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Pai Gow Tiles Optimal Strategy – Wizard of Odds in strategy

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strategy with Optimal strategy for Pai Gow Tiles.

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Pai Gow Tiles Optimal Strategy

Following is the optimal strategy for Pai Gow Tiles with exceptions based on whether the dealer is banking or you are banking. This strategy is optimal against the Traditional Way. It should be nearly optimal against any casino house way.
The approach with this strategy is a little different than usual. It is separated into two sections: pairs and non-pairs. If the tile combination contains at least one pair, follow the rules in the Pairs section. Otherwise, skip to the second section.
Determine the combination code for a hand by determing each tile’s code as listed above, and then sorting the four codes from lowest to highest. For example, if the tiles are Teen, high 4, Gee, and 11, their respective codes are 2, 4, 3, and 1. Then sort the digits to get the code 1234. Look up the rule for the 4-digit code in the table below.
Combinations which have only one way to play are included but are greyed-out .

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  0 and 0, except with H7s when banking
high 1/6 when dealer is banking; 0/7 when banking
high 1/4 when dealer is banking; 0/5 when banking
high 1/5 when dealer is banking; 0/6 when banking
high 1/6 when dealer is banking; 0/7 when banking
1/high 7 when dealer is banking; 0/8 when banking
0/6 except play 2/4 with 0-0-L2-H4 when dealer is banking
6/6 (separate H0 and H6 if applicable)
4/4 when dealer is banking; 0/8 when banking
4/high 6 except play high 4/6 with 0-0-L4-H6 when dealer is banking
high 6/8 except play 6/high 8 with 0-0-H6-L8 when dealer is banking
6/high 9 except play high 6/9 with L6 when banking
high 6/7 (separate H0 and H6 if applicable)
7/8 except play 6/9 with H0-1-3-H8, and play 6/9 with H0-1-3-L8 when banking
high 4/5 with L0; 1/8 with H0 when dealer is banking
5/8 except play 4/9 with H0-1-L4-H8, and play 4/9 with L0-1-H4-H8 when banking
high 6/7 (separate H0 and H6 if applicable)
7/8 except play 6/9 with H0-1-6-H8, and play 6/9 with H0-1-L6-L8 when banking
4/4 except play 2/high 6 with L0-2-2-L4
6/9 with H2; 7/8 with L2 when dealer is banking
6/Gong except play 8/8 with L0-L2-3-H8
2/8 when dealer is banking; 4/6 when banking
6/7 except play 4/9 with L0-H2-H4-7; when banking play 4/9 except play 6/7 with L0-L2-L4-7
6/8 except play 4/Gong with 0-H2-H4-L8; also play 4/Gong when banking with H0-H2, H2-H4, H2-L8, and H4-L8
6/9 except play 4/Wong with L0-2-H4-9
7/7 except play 5/9 with L0-H2-5-7; also play 5/9 with H0-H2-5-7 when banking
7/8 except play 5/Gong with H0-H2-5-L8; also play 5/Gong with L0-H2-5-L8 and H0-H2-5-H8 when banking
6/9 except play 7/8 with H0-L2-6-7 when dealer is banking
6/Gong except play 8/8 with L0-L2-L6-H8; also play 8/8 with L0-L2-L6-L8, L0-L2-H6-H8, and L0-H2-L6-H8 when dealer is banking
8/9 except play 7/Gong with H0-2-7-L8 and H0-L2-7-H8
9/9 except play 7/Wong with H0-L2-7-9
9/Gong except play 8/Wong with 0-L2-H8-9; also play 8/Wong with L0-H2-H8-9 when dealer is banking
6/8 except play 5/9 with H0-3-5-H6 when dealer is banking
0/7 except play 1/6 with L0-H4-H6-7 when dealer is banking
when dealer is banking, play 2/high 8 except play 4/6 with H0-L4-8-8; when banking, play 4/6 except play 2/high 8 with L0-L4-8-8
2/8 except play 4/6 with H0-6-6-H8; also play 4/high 6 with L0-6-6-H8 when banking
5/6 except play 4/7 with H0-H6-L7-L8; also play 3/8 with L0-H6-L7-L8 when banking
6/6 except play 5/7 with H0-H6-7-9; also play 5/7 with L0-H6-L7-9 when banking
7/Gong except play 8/9 with 1-L2-3-H8 when dealer is banking
6/9 except play 5/Gong with 1-2-H4-L8 and 1-H2-4-L8; also play 5/Gong with 1-L2-L4-L8 and 1-H2-H4-H8 when banking
7/9 except play 6/Gong with 1-H2-5-L8; also play 6/Gong with 1-L2-5-L8 when banking
7/Gong except play 8/9 with 1-L2-L6-H8
6/8 when dealer is banking; 5/high 9 when banking
0/8 except play 1/7 with 1-H4-H6-7 when dealer is banking
5/7 except play 3/9 with 1-H6-L7-L8 when banking
high 8/Wong when dealer is banking; 8/high Wong when banking
high 8/Wong when dealer is banking; 8/high Wong when banking
4/9 with H8; 3/Gong with L8; except play 5/8 with L2-3-H7-L8 and L2-3-7-H8 when dealer is banking
6/8 except play 4/Gong with H2-3-8-8 when banking
7/8 except play 5/Gong with H2-3-L8-9
6/6 except play 2/Gong with H2 when banking
6/7 except play 2/Wong with L2-4-L8-9 and 3/Gong with H2-4-L8-9; also play 3/Gong with L2-H4-L8-9 when banking
5/7 with H8; 2/Gong with L8; except play 3/9 with H2-5-7-H8 when banking
4/9 with H8; 3/Gong with L8; except play 5/8 with L2-6-7-H8 and 4/9 with H2-H6-7-L8 when dealer is banking, and 4/9 with H2-L6-L7-L8 when banking
6/8 except play 4/Gong with H2-6-8-8 when banking
7/8 with H8; 5/Gong with L8; except play 7/8 with L2-L6-L8-9 when dealer is banking
4/7 except play 2/9 with 3-H4-H6-L8 and 3-L4-6-L8
5/6 when dealer is banking; high 4/7 when banking
2/3 except play 0/5 with L4-6-6-9 when banking
2/3 except play 1/4 with H4-6-7-H8 when dealer is banking, and 0/5 with H8 when banking
0/7 except play 3/4 with H4-6-L8-9 and L4-H6-L8-9 when dealer is banking
3/4 except play 1/6 with 5-H6-H7-9 when dealer is banking
5/6 except play high 4/7 with L6-8-8-9 when banking

Super Aces Bonus Video Poker Strategy – Wizard of Odds in strategy

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Full-Pay Optimal Strategy (100.76%)

8/5 Bonus Poker

10/7 Double Bonus

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4 of a kind or better
3 aces
4 to a royal flush
Straight, flush, or full house
3 deuces through kings
4 to a straight flush
Pair of aces
Two pair
Pair of Jacks, Queens, or Kings [1]
3 to a royal flush [1]
4 to a flush
4 to a straight: 89TJ, 9TJQ, or TJQK
Pair of deuces through tens
3 to a straight flush: 8TJ, 9TJ, or 9JQ
4 to a straight: 2345, 3456, 4567, 5678, 6789, 789T, or JQKA
3 to a straight flush: 345, 456, 567, 678, 789, 89T, 89J, 8JQ, 9TQ, 9JK, or 9QK
Suited JQ, JK, QK, JA, QA, KA [2]
4 to a straight: 9JQK, TJQA, TJKA, or TQKA [2]
Ace
Unsuited JQK
3 to a straight flush: 234, 235/245, 346/356, 457/467, 568/578, 679/689, 78T/79T, 78J/79J/7TJ, 89Q, 8TQ, or 9TK
4 to a straight: 89JQ, 8TJQ, 9TJK, or 9TQK
Unsuited JQ, JK, or QK [3]
Suited TJ, TQ, or TK [3] [4]
Jack, Queen, or King [4]
3 to a straight flush: 236/246/256, 347/357/367, 458/468/478, 569/579/589, or 67T/68T/69T
4 to a straight: 2346/2356/2456, 3457/3467/3567, 4568/4578/4678, 5679/5689/5789, 678T/679T/689T
Discard everything

Suited TJQ or JQK beats a pair of Jacks, Queens, or Kings if there is no straight or flush penalty to the 3-card royal
Unsuited 9JQK, TJQA, TJKA, and TQKA beats suited JK, QK, JA, QA, or KA if there is a flush penalty to the 2-card royal
Suited TJ beats unsuited JK if there is no 8 or flush penalty to the TJ
King beats suited TK if there is a flush penalty to the TK

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Super Aces Bonus Video Poker Strategy

The following strategy is the optimal strategy for 8/5 Super Aces Bonus Poker , which returns 99.94%. To use it, make the play which is closest to the top of the list, noting the exceptions.

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Basic Video Poker Info

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Return tables:

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4-5 Bonus Poker
7 Stud Poker
Ace & Deuce Bonus Poker
Ace Invaders
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ACE$ Bonus Poker
Aces and Eights
Aces and Faces
Acey Deucey Poker
All Aces
All American Video Poker
American Poker
Anything’s Wild Video Poker
Atomic Fever
Barnyard Poker
Big Split Poker
Big Times Draw Poker
Big Win Poker
Black Jack Bonus Poker
Bonus Deuces Wild
Bonus Poker
Bonus Poker Deluxe
Bonus Poker Plus
Bonus Royals Video Poker
Bonus Video Poker
Build a Wheel Poker
Chase The Royal
Deuce on the Deal
Deuces and Joker Wild
Deuces Wild
Dice Fever
Double Aces and Faces
Double Bonus
Double Bonus Deuces Wild
Double Bonus Poker Plus
Double Deuces
Double Double Aces & Faces
Double Double Bonus
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Double Draw Aces
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Double Jackpot Poker
Double Joker
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Double Super Times Pay
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Going for Fours
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Royal Court
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Sequential Royal
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Spin Fever
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Jacks or Better quiz
Probability distribution for each hand by number of cards held in Full-Pay Deuces Wild
Video poker programming tips
San Diego County video poker survey
100% Rebate on Video Poker Losses Promotions
Effect of Strategy Mismatches in Video Poker

Strategies

Full-Pay Jacks or Better:

Simple Strategy (return of 99.46%)
Intermediate Strategy (return of 99.52%)
Optimal Strategy (return of 99.54%)

Full-Pay Deuces Wild:

Simple Strategy (return of 100.71%)
Optimal Strategy (return of 100.76%)
3 to a wild royal (ace-high) vs. Deuce only
2 to a royal (king-high) with a straight penalty
2 to a royal (king-high) with no penalty

Quick Quads:

9/6 Jacks or Better
8/5 Bonus Poker
9/7 Double Bonus
9/6 Double Double Bonus
8/5 Triple Bonus

Other Strategies:

‘Not So Ugly Ducks’
8/5 Bonus Poker
10/7 Double Bonus
10/6 Double Double Bonus

Dealer Exposes Both Cards – Wizard of Odds with strategy

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strategy related I get asked a lot why this strategy calls for hitting 11 against a total of 10, when in regular blackjack the player should double. In blackjack, we can assume the dealer does not have an ace as his hole card. That increases the expected value of doubling.

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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Dealer Exposes Both Cards

Sometimes either accidentally or as part of a promotion the dealer will expose both cards. This is not to be confused with double exposure , in which ties lose. The following is the basic strategy, based on an infinite number of decks, when both dealer cards are exposed and the dealer stands on soft 17.
The player advantage of this game is about 10.1%, give or take a little depending on the specific rules.
I get asked a lot why this strategy calls for hitting 11 against a total of 10, when in regular blackjack the player should double. In blackjack, we can assume the dealer does not have an ace as his hole card. That increases the expected value of doubling. In double exposure, there is no such guarantee the dealer does not have an ace as his third card, giving him a 21, making doubling more risky.

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