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Single Deck Blackjack

Single-deck vs. Multiple-deck games

If you walk into a casino to play blackjack and notice several single-deck and six-deck blackjack games, which on would you play? You preference will probably be the single-deck game; because you remember reading somewhere that a single-deck game is a better game for players. But do you know why? And is it always a better game for players than multiple-deck games?

Many blackjack theoreticians have determined that the number of decks of cards in play has a great influence on the casino’s edge over a typical basic strategy player. The table below shows the effect the number of decks has on the casino’s edge (assuming typical Las Vegas Strip rules).

Number of Decks Casino’s Edge
1 -0.01
2 0.32
3 0.43
4 0.49
5 0.52
6 0.54
7 0.56
8 0.57


As the number of decks increase, so does the casino’s edge. But you may have noticed that the increase is not at a consistent rate. The rate increases rapidly and then begins to taper off as the number of decks increases. When you move from a single deck game to a double deck game, the casino’s edge increases from a player’s advantage of 0.01 percent to a casino’s advantage of 0.32 percent. This represents an increase in the casino’s favor of 0.33 percent. With more than six decks, the increase in the casino’s edge becomes very small and levels out to about 0.6 percent. This is one reason why you will never see more then eight decks being used on a blackjack table. Even if it were possible for the casinos to be able to deal a game with one hundred decks of cards, their edge would be about the same as an eight-deck game.

There are several reasons why the casino’s edge increases when more card are put into play and at first glance, it may be hard to understand why this is so.

There are more blackjacks in single-deck games vs. multiple-deck games.

Since the percentage of Aces and Tens in single-deck games are the same in a multiple deck game you are probably wondering how this statement can be true. Well the effect of removing a card from a single-deck game affects the percentages of the remaining cards to a much greater extent than in a multiple-deck game.

Suppose you shuffled a single a single deck of cards and wanted to know what your chances are that the first card you select from the shuffled deck will be an Ace and the second card a ten, Jack, Queen or King to give you a blackjack hand.

Because there are only four Aces in a single deck of cards, the chance of drawing one of those Aces is expressed as a ratio of 4 over 52. Once you draw the Ace, you’re left with only 51 cards out of which to draw a ten-value card. There are 16 ten-value cards in a deck of cards, so the chance of drawing a ten-value card as the second card is expressed in the ratio of 16 over 51. If you multiply these two ratios, you find that the probability of drawing an Ace, then a ten-value card from a 52-card deck is 2.41 percent:

4/52 x 16/51 = 2.41 percent


Of course you could have just as easily drawn the ten-value card first, followed by the Ace. Therefore, the overall probability of getting a blackjack in a single-deck game is twice 2.41 percent, or 4.82 percent. This translates into approximately one blackjack every 20.72 hands dealt to you. This is an important statistic – if you are not getting a blackjack hand at least once out of every 21 hands, don’t be to surprised if you are not winning.

The following chart summarizes the probabilities of getting a blackjack for double, four, six and eight-deck games using similar calculations. On average, a player will get fewer blackjacks as the number of decks increases. In fact, you’ll only be 98 percent as successful at drawing a blackjack in an eight-deck game compared to a single-deck game, which makes the single deck game better.

Probability of getting blackjack vs. number of decks of cards
   
Number of decks Probability
1 1 in every 20.72 hands
2 1 in every 20.93 hands
4 1 in every 21.02 hands
6 1 in every 21.07 hands
8 1 in every 21.07 hands


Although getting more blackjacks is good for the player, it’s even better when you get a blackjack and the dealer doesn’t. This brings us to reason number two of why the casino’s edge increases when the number of decks of cards increases:

The dealer’s chances of duplicating a blackjack decrease as the number of decks decreases.

When a player gets a blackjack and the dealer does not, the player is paid out at 3 to 2. But if the dealer also has a blackjack, then the hand is a tie and the player wins nothing. Therefore, the less chance the dealer has of getting a blackjack, the more times you will be paid the bonus 3 to 2 payoff and your earnings potential will increase.

Once you get a blackjack, the dealer has a 20 percent less chance of getting a blackjack in a six or eight deck game compared to a single deck game.

Why?

The answer, in laymen’s terms, is that once you remove an Ace and ten-value card in an single deck game, there is still a large pool of non-tens/Aces cards left. This decreases the dealers’ chance of drawing another Ace and ten-value card.

The math proves the point. Once you remove an Ace and a ten value card from a single deck of cards, the probability of the dealer getting a blackjack is:

Probability of drawing an Ace = 3/50

Probability of getting a ten-value card = 15/49

When you multiply the above ratios, then double the result to take into consideration the reverse (drawing a ten-value card first, then the Ace), the overall probability of you and the dealer both getting a blackjack is once in every 27.25 hands. The corresponding probabilities for two, four, six and eight decks are summarized in the table below.

Probability of dealer getting blackjack after player gets a blackjack vs. number of decks
   
Number of decks Probability
1 1 in every 27.25 hands
2 1 in every 23.74 hands
4 1 in every 22.34 hands
6 1 in every 21.92 hands
8 1 in every 21.71 hands


Blackjack pushes are about 20 percent more likely in a six or eight deck game, which reduces our earnings potential. This makes the single deck game a much better game.

When you double down, you are more likely to get the card you want in a single deck game compared to a multiple deck game.

The mathematical basis for this is the same as the reasons given above – namely, the effect of removing a card is much more pronounced in single deck games than that of multiple deck games.

Lets look at an example with the player drawing a two card 11 and the dealer showing a 5. The player is looking for a 10 draw to finish off the hand with a total of 21. In a single deck game, the chance of the player getting a ten-value card after the three cards are removed from the deck is expressed as the ratio of 16 over 49, or 32.6 percent.

When we increase the game to a six deck game, the ratio becomes 96 over 309 or 31.07 percent. This means that a player is 5 percent less likely to reach 21 in a six deck game when compared to a single deck game. Or to put it another way, you are more likely to be successful doubling down in a single deck game than in a multiple deck game, making a single deck game the better game.

As the number of decks increase, the casino’s advantage on the insurance bet increases.

When the dealer’s upcard is an Ace, the dealer will offer to the players the option of making an insurance bet which is equal to half of the player’s current bet. The player wins the insurance bet at 2 to 1 odds if the dealer’s downcard is a ten-value card giving him a blackjack. If the dealer’s downcard is not a ten-value card, then the player’s insurance bet is lost.

It is very easy to calculate the casino’s advantage on the insurance bet. In a single deck game, the probability that the dealer’s downcard will be a ten-value card is 16 over 51 (one card is already removed from the deck – the dealer’s ace). The probability that the dealer’s downcard will be a non-ten value card is 35 over 51. To compute the casino’s edge, you multiply the corresponding probabilities by the payoff) +2 when you win and -1 when you lose) and add up the result:

(16/51 x 2) + (35/51 x -1) = -5.8 percent


The casino’s edge on the insurance bet for a six deck game is

(96/311 x 2) + (215/311 x -1) = -7.4 percent


Taking insurance is a bad bet in a single deck game (the casino’s edge is 5.8 percent), but it becomes an even worse bet in a six deck game (the casino’s edge is 7.4 percent).

When less is more

On the surface, it appears that a single deck game is always a better game than a six deck game, but be careful. The casinos can increase the house edge by altering the rules which they can and often do.

Presently, the best single deck blackjack rules are ones in which the playing rules are: dealer stands on soft 17, players can double down after pair splitting, and re-splits are allowed. The player has a .13% edge over the casino in this type of game, which means a basic strategy player has a slight edge over the casino without card counting.

If a casino removes the option that allows a player to double down after pair splitting, the player’s edge would drop to .01%. The player still has the edge, all be it a tiny one. By simply making the dealer hit on soft 17s rather than standing, the casino gets the edge at 0.18 percent. The very worst rule from the player’s perspective is when casinos pay even money on blackjacks.

This next table summarizes the casino’s edge for various single deck blackjack games currently offered in casinos throughout the country. It shows you how the casinos can increase their advantage in single deck games simply by altering the playing rules.

Casino’s edge in single deck games vs. playing rules
   
DAS = Double after pair splitting
HIT 17 = Dealer hits on soft 17
RAS = Re-split Aces
Stand 17 = Dealer stands on soft 17
LS = Late surrender
   
Rules Casino’s Edge
Stand 17, DAS -0.13%
Stand 17 -0.01%
Hit 17, DAS, LS +0.12%
Hit 17, DAS +0.06%
Hit 17, LS +0.10%
Hit 17, re-split aces allowed +0.15%
Hit 17 +0.18%
Hit 17, No re-splits +0.22%
Stand 17, LS, Double only on 10 +0.23%
Stand 17, Double only on 10 +0.25%
Stand 17, Double only on 10, no re-splits +0.29%
Hit 17, Double only on 9 +0.32%
Hit 17, LS, Double on 10 only +0.41%
Hit 17, Double on 10 only +0.44%
Stand 17, DAS, RSA, BJ pay even money +2.6%


In most cases, a single deck game with one poor rule such as the dealer hitting on a soft 17, is still better then most six or eight deck games. But look around there are favorable six deck game being offered where the casino’s edge is only 0.26 percent, making it very competitive to some single-deck games. Sometime in the same casino that ups the casino’s edge on their single deck games.

For the most part, single-deck games are a better game for the basic strategy player. But be smart and check the playing rules to be sure that the casino hasn’t negated the inherent low casino edge of single deck games with a bunch of unfavorable rules.

Number of decks Casino’s Edge Difference
1 +0.01 -
2 -0.32 0.33
3 -0.43 0.11
4 -0.49 0.06
5 -0.52 0.03
6 -0.54 0.02
7 -0.56 0.02
8 -0.57 0.01




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