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Final Answers
© 2000-2015   Gérard P. Michon, Ph.D.

Blackjack  /  21

I'm not into anything bad...  Just blackjack.
Frankie Muniz  (b. 1985) 
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Related articles on this site:

Related Links (Outside this Site)

The Wizard of Odds  by  Michael Schackleford (b. 1965).
Blackjack Calculator  by  Jörg Bewersdorff  (2002).
 
Wikipedia :   Blackjack   |   Pontoon   |   Spanish 21   |   Blackjack Hall of Fame

Videos:   How to PLAY Blackjack   |   How to DEAL Blackjack
History of Card Counting

 
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Blackjack / Twenty-One


(2013-09-01)   Blackjack Glossary

  • 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.

 Blackjack
(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
%RuleStripRenoNJEurope
04 decks    
0Hole Cardyes   

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.

 Come back later, we're
 still working on this one...

House-Edge for Different Blackjack Rules


(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 CardSplit
Pair
23456789XA
18 SSSSS SSSSS 9,9
17 SSSSS SSSSS  
16 SSSSS HH hhh 8,8
15 SSSSS HHHhH  
14 SSSSS H HHHH 7,7
13 SSSSS HHHHH  
12 HHSSS HHHHH 6,6
11 HHHHHHHHH H  
10 HHHHHHHH HH 5,5
9 H HHHH HHHHH  
8 HHHHHHHHHH 4,4
6 HHHHHH HHHH 3,3
4 HHHHHH HHHH 2,2
 
Soft
Total
Dealer's Up Card
23456789XA
s 18 S SSSS SS HHH
s 17 H HHHH HHHHH
s 16 HH HHH HHHHH
s 15 HH HHH HHHHH
s 14 HHH HH HHHHH
s 13 HHH HH HHHHH
A,A HHHHH HHHHH
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.

Blackjack Basic Strategy Calculator  by  Michael Schackleford  (his simplified strategy gives up 0.53%).
BAD Advice Video  (popular misconceptions disguised as professional advice)
The Five Most Misplayed Hands in Blackjack  according to Henry Tamburin


(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  zxk/k! in the product:

(1 + z11 x / 1! + z22 x2/ 2! + z33 x3/ 3! + z44 x4/ 4! )
(1 + ...

 Come back later, we're
 still working on this one...

Probability of outcomes (%) if dealer stands on soft 17  (infinite shoe)
 Up Card  01718192021BJ
A       4 / 13
X       1 / 13
9       0
8       0
7       0
6       0
5       0
4       0
3       0
2       0
Unknown       8 / 169

Blackjack Basic Strategy Calculator


(2013-09-08)   History of Blackjack Counting

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.

 Come back later, we're
 still working on this one...

History of Blackjack and Card Counting


(2013-09-01)   Hi-Lo Counting System  (Harvey Dubner, 1963)

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 still working on this one...

Hi-Lo Count


(2013-09-01)   Knock-out Counting  (Zadehkoochak's All Sevens, 1992)
Rediscovered in 1996 by Ken Fuchs & Olaf Vancura  (K&O).

 Come back later, we're
 still working on this one...

KO Blackjack (Ken-Olaf)  by  Ken Fuchs & Olaf Vancura.
The Book of British Blackjack  by  Mohsen Zadehkoochak (1992)


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

 Come back later, we're
 still working on this one...

Flat-Betting:  Casino Backoff for Card Counting  by  Colin Jones  (Blackjack Apprenticeship).
The Book of British Blackjack  by  Mohsen Zadehkoochak (1992)

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