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Probability of holding
First betting interval
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Seven-Card Stud
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Blackjack
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Glossary

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Blackjack

Blackjack is played at a casino table like that shown below.  Usually seven players can be accommodated at the table, with the dealer facing them. 

      Up to eight packs of cards are used, and are shuffled by the dealer.  One player is allowed to cut the cards by inserting an indicator card into the combined pack.  The dealer completes the cut and places the pack face down in a dealing shoe, with the indicator card a few cards (up to 50) from the bottom of the pack these last cards will not be used.

The object of the game

The object, from the player’s point of view, is to obtain a total card count, with the two cards dealt or with others as well, that is higher than that of the dealer, but not exceeding a maximum of 21.  Should a player’s count exceed 21 he has busted and loses.  A count of 21 with two cards (Ace and a ten-count) is a natural or blackjack and beats any other hand.  When a player wins a blackjack the dealer pays him at odds of 3 to 2 (this is sometimes stated on the table).  All other bets are settled at 1 to 1, and all ties are a stand-off and the player retains his stake.  When the dealer has a blackjack he wins all stakes, except from a player with a blackjack, in which case the bet is a stand –off.

      All cards the bet is a stand–off.

  • King, Queen and Jack count as 10.
  • The Ace when held by the player can count one or 10 at his discretion.  It also has these values when held by the dealer, but subject to restrictions, as we will see.  A hand which counts an Ace as 11 is known as a ‘soft’ hand (e.g. Ace, 6 is a ‘soft 17’).  Once the Ace is counted as one it is a ‘hard’ hand (e.g. Ace, 6, 10 is a ‘hard

The play

Before the deal, players put their stakes in the betting space before them, subject to the casino’s limits.
            The dealer burns the first card from the shoe, then deals one card to each player face up, beginning with the player on his left, and ending with one to himself.  He then deals a second card all round, but this time his own card is face down.
            If the dealer’s face-up card is an Ace, he invites all players to ‘insure’ against him holding a blackjack.  A player who wishes to do so puts up a premium of half his stake.  The dealer then looks at his face-down card and if it is a ten-count, declares his blackjack.  Players who insured are paid at odds of 2 to 1, and therefore  retain their stake and premium, and neither win nor lose on the deal.  If the dealer’s face-up card is a ten-count, he also looks at  his face-down card.  Should he have a blackjack he declares it and settles all bets.  In this case, insurance does not arise.
            When the dealer not have a blackjack, his face-down card remains face down, so his total count is unknown, and he deals with all players in turn from his left.

Each  player has four options.

  • If he is satisfied with his count (say, if it is 19 or 20 ) he will stand.
  • He can draw another card, dealt face up.  A traditional way of doing this is to say to the dealer, ‘Hit me.’  He can continue to draw cards until satisfied with his count.  If he busts (i.e. exceed 21) he loses, and the dealer collects his stake.
  • If he has two cards of the same rank, he may split his pairs.  If he does, in effect each card becomes the first card of a separate hand, and the player puts a stake equal to his original take on the second card.  The dealer deals a second card and the player plays each hand in turn.  Should the second card in a split hand form another pair, he may split them again.

If a player splits a pair of Aces, he may not draw a third card to either hand.  If he receives another Ace, he may split again.  A blackjack scored with a split hand wins immediately, but is paid only at 1 to 1, not 3 to 2.

  • He can double down.  This allows him to double his stake and receive a third card face down.   This completes his hand, and the wild card remains face down until the settlement.

The dealer’s hand

When the hands of all players who have not bust are complete, the dealer faces his second card to expose his hand.  He has no options in playing his hand.  If his count is 16 or fewer he must draw and continue until his count is 17, 18, 19, 20 or 21, when he must stand.  Should the dealer bust, all the players still in the game win.
            The dealer may count an Ace as either one or 11, but only if his total does not reach one of 17-21.  As soon as one of those numbers can be made, he must stand.  For example, if he holds Ace-6, he would do best to draw or double down, according to the dealer’s up-card.
            When the dealer stands, he pays all players with a count higher than him, and collects the stakes of those with a lower count.  Where counts are tied, the player retains his stake.

Strategy

As stated above, a player’s main choices are whether to stand, hit or double down.  Experts have worked out the optimum play and this is shown in Table 15 and 16 (overleaf).

TABLE 15 :  Players optimum play at Blackjack
Hard 2 –card total

Player
Points

Dealer’s face-up card

2

3

4

5

6

7

8

9

10

A

17

S

S

S

S

S

S

S

S

S

S

16

S

S

S

S

S

H

H

H

H

H

15

S

S

S

S

S

H

H

H

H

H

14

S

S

S

S

S

H

H

H

H

H

13

S

S

S

S

S

H

H

H

H

H

12

H

H

S

S

S

H

H

H

H

H

11

D

D

D

D

D

D

D

D

D

D

10

D

D

D

D

D

D

D

D

H

H

9

D

D

D

D

D

H

H

H

H

H



TABLE 16:  Players optimum play at Blackjack
Soft  2 –card total

Player
Points

Dealer’s face-up card

2

3

4

5

6

7

8

9

10

A

19

S

S

S

S

S

S

S

S

S

S

18

S

S

S

S

S

S

H

H

H

H

17

D

D

D

D

D

H

H

H

H

H

16

H

H

H

H

D

H

H

H

H

H

15

H

H

H

H

D

H

H

H

H

H

14

H

H

H

H

D

H

H

H

H

H

13

H

H

H

H

D

H

H

H

H

H

S= stand   H = hit   D = double down

Always stand on hard hands of 17 or more and soft hands of 19 and 20.
            The other choice involves whether or not to split pairs.  Again experts have worked out the optimum play, and this is shown in Table 17.

TABLE 17:  Advisability of splitting pairs.

Player
holds

Dealer’s face-up card

2

3

4

5

6

7

8

9

10

A

A

S

S

S

S

S

S

S

S

S

S

10

X

X

X

X

X

X

X

X

X

X

9

S

S

S

S

S

X

X

X

X

X

8

S

S

S

S

S

S

S

X

X

S

7

S

S

S

S

S

S

X

X

X

X

6

H

H

S

S

S

X

X

X

X

X

5

X

X

X

X

X

X

X

X

X

X

4

X

X

X

X

X

X

X

X

X

X

3

S

S

S

S

S

S

X

X

X

X

2

S

S

S

S

S

S

X

X

X

X

S = split   X = do not split

Insurance

It is not a good idea to take insurance.  It is really a side-bet offering odd of 2 to 1 for what is really a 9 to 4 chance.  Although the player appears to have the advantage, in that he has all the options and receives the bonus payment for blackjacks, the casino, of course, wouldn’t offer the game if it did not have an edge.  The edge comes from the fact that the player plays first, and always loses if he busts loses to the other three but still wins from four thus it is not strictly true to say that ties are a stand-off.  However, a player who makes the right options will find the casino edge very small, not more than one per cent.

Variants

Some casinos will have variations on the above, such as any of the following:

  • The dealer will draw on soft 17 (the rule should be printed on the table).
  • The casino will not offer insurance.
  • The players’ cards will be dealt face down.
  • Doubling down will be restricted to certain hands (usually 9, 10 or 11).
  • Splitting pairs might be restricted.

Most of these are harmless and will not seriously affect the players’ chances.  However, one variation, known as the ‘London deal’, does affect the players’ chances.  It entails the dealer not dealing his second card until after the players have bet.  This was originally meant to prevent the possibility of cheating by collusion between dealer and player, but means players might increase their stakes only to find the dealer ultimately holds a blackjack.  If this is in operation, it is best not to double down, to split only Aces, and to bet conservatively when dealer’s first card is an Ace or a 10-count card.