strategy with The Wizard of Odds shares the mathematically-correct basic strategy charts for double-deck blackjack.

Appendices

1: Total dependent expected return table for an infinite deck

2a: Probabilities of dealer blackjack after peek

2b: Probabilities of dealer blackjack before peek

3a: Exceptions to single-deck S17 basic strategy

3b: Exceptions to double-deck S17 basic strategy

3c: Exceptions to single-deck H17 basic strategy

4: Blackjack standard deviation details

5: Infinite deck expected return by player hand and dealer upcard

6: Fine points of when to surrender

7: Effect of card removal

8: Analysis of blackjack side bets

9: Composition-dependent expected returns for 1 to 8 decks

10: Continuous shuffling machine vs. cut card

11: Value and strategy for 678 and 777 bonuses

12: Risk of ruin statistics

13: Probabilities in the first four cards

14: Value of each initial player card

15: House edge using total-dependent vs. composition-dependent basic strategy

16: Basic strategy when dealer exposes both cards

17: The Ace-Five card counting method

18: Basic strategy exceptions for three to six cards

19: Blackjack splitting strategy when a back-player is betting

20: Blackjack doubling strategy when doubling after splitting aces is allowed

21: Details on the Wizard’s Simple Strategy

Miscellaneous

My comments on the movie ’21’

Australian Blackjack

Introduction to Card Counting

Rule Variations

Blackjack ‘Charlie’ Rule

Rummy (Blackjack variant popular in Costa Rica)

External Links

Macau Blackjack rules

Simple Blackjack Explanation

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Double-Deck Blackjack Strategy

To use the basic strategy, look up your hand along the left vertical edge and the dealer’s up card along the top. In both cases an A stands for ace. From top to bottom are the hard totals, soft totals, and splittable hands. There are two charts depending on whether the dealer hits or stands on soft 17.

Ideally, the basic strategy shows the play which, on average, will result in the greatest win or the least loss per initial hand played. The way I usually go about this is to look at the initial 2-card hands only. Generally, this will result in the overall best play. However, soft 18 against a dealer ace when the dealer stands on soft 17 provides the only known exception that I am aware of for any number of decks. As my blackjack appendix 9 shows, a 2-card soft 18 vs A has an expected value of hitting of -0.100359, and of standing -0.100502. So with two cards it is very slightly better to hit. However, not all soft 18’s are composed of two cards. The more the cards in the player’s hand the more the odds favor standing. Simulations show that if forced to always hit or always stand, it is better to stand. I would like to thank Don Schlesinger for bringing this unusual play to my attention.

Copyright © 1998-2016 Wizard of Odds Consulting, Inc. All rights reserved.

Privacy & Terms .

strategy is Learn Pai Gow Poker strategy against the Foxwoods house way.

Never split 2s, 3s, or 4s

Keep 5s together with Ten-high or better, otherwise split

Keep 6s or 7s together with Queen-high or better, otherwise split

Keep 8s or 9s together with King-high or better, otherwise split

Keep 10s or Jacks together with Ace-high, otherwise split

Always split Queens, Kings, or Aces

Never split 2s, 3s, or 4s

Keep 5s together with Ten-high or better, otherwise split

Keep 6s together with Queen-high or better, otherwise split

Keep 7s or 8s together with King-high or better, otherwise split

Keep 9s, 10s, or Jacks together with Ace-high, otherwise split

Always split Queens, Kings, or Aces

Never split 2s, 3s, or 4s

Keep 5s together with Ten-high or better, otherwise split

Keep 6s or 7s together with Queen-high or better, otherwise split

Keep 8s or 9s together with King-high or better, otherwise split

Keep 10s, Jacks, or Queens together with Ace-high, otherwise split

Always split Kings or Aces

Never split 2s, 3s, or 4s

Keep 5s together with Ten-high or better, otherwise split

Keep 6s together with Queen-high or better, otherwise split

Keep 7s together with Queen-Ten or better, otherwise split

Keep 8s together with King-high or better, otherwise split

Keep 9s together with King-Jack or better, otherwise split

Keep 10s together with Ace-high, otherwise split

Keep Jacks together with Ace-Five or better, otherwise split

Keep Queens together with Ace-Ten or better, otherwise split

Keep Kings together with Ace-Queen, otherwise split

Always split Aces

Never split 2s, 3s, or 4s

Keep 5s together with Ten-high or better, otherwise split

Keep 6s together with Queen-high or better, otherwise split

Keep 7s together with Queen-Jack or better, otherwise split

Keep 8s together with King-high or better, otherwise split

Keep 9s together with King-Queen or better, otherwise split

Keep 10s together with Ace-high, otherwise split

Keep Jacks together with Ace-Six or better, otherwise split

Keep Queens together with Ace-Jack or better, otherwise split

Keep Kings together with Ace-Queen, otherwise split

Always split Aces

Never split 2s, 3s, or 4s

Keep 5s together with Ten-high or better, otherwise split

Keep 6s together with Jack-Ten or better, otherwise split

Keep 7s together with Queen-Ten or better, otherwise split

Keep 8s together with King-high or better, otherwise split

Keep 9s together with King-Jack or better, otherwise split

Keep 10s together with King-Queen or better, otherwise split

Keep Jacks together with Ace-high, otherwise split

Keep Queens together with Ace-Ten or better, otherwise split

Keep Kings together with Ace-Queen, otherwise split

Always split Aces

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Pai Gow Poker Strategy

The Pai Gow Poker strategies on this page are designed to be used against the Foxwoods house way . They may or may not be as effective against other house ways.

Please choose the strategy you would like to see:

Dealer Banker

Player Banker

Single Strategy

Please choose the level of detail you would like to see:

Simple

Intermediate

Advanced

The Simple Dealer-Banker Strategy has a house edge of 2.6892% when the dealer is banking. For comparison, the House Way has a house edge of 2.7212%, and optimal strategy has a house edge of 2.5122%.

The Intermediate Dealer-Banker Strategy has a house edge of 2.5733% when the dealer is banking. For comparison, the House Way has a house edge of 2.7212%, and optimal strategy has a house edge of 2.5122%.

The Advanced Dealer-Banker Strategy has a house edge of 2.5161% when the dealer is banking. For comparison, the House Way has a house edge of 2.7212%, and optimal strategy has a house edge of 2.5122%.

The Simple Player-Banker Strategy has a house edge of 0.2089% when you are banking. For comparison, the House Way has a house edge of 0.2540%, and optimal strategy has a house edge of 0.0442%.

The Intermediate Player-Banker Strategy has a house edge of 0.0986% when you are banking. For comparison, the House Way has a house edge of 0.2540%, and optimal strategy has a house edge of 0.0442%.

The Advanced Player-Banker Strategy has a house edge of 0.0476% when you are banking. For comparison, the House Way has a house edge of 0.2540%, and optimal strategy has a house edge of 0.0442%.

The Simple Single Strategy has a house edge of 1.4512% when taking turns banking. For comparison, the House Way has a house edge of 1.4876%, and the optimal single strategy has a house edge of 1.2893%.

The Intermediate Single Strategy has a house edge of 1.3461% when taking turns banking. For comparison, the House Way has a house edge of 1.4876%, and the optimal single strategy has a house edge of 1.2893%.

The Advanced Single Strategy has a house edge of 1.2925% when taking turns banking. For comparison, the House Way has a house edge of 1.4876%, and the optimal single strategy has a house edge of 1.2893%.

Section 1 applies to hands that cannot form a Straight, Flush, Straight Flush, or Royal Flush. Section 2 applies to hands that can. The rules in each section are based upon the various rank multiples possible for that section.

The rules in this section apply only to hands that cannot form a Straight, Flush, Straight Flush, or Royal Flush.

Play a pair of Kings in the low hand if possible, otherwise play a pair of Aces in the low hand.

Play a pair of Aces in the low hand.

Play a pair of Aces in the low hand.

Split the Four of a Kind if it is at least two ranks higher than the Three of a Kind, otherwise split the Three of a Kind.

In the following list of exceptions, an A refers specifically to a Natural Ace.

In the following list of exceptions, an A refers specifically to a Natural Ace.

In the following list of exceptions, an A refers specifically to a Natural Ace.

Split 5s with the following kicker combinations:

Keep 6s together with Queen-high or better, otherwise split, except with the following kicker combinations:

Keep 7s together with Queen-Jack or better, otherwise split, except with the following kicker combinations:

Keep 8s together with King-high or better, otherwise split

Keep 9s together with King-Queen or better, otherwise split, except with the following kicker combinations:

Keep 10s together with Ace-high, otherwise split, except with the following kicker combinations:

Keep Jacks together with Natural Ace-high, or Joker-Eight or better, otherwise split, except with the following kicker combinations:

Keep Queens together with Natural Ace-Ten or better, or Joker-Jack or better, otherwise split

Keep Kings together with Ace-Queen, otherwise split

Split 5s with the following kicker combinations:

Keep 6s together with Queen-high or better, otherwise split, except with the following kicker combinations:

Keep 7s together with Queen-Jack or better, otherwise split, except with the following kicker combinations:

Keep 8s together with King-high or better, otherwise split

Keep 9s together with King-Queen or better, otherwise split, except with the following kicker combinations:

Keep 10s together with Ace-high, otherwise split

Keep Jacks together with Natural Ace-high, or Joker-Nine or better, otherwise split, except with the following kicker combinations:

Keep Queens together with Ace-Jack or better, otherwise split

Keep Kings together with Natural Ace-Queen, otherwise split

Split 5s with the following kicker combinations:

Keep 6s together with Queen-high or better, otherwise split, except with the following kicker combinations:

Keep 7s together with Queen-Jack or better, otherwise split, except with the following kicker combinations:

Keep 8s together with King-high or better, otherwise split, except with the following kicker combination:

Keep 9s together with King-Eight or better, otherwise split, except with the following kicker combinations:

Keep 10s together with King-Queen or better, otherwise split

Keep Jacks together with Natural Ace-high, or Joker-Eight or better, otherwise split, except with the following kicker combinations:

Keep Queens together with Ace-Ten or better, otherwise split, except with the following kicker combinations:

Keep Kings together with Ace-Queen, otherwise split

Play a pair from the higher set in the low hand.

Play the higher pair in the low hand.

Play the higher pair in the low hand.

The following table indicates the minimum low hand needed to play a Full House in the high hand. Look up the cell at the intersection of the Three of a Kind and the Pair. If the cell contains ‘SP’ or you cannot make the minimum low hand indicated, split the Full House by playing the pair in the low hand, otherwise play the Full House.

The following table indicates the minimum low hand needed to play a Full House in the high hand. Look up the cell at the intersection of the Three of a Kind and the Pair. If the cell contains ‘SP’ or you cannot make the minimum low hand indicated, split the Full House by playing the pair in the low hand, otherwise play the Full House.

The following table indicates the minimum low hand needed to play a Full House in the high hand. Look up the cell at the intersection of the Three of a Kind and the Pair. If the cell contains ‘SP’ or you cannot make the minimum low hand indicated, split the Full House by playing the pair in the low hand, otherwise play the Full House.

The following tables indicate the minimum low hand needed to play a Full House in the high hand. Use the first table for hands that do not have the Joker as a kicker; use the second table for hands that do. Look up the cell at the intersection of the Three of a Kind and the Pair. If the cell contains ‘SP’ or you cannot make the minimum low hand indicated, split the Full House by playing the pair in the low hand, otherwise play the Full House.

The following tables indicate the minimum low hand needed to play a Full House in the high hand. Use the first table for hands that do not have the Joker as a kicker; use the second table for hands that do. Look up the cell at the intersection of the Three of a Kind and the Pair. If the cell contains ‘SP’ or you cannot make the minimum low hand indicated, split the Full House by playing the pair in the low hand, otherwise play the Full House.

The following tables indicate the minimum low hand needed to play a Full House in the high hand. Use the first table for hands that do not have the Joker as a kicker; use the second table for hands that do. Look up the cell at the intersection of the Three of a Kind and the Pair. If the cell contains ‘SP’ or you cannot make the minimum low hand indicated, split the Full House by playing the pair in the low hand, otherwise play the Full House.

Play the the highest two kickers in the low hand, except with three Aces, play an Ace and the highest kicker in the low hand.

Play the highest two kickers in the low hand.

Play the highest two kickers in the low hand.

Play the highest two kickers in the low hand.

Play the highest two kickers in the low hand.

Play the highest pair in the low hand.

Determine the best low hand that can be made by playing both pairs in the high hand. Then determine the point total of the two pairs (for example, with Queens and 3s, the point total is 12 + 3 = 15). Then play as follows:

Determine the best low hand that can be made by playing both pairs in the high hand. Then determine the point total of the two pairs (for example, with Queens and 3s, the point total is 12 + 3 = 15). Then play as follows:

Determine the best low hand that can be made by playing both pairs in the high hand. Then determine the point total of the two pairs (for example, with Queens and 3s, the point total is 12 + 3 = 15). Then play as follows:

Determine the best low hand that can be made by playing both pairs in the high hand. Then determine the point total of the two pairs (for example, with Queens and 3s, the point total is 12 + 3 = 15). Then play as follows:

Determine the best low hand that can be made by playing both pairs in the high hand. Then determine the point total of the two pairs (for example, with Queens and 3s, the point total is 12 + 3 = 15). Then play as follows:

Determine the best low hand that can be made by playing both pairs in the high hand. Then determine the point total of the two pairs (for example, with Queens and 3s, the point total is 12 + 3 = 15). Then play as follows:

Look up the cell at the intersection of the two pairs. If you can make the specified low hand or better, then play it. If the cell contains ‘SP’ or you cannot make the specified low hand, play the lower pair in the low hand. Use the second table if you have the Joker, otherwise use the first table.

Look up the cell at the intersection of the two pairs. If you can make the specified low hand or better, then play it. If the cell contains ‘SP’ or you cannot make the specified low hand, play the lower pair in the low hand. Use the second table if you have the Joker, otherwise use the first table.

Look up the cell at the intersection of the two pairs. If you can make the specified low hand or better, then play it. If the cell contains ‘SP’ or you cannot make the specified low hand, play the lower pair in the low hand. Use the second table if you have the Joker, otherwise use the first table.

Play the highest two kickers in the low hand.

Play the highest two kickers in the low hand.

With a pair of Aces, look at the three highest kickers. If they match one of the combinations below, play the first and third-highest kickers in the low hand:

Play the highest two kickers in the low hand.

With a pair of Aces, look at the three highest kickers. If they match one of the combinations below, play the first and third-highest kickers in the low hand:

Play the highest two kickers in the low hand.

Play the highest two kickers in the low hand.

With a pair of Natural Aces, look at the three highest kickers. If they match one of the combinations below, play the first and third-highest kickers in the low hand:

With a Joker-Ace pair, look at the three highest kickers. If they match one of the combinations below, play the first and third-highest kickers in the low hand:

Play the highest two kickers in the low hand.

With a pair of Natural Aces, look at the three highest kickers. If they match one of the combinations below, play the first and third-highest kickers in the low hand:

With a Joker-Ace pair, look at the three highest kickers. If they match one of the combinations below, play the first and third-highest kickers in the low hand:

Play the second and third highest cards in the low hand.

Play the second and third highest cards in the low hand.

If the highest four cards fall within the ranges listed below, play the second and fourth-highest cards in the low hand:

Play the second and third highest cards in the low hand.

If the highest four cards fall within the ranges listed below, play the second and fourth-highest cards in the low hand:

Play the second and third highest cards in the low hand.

If the highest four cards fall within the ranges listed below, play the second and fourth-highest cards in the low hand:

Play the second and third highest cards in the low hand.

Look at the four highest-ranking cards. If they appear in the following table, apply the corresponding rule. An A in this table refers specifically to a Natural Ace.

Play the second and third highest cards in the low hand.

Look at the four highest-ranking cards. If they appear in the following table, apply the corresponding rule. An A in this table refers specifically to a Natural Ace.

Play the second and third highest cards in the low hand.

Look at the four highest-ranking cards. If they appear in the following table, apply the corresponding rule. An A in this table refers specifically to a Natural Ace.

The rules in this section apply only to hands that can make one or more Straight, Flush, Straight Flush, and/or Royal Flush. The term ‘Straight/Flush’ refers to any one or more of these four hand types.

Play the highest Straight/Flush which leaves a pair of Aces in the low hand.

Play the Straight/Flush if the resulting low hand is a pair of 7s or better, otherwise play the Three of a Kind in the high hand and the pair in the low hand.

Play the Straight/Flush if the resulting low hand is a pair of 7s or better, otherwise play the Three of a Kind in the high hand and the pair in the low hand.

Play the Straight/Flush if the resulting low hand is a pair of 7s or better, otherwise play the Three of a Kind in the high hand and the pair in the low hand.

Play the Straight/Flush if the resulting low hand is a pair of 7s or better, otherwise play the Three of a Kind in the high hand and the pair in the low hand.

Play the Straight/Flush if the resulting low hand is a pair of 7s or better, otherwise play the Three of a Kind in the high hand and the pair in the low hand.

With 7s full of Aces, play the Aces in the low hand if the other two cards are any of the following combinations:

Play the Straight/Flush if the resulting low hand is a pair of 7s or better, otherwise play the Three of a Kind in the high hand and the pair in the low hand.

With 7s full of Aces, play the Aces in the low hand if the other two cards are any of the following combinations:

Play the best low hand that leaves a Straight/Flush in the high hand.

Play the best low hand that leaves a Straight/Flush in the high hand.

Play the best low hand that leaves a Straight/Flush in the high hand.

Play the pair of Aces in the low hand.

Determine the best low hand that can be made by playing both pairs in the high hand. Then determine the point total of the two pairs (for example, with Queens and 3s, the point total is 12 + 3 = 15). Then play as follows:

Determine the best low hand that can be made by playing both pairs in the high hand. Then determine the point total of the two pairs (for example, with Queens and 3s, the point total is 12 + 3 = 15). Then play as follows:

Determine the best low hand that can be made by playing both pairs in the high hand. Then determine the point total of the two pairs (for example, with Queens and 3s, the point total is 12 + 3 = 15). Then play as follows:

Determine the best low hand that can be made by playing both pairs in the high hand. Then determine the point total of the two pairs (for example, with Queens and 3s, the point total is 12 + 3 = 15). Then play as follows:

Determine the best low hand that can be made by playing both pairs in the high hand. Then determine the point total of the two pairs (for example, with Queens and 3s, the point total is 12 + 3 = 15). Then play as follows:

Determine the best low hand that can be made by playing both pairs in the high hand. Then determine the point total of the two pairs (for example, with Queens and 3s, the point total is 12 + 3 = 15). Then play as follows:

Look up the cell at the intersection of the two pairs. If you can make the specified low hand or better, then play it. If the cell contains ‘SP’ or you cannot make the specified low hand, play the lower pair in the low hand. A superscript number in a cell means that the corresponding exception applies. Use the second table if you have the Joker, otherwise use the first table.

1 Play the best high hand instead of splitting the pairs

2 If the best high hand is a Flush or better, play that instead of splitting the pairs

3 If the best high hand is a Straight Flush or better, play that instead of splitting the pairs

Look up the cell at the intersection of the two pairs. If you can make the specified low hand or better, then play it. If the cell contains ‘SP’ or you cannot make the specified low hand, play the lower pair in the low hand. A superscript number in a cell means that the corresponding exception applies. Use the second table if you have the Joker, otherwise use the first table.

1 Play the best high hand instead of splitting the pairs

2 If the best high hand is a Flush or better, play that instead of splitting the pairs

3 If the best high hand is a Straight Flush or better, play that instead of splitting the pairs

Look up the cell at the intersection of the two pairs. If you can make the specified low hand or better, then play it. If the cell contains ‘SP’ or you cannot make the specified low hand, play the lower pair in the low hand. A superscript number in a cell means that the corresponding exception applies. Use the second table if you have the Joker, otherwise use the first table.

1 If the best high hand is a Flush or better, play that instead of splitting the pairs

2 If the best high hand is a Straight Flush or better, play that instead of splitting the pairs

Play the best low hand that leaves a Straight/Flush in the high hand.

Play the best low hand that leaves a Straight/Flush in the high hand.

Play the best low hand that leaves a Straight/Flush in the high hand.

With a pair of 9s, 10s, Jacks, or Queens, play Ace-King in the low hand whenever possible

Play a pair of Aces in the high hand if it improves the low hand from Jack-high or lower to Queen-Ten or better

Play the best low hand that leaves a Straight/Flush in the high hand.

With a pair of 9s, 10s, Jacks, or Queens, play Ace-Queen or Ace-King in the low hand whenever possible

Play a pair of Aces in the high hand if it improves the low hand from Jack-high or lower to Queen-Ten or better

Play the best low hand that leaves a Straight/Flush in the high hand.

Note the low hand created by following the above rule. In the appropriate table below, locate the intersection of that low hand’s higher-ranking card, and the pair you have. If the cell indicates a low hand, and you are able to play that low hand (or better) by sacrificing the Straight/Flush, then do so. Use the first table if you do not have the Joker, and the second table if you do.

1 Do not improve the low hand if it is Queen-Jack

Play the best low hand that leaves a Straight/Flush in the high hand.

Note the low hand created by following the above rule. In the appropriate table below, locate the intersection of that low hand’s higher-ranking card, and the pair you have. If the cell indicates a low hand, and you are able to play that low hand (or better) by sacrificing the Straight/Flush, then do so. Use the first table if you do not have the Joker, and the second table if you do.

1 Do not improve the low hand if it is Queen-Jack

Play the best low hand that leaves a Straight/Flush in the high hand.

Note the low hand created by following the above rule. In the appropriate table below, locate the intersection of that low hand’s higher-ranking card, and the pair you have. If the cell indicates a low hand, and you are able to play that low hand (or better) by sacrificing the Straight/Flush, then do so. Use the first table if you do not have the Joker, and the second table if you do.

1 Do not improve the low hand if it is Queen-Jack

Play the best low hand that leaves a Straight/Flush in the high hand.

Play the best low hand that leaves a Straight/Flush in the high hand.

Copyright © 1998-2016 Wizard of Odds Consulting, Inc. All rights reserved.

Privacy & Terms .

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 7 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 7 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 7 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 4 th and 5 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 5 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 5 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 7 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 4 th and 6 th highest cards in the low hand

Play the 4 th and 5 th highest cards in the low hand

Play the 3 rd and 5 th highest cards in the low hand

Play the 4 th and 6 th highest cards in the low hand

Play the 2 nd and 5 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 5 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 5 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 7 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 5 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 7 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 5 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 7 th highest cards in the low hand

Play the 2 nd and 7 th highest cards in the low hand

Play the 3 rd and 6 th highest cards in the low hand

Play the 3 rd and 5 th highest cards in the low hand

Play the 4 th and 5 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 5 th highest cards in the low hand

Play the 2 nd and 5 th highest cards in the low hand

Play the 2 nd and 5 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 5 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 5 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 7 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 3 rd and 5 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 4 th and 6 th highest cards in the low hand

Play the 3 rd and 6 th highest cards in the low hand

Play the 3 rd and 5 th highest cards in the low hand

Play the 4 th and 6 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 5 th highest cards in the low hand

Play the 2 nd and 5 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 5 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 3 rd and 5 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 5 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 5 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 5 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 7 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 7 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 7 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 4 th and 5 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 7 th highest cards in the low hand

Play the 2 nd and 4 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 4 th and 5 th highest cards in the low hand

Play the 4 th and 5 th highest cards in the low hand

Play the 3 rd and 5 th highest cards in the low hand

Play the 4 th and 6 th highest cards in the low hand

Play the 2 nd and 5 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 2 nd and 6 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

Play the 3 rd and 4 th highest cards in the low hand

strategy related The Wizard of Odds explains when to stand on ace/king in Caribbean Stud Poker.

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Caribbean Stud Poker Optimal Strategy

Footnotes:

*: Extremely borderline play. Correct strategy depends not only on the number of suited cards but which ones are suited. See table below for how to play these situations.

I would like to thank Stanly Ko and Professor John M. Gwynn, Jr. foralerting me to these borderline plays.

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Raise if the suit of dealer’s card matches the suit of one or more of your cards.

Raise if the suit of dealer’s card matches the suit of two or more of your cards.

Raise if the suit of dealer’s card matches the suit of three or more of your cards.

Raise if the suit of dealer’s card matches the suit of four of your cards.

A/K/Q, A/K/8, A/K/7, A/Q/8, A/Q/7, A/8/7, K/Q/8, K/Q/7, K/8/7

strategy begin

Strategies

Jacks or Better

Simple Strategy (99.46%)

Intermediate Strategy (99.52%)

Optimal Strategy (99.54%)

Deuces Wild

NSUD Intermediate Strategy

Full-Pay Simple Strategy (100.71%)

Full-Pay Optimal Strategy (100.76%)

8/5 Bonus Poker

10/7 Double Bonus

9/6 Double Double Bonus

8/5 Super Aces

Quick Quads

9/6 Jacks or Better

8/5 Bonus Poker

9/7/5 Double Bonus

9/6 Double Double Bonus

8/5 Triple Bonus

Ultimate X

Jacks or Better

Bonus Poker

Bonus Poker Deluxe

Double Bonus

Double Double Bonus

Joker Poker

(more) 2222; 3333; 4444; 5555; 6666; 7777; 8888; 9999; TTTT; JJJJ; QQQQ; KKKK…

(more) 2233; 2244; 2255; 2266; 2277; 2288; 2299; 22TT; 22JJ; 22QQ; 22KK; 22AA…

(more) A234; A235; A245; A345; 2345; 2346; 2356; 2456; 3456; 3457; 3467; 3567…

(more) 2347; 2348; 2349; 234T; 234J; 234Q; 234K; 2357; 2358; 2359; 235T; 235J…

(more) A23; A24; A25; A34; A35; A45; 234; 235; 245; 346; 356; 457; 467; 568…

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The following table shows the results when following perfect strategy (basic strategy and all of the exceptions):

The following table shows the results when following basic strategy only (not its exceptions):

The following table shows the basic strategy:

The following table shows the exceptions to the basic strategy:

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Full House; Straight Flush; Royal Flush

222; 333; 444; 555; 666; 777; 888; 999; TTT; JJJ; QQQ; KKK; AAA

TJA; TJQ; TJK; TQA; TQK; TKA; JQA; JQK; JKA; QKA

2345; 3456; 4567; 5678; 6789; 789T; 89TJ; 9TJQ

345; 456; 567; 678; 789; 89T; 89J; 8TJ; 8JQ; 9TJ; 9TQ; 9JQ; 9JK; 9QK

236; 246; 256; 347; 357; 367; 458; 468; 478; 569; 579; 589; 67T; 68T; 69T

strategy begin Four Poker is a new poker variation invented by Roger Snow and marketed by Shufflemaster. The game is similar to Three Card Poker but as the title suggests, four cards are used instead of three. Also, there is no dealer qualifying hand and the player can raise up to three times his ante.

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Four Poker is a new poker variation invented by Roger Snow and marketed by Shufflemaster. The game is similar to Three Card Poker but as the title suggests, four cards are used instead of three. Also, there is no dealer qualifying hand and the player can raise up to three times his ante. However, the dealer gets one extra card to form his best hand.

Notes:

1 I have an unconfirmed report that in Atlantic City if the player folds his Aces Up bet will still remain alive.

Of these pay tables for the Aces Up side bet, number five is the most popular. The only exceptions that I’m aware of are an unconfirmed report that that Tulalip in Washington uses pay table 4 and the Grand Casino Hinckley in Minnesota uses pay table 1.

The following return table is based on optimal player strategy under the 2-20-25 Ante Bonus pay table. The lower right cell shows a house edge of 2.79%.

The average final bet under optimal strategy is 2.142342 units, making the element of risk , -0.027879/2.142342 = 1.30%. The standard deviation, relative to the original bet, is 2.71.

A simple strategy to this game, first proposed by Stanley Ko, is as follows.

According to the second edition of ‘Beyond Counting’ by James Grosjean, this ‘simple strategy’ results in a house edge of 3.396%.

The following intermediate strategy was created to balance power and simplicity by our own JB.

Against the 2-20-25 Ante Bonus pay table, the house edge is 2.8526% and the element of risk is 1.3233%.

I’m proud to present the following advanced strategy, also created by my sidekick JB.

Against the 2-20-25 Ante Bonus pay table, the house edge is 2.8498% and the element of risk is 1.3216%. Here is a house edge comparison of various known strategies.

To put it another way, here are the cost of errors:

The next table shows the probability of each hand and the return under pay table five of the Aces Up side bet. The lower right cell shows a house edge of 3.89%.

The next table shows the house edge according to all four Aces Up pay tables.

Note: There is also a similar game called Crazy Four Poker .

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