get the probability of drawing a blackjack from a single deck, we multiply the chance of drawing an Ace by the chance of drawing a ten-value card. In a single deck of 52 cards there are 4 Aces and 16 ten-valued cards (4 each of Ten, Jack, Queen, and King).
p(Ace) = 4/52 = 1/13
p(Ten) = 16/51
Note that the second line reduces the number of cards in the divisor to 51, to account for the removed Ace. And that’s where the difference lies.
We also need to double the result since we could draw either (Ace,Ten) or (Ten,Ace). Our final result is:
p(Blackjack) = p(Ace) * p(Ten) * 2 = (1/13) * (16/51) * 2 = 4.83%
The probability of drawing a blackjack from a single deck is 4.83%.
Same idea with two decks, with different numbers. 104 total cards, including 8 Aces and 32 ten-value cards…
p(Blackjack) = 8/104 * 32/103 * 2 = 4.78%.
The probability of drawing a blackjack from two decks is 4.78%.
More decks means slightly fewer blackjacks. In six decks, the probability drops further yet to 4.75%.
The same effect impacts double downs. If you double your initial hand of (6,5) for a total of 11, then you are slightly more likely to draw a face card to make 21 if the game uses fewer decks.
Astute readers may notice that the dealer gets the benefit of these changes as well. That’s right, the dealer gets more blackjacks in single deck, and the dealer draws to 21 more often just like the player. But note that a player wins 3:2 for blackjack, while the dealer gets only even money. And for hands like the double down example, the player wins twice the initial bet. So while both player and dealer get more of these good hands, the player is rewarded more handsomely for his.
It’s not all good news with less decks. For the same reason, you will get fewer dealt hands of 20! Once you remove the first ten-value card, there are only 15 tens left in 51 cards in single deck, while in double deck your chances are better with 31 out of 103.
This impact of fewer pat 20s affects players and dealers equally, so it’s really a wash.
The bottom line is that, all other things being equal, you should play in games with fewer decks. Just make sure they pay 3:2 on blackjack!