Blackjack:
Two-card hand consisting of an ace and a ten-value.

Duke :
Two-card hand consisting of two ten-valued cards.

Flat-Betting : A rule which casinos may impose on a player suspected of counting cards,
whereby that player is only allowed one size of bets between shuffles.

Pat :
Non-busted hand totalling 17 or more.

Snapper : Another name for a blackjack.
Also a chip worth 2½.

Stiff :
Hand with a hard total between 12 and 16.

(2012-08-15) Casino Rules

In casino blackjack,
the dealers plays according to fixed rules, irrespective of the player hands.
They hit until they hold a total of 17 or more (a so-called "pat hand").
One common variant of the rule (which favors the dealer) is that
a dealer hits "soft 17" (i.e., an hand with at least one ace which would add
up to 8 if aces were always counted as 1).

Single or Multiple-Deck Blackjack :

Blackjack pays 3 to 2 :

Historically, games used to be offered where blackjacks (natural 21)
paid 2 to 1. This gives too much of an advantage to the player.
Some modern games pay only 7 to 5 or 6 to 5, which isn't a good enough compensation.
For an acceptable reduction in the house edge which makes blackjack
attractive to players, it's about right to
play blackjacks 3 to 2. This is what's offered by most casinos
(except for single-deck play).

Does 21 tie a blackjack ?

Reno Doubling

Doubling-down is only allowed on a total of 10 or 11.

Major Rule Variations

%

Rule

Strip

Reno

NJ

Europe

0

4 decks

0

Hole Card

Novelties :

"Triple 7", "6-7-8" and "6-card 21" pay 3 to 2.

"Six-card Charlie". Six-cards without busting is an automatic win.

(2012-08-15) Basic Strategy (against multiple-deck shoe)
Playing by "the Book": Player Hand vs. Dealer's Up Card.

The first accurate basic strategy for blackjack (assuming single-deck play)
was devised between 1953 and 1956 by
"The Four Horsemen of Aberdeen":
Roger Baldwin,
Wilbert Eddie "Preach" Cantey
(1931-2008),
Herbert Maisel and
James McDermott.
They were statisticians in the U.S. army at the time, using only desktop mechanical calculators.
Their result was published as an 11-page article in the
Journal of the American Statistical Association entitled
"The Optimum Strategy in Blackjack" (Sept. 1956).
They introduced the first rudimentary system of card-counting in their book
"Playing Blackjack to Win" (92 pages, 1957) five years before Edward O. Thorpe
formally proposed one (in "Beat the Dealer", 1962).

It's understood that you should stand
(stay, don't ask for more cards) when holding a total of 19 or more.
Likewise, you should simply hit (ask for more cards)
when holding 8 or less.
Otherwise, proceed as indicated by the following tables,
where each line corresponds to the total you hold and
each column to the dealer's up card.
Use the right chart for "soft" totals
(where one ace is counted as 11) and the left chart
otherwise (which also indicates when it's advisable
to split a pair corresponding to that total).

Hard Total

Dealer's Up Card

Split Pair

2

3

4

5

6

7

8

9

X

A

18

S

S

S

S

S

S

S

S

S

S

9,9

17

S

S

S

S

S

S

S

S

S

S

16

S

S

S

S

S

H

H

h

h

h

8,8

15

S

S

S

S

S

H

H

H

h

H

14

S

S

S

S

S

H

H

H

H

H

7,7

13

S

S

S

S

S

H

H

H

H

H

12

H

H

S

S

S

H

H

H

H

H

6,6

11

H

H

H

H

H

H

H

H

H

H

10

H

H

H

H

H

H

H

H

H

H

5,5

9

H

H

H

H

H

H

H

H

H

H

8

H

H

H

H

H

H

H

H

H

H

4,4

6

H

H

H

H

H

H

H

H

H

H

3,3

4

H

H

H

H

H

H

H

H

H

H

2,2

Soft Total

Dealer's Up Card

2

3

4

5

6

7

8

9

X

A

s 18

S

S

S

S

S

S

S

H

H

H

s 17

H

H

H

H

H

H

H

H

H

H

s 16

H

H

H

H

H

H

H

H

H

H

s 15

H

H

H

H

H

H

H

H

H

H

s 14

H

H

H

H

H

H

H

H

H

H

s 13

H

H

H

H

H

H

H

H

H

H

A,A

H

H

H

H

H

H

H

H

H

H

Always split a pair of aces (or eights).
Never split Xs (K,Q,J,10) or fives.
Else, split if entry is underscored.

Bold (H, S): Double-down if allowed.
Lowercase (h): Surrender if allowed.
S = Stay (refuse cards). H or h = Hit.

Only clueless people or card counters will ever perform the following
weird plays, which automatically attract the attention of casino surveillance:

Doubling down a stiff (i.e., a hard total of 12 or more).

Splitting a pair of ten-value cards.

Doubling-down a blackjack !

What the above tables summarize are the following rules:

Hitting :

Hit a stiff (hard 12-17) against an up-card of 7 or more.

Hit a 12, except against 4,5,6.

Hit soft 17, stand on hard 17.

Hit soft 18 against 9, X or A.

Pair Splitting :

Always split Aces and 8s.

Never split Ts (always stand).

Split 9s against 2,3,4,5,6,8,9 (stand against 7,X,A).

Split 7s against 7 or less.

Split 6s against 6 or less.

Never split 5s (hit against A or X, otherwise double-down).

Split 4s only against 5 or 6.

Split 2s or 3s against 4,5,6,7.

Doubling-Down :

Double-down 11 except against an ace.

Double-down 10 except against X or A.

If allowed, double-down 9, S17, S18 against 3,4,5,6.

If allowed, double-down S15 or S16 against 4,5,6.

If allowed, double-down S13 or S14 against 5,6.

Surrendering :

If allowed, surrender H16 against 9,X,A.

If allowed, surrender H15 against X.

The above rules and the corresponding charts are for multiple decks.
With a single deck, there are only a few differences:

Double-down with a soft 19 (off-chart) against a 6.

Don't hit a pair of 7s against a ten. Surrender if possible, else stand.

Surrender a pair of 7s against an ace, if you're allowed. Otherwise hit.

With a hard 16 consisting of three or more cards, stand against a ten.

(2013-08-30) What to do when you're not allowed to split a pair of aces?
Answer: If allowed, double-down against a 6 or hit otherwise.

This rare situation would arise if the casino rules don't allow resplitting a
pair of aces but do allow hitting or doubling-down after a split
(many casino will just serve a single card to each half of a splitted pair of aces).

Although I'm not aware of a single house whose rules allow this,
a truly complete basic strategy should cover that case...
It's properly covered in the above charts, because this page
is part of a mathematical site !

(2013-08-19) Blackjack enumerations using polynomials
How many sequences of k cards have a blackjack score of n ?

Let's use
generating polynomials method, introduced elsewhere on this site.
If the value of aces was always 11, the answer (with a full deck)
would be the coefficient of z^{n }x^{k}/k! in the product:

In 1820, legalized and house-banked blackjack appeared in New Orleans.
In the mid-1800s, a French woman nicknamed "Madame Moustache"
(Eleanore Alphonsine Dumant, c.1834-1879)
banked and dealt the game of 21 against any taker, in various places throughout the Old West,
including her own parlor (called "Vingt-et-un")
on Broad Street, in Nevada City, CA.

In 1931, the state of Nevada legalized gambling and house-banked blackjack was established.

System Smitty
(Benjamin F. Smith)
and Greasy John were known to consistently win at blackjack in the 1950s.
They never revealed their systems.