Single deck blackjack
Single deck blackjack, with decent rules, is a very good game.
Find a single deck played to the rules S17/ DOA / no DAS and you have
a game with approximately a 0% house edge and 100% average return; 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:
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More blackjacks
•
Less dealer blackjacks when player has blackjack
•
Greater value for doubles
•
Increased chance of the dealer busting
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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 single deck.
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 5
and a 6 for an 11 total, and the dealer has a 9. Out of the remaining
49 cards there are sixteen 10s, 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 10s, or a 413/128 = 31% chance
of pulling a 10.
Looking at it the other way round: in the single deck
there are 18 remaining 2s through 6s 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 5 would
be very useful to the dealer. The proportion of remaining 5s 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.
The above 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, basic strategy for both S17 and H17 games.
Dealer final hand probabilities based on up card gives the probability of all dealer outcomes
based on the upcard.
•
BJ Info
Single deck basic strategy chart,
customisable, from Ken Smith's basic strategy engine.
6:5 Blackjack? Just say No! Ken makes the point that there may well come a time that
casinos will replace all standard blackjack games with the 6:5 blackjack payoff if players don't take a stance against it.
•
Modern blackjack
6:5 Blackjack uses a chart to graphically illustrate the cost of the single eck 6:5 game.
•
Las Vegas Sun
New blackjack odds further tilt advantage toward the house
is another diatribe against 6:5 blackjack which reserves its best line for the end: “if you come across a table that pays 6-5 for blackjacks, don't worry about
whether to hit, stand or double down...just split.”
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