Single deck blackjack

Single deck blackjack, with decent rules, is a very good game. Find a single deck played to the rules S17, D.O.A, no D.A.S and you have a game with 0% house edge and 100% average "payout"; add just one more deck and the house edge increases to 0.33%; go up to eight decks and the house edge hits 0.59%.

Why do more decks have such a pronounced effect?

Answer: the effect of the removal of individual cards is much greater in single deck than multi-deck. This has four consequences which are advantageous to the player:

• More blackjacks
• Less dealer blackjacks when player has blackjack
• Greater value for doubles
• Increased chance of the dealer busting

• Related single deck blackjack pages

More blackjacks

How can there be "more" blackjacks in one deck than in two, five or twenty? It comes down to the greater likelihood of pulling a ten on an ace, or an ace on a ten, in single deck, based on the increased significance of the removal of individual cards.

In a deck of 52 cards there are four aces, so you have a 4/52 chance of pulling an ace as your first card. Having pulled your ace, you have a 16/51 chance of pulling a ten on your ace to make your blackjack. Doing the whole thing the other way around, you have a 16/52 chance of pulling a ten as your first card, followed by a 4/51 chance of pulling an ace. Add those two scenarios together - ((4/52) × (16/51)) + ((16/52) × (4/51)) - and you get 4.826%, which works out at one blackjack in every 20.71 hands.

Now do the same calculation for eight decks: ((32/416) × (128/415)) + ((128/416) × (32/415)) - and you get 4.745%, or one blackjack in every 21.07 hands. Although the difference seems practically very small, getting that extra 3:2 payoff two percent more often in single deck is important.

Less dealer blackjacks when player has blackjack

The chances of the dealer having a blackjack to push the player's blackjack are much reduced in single deck. The removal of the ace has the most notable effect, since the ace-richness of the deck is reduced by fully 25%, the player having one of the four aces in his blackjack. The calculations are the same as the above blackjack calculations, except that there are now three aces out of the 52 card deck and fifteen tens, and the deck is two cards short (player blackjack cards), giving us the following sum: ((3/50) × (15/49)) + ((15/50) × (3/49)) = 0.0367, or 3.67%. For eight-deck, we have: ((31/414) × (127/413)) + ((127/414) × (31/413)) = 0.046, or 4.6%. The chances of a dealer blackjack pushing player blackjack are 25% greater in eight-deck.

Greater value for doubles

A hard double hand - 9, 10 or 11 - is comprised of those small cards you don't want to receive as your "double" card - ideally you would like a ten card on any of those hands. While this is also true of multi-deck games, those two small cards are greater in relation to the remaining cards in single deck than in multi-deck.

For example, suppose you're dealt a five and a six for an eleven total, and the dealer has a nine. Out of the remaining 49 cards there are sixteen tens, giving you a 16/49 = 32.6% chance of pulling a ten. Assuming the same situation at the start of an eight deck game, out of the remaining 413 cards there are 128 tens, or a 413/128 = 31% chance of pulling a ten.

Looking at it the other way round: in the single deck there are 18 remaining twos through sixes out of the 49 remaining cards; 18/49 = 36.7% chance of pulling a small card on your eleven double. In the eight deck game, it works out to 158/413 = 38.3% chance of pulling a small card.

Increased chance of the dealer busting

Correct player strategy against small dealer upcards is to stand on hands which can be busted with the draw of an extra card - hands such as 10/6, 8/7, 9/5, 8/6, 8/5 etc (see the generic basic strategy chart). Typically, those player hands will contain at least one small card that would be useful to the dealer, and the removal of that one small card is again more pronounced in single than multi deck.

To give an example: Suppose you have 8/5 against a dealer 6; the five would be very useful to the dealer. The proportion of remaining fives to total unseen cards in single deck is 3/49 or 6.1%. In eight-deck the proportion is 31/413, or 7.5% - giving the dealer an extra 1.4% of fives available to him in the multi-deck game. This is only one example of MANY possible permutations; however, if you add together all the 49 possible "small two cards versus dealer small upcard" permutations, the collective value works out at -19.78% in single deck and -20.87% in eight-deck. Translated into money terms, based on a \$10 bet you would "average" a loss of \$1.97 in single deck and \$2.08 in eight deck.

Individually, all these little extras don't seem to amount to much, and neither are they at all intuitively obvious; they DO, however, make a big difference to the overall return of the single deck game in relation to multi-deck.

Related single deck blackjack pages

Wizard Of Odds - single deck basic strategy charts
Wizard Of Odds - dealer final hand probabilities based on up card

BJ Math - single deck S17 expected value charts
BJ Math - single deck H17 expected value charts
BJ Math - blackjack probabilities

BJ Info - single deck basic strategy chart (you can customise it)
BJ Info - 6:5 Blackjack? Just say No!

Modern blackjack: 6:5 Blackjack

Las Vegas Sun - Taking a hit: new blackjack odds further tilt advantage toward the house