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(2013-09-01)  

• 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 ablackjack. Also achip worth 2½.
• Stiff : Hand with a hard total between 12 and 16.

(2012-08-15)  

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 thata dealer hits "soft 17" (i.e., an hand with at least one ace which would addup 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 blackjackattractive to players, it's about right toplay 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)  
Playing by "the Book": Player Hand  vs.  Dealer's Up Card.

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 andeach column to the dealer's up card. Use the right chart for "soft" totals (where one ace is counted as 11)  and the left chartotherwise  (which also indicates when it's advisableto split a pair corresponding to that total).

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)  
Answer:  If allowed, double-down against a 6 or hit otherwise.

This rare situation would arise if the casino rules don't allow resplitting apair 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 theabove charts, because this pageis part of a mathematical  site !

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

Let's usegenerating 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  zⁿ x^k/k! in the product:

(1 + z¹¹x / 1! + z²²x²/ 2! + z³³x³/ 3! + z⁴⁴x⁴/ 4! )
(1 + ...

(2013-09-08)  

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, inNevada 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.

(2013-09-01)  

(2013-09-01)  
Rediscovered in 1996 by Ken Fuchs & Olaf Vancura  (K&O).

(2013-09-01)  
Counting isn't illegal but casinos may restrict or deny access to anyone...