RULES

The game cloth displays betting zones and a hand divider line.
The game shall use a single 28-tiles/cards set. Each tile/card shall have two numbers. Each possible combination of the numbers 1 to 7 shall be a tile/card as follow:
1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 1-7, 2-2, 2-3, 2-4, 2-5, 2-6, 2-7, 3-3, 3-4, 3-5, 3-6, 3-7, 4-4, 4-5, 4-6, 4-7, 5-5, 5-6, 5-7, 6-6, 6-7, 7-7.
The length of each tile/card shall be exactly double the width.
Alternatively use a single 28-tile/card set. Each tile/card shall have two symbols. Each possible combination of the symbols 8 to A.
 

1.                  Play begins with the player making a Casino Double-Hand Poker wager, in addition three side bets are available.

2.                  The player and dealer shall each receive 3 random tiles/cards from the set.

3.                  The player will set his tiles/cards into a 3-number high hand and a 3-number low hand. This can be achieved by setting the tiles/cards across or alongside a line on a dedicated gaming cloth. The line is called a ‘hand divider’. The 3-number low hand shall be set at the front of the line, the 3-number high hand at the rear. e.g.

4.                  The highest hand is a 3 of a kind, followed by a straight, followed by a pair, and finally 3 singletons. Second to the type of hand the poker value of the tiles/cards shall be considered, as in standard poker.

5.                  After the player has set his hand the dealer shall turn over his own tiles/cards.

6.                  The “level” of a hand shall be defined as type of the hand without regard to the individual ranks. For example the highest level is a 3 of a kind, and second highest is a straight.

7.                  The dealer shall first attempt to set both hands to a pair or higher. If this can be achieved the dealer shall set the low hand as high as possible as long as the high hand retains the highest possible level.

8.                  If the dealer can not place at least a pair in both hands then the dealer shall determine the highest possible level of the high hand without condition on the low hand. Then the dealer will set the low hand as high as possible as long as the high hand is the highest possible level.

9.                  The player’s high hand shall be compared to the dealer’s high hand. Likewise, the player’s low hand shall be compared to the dealer’s low hand. In both cases the hand with the higher poker value shall win.

10.              If the player and dealer hand are exactly the same the tie shall go to the dealer.

11.              If both of the player’s hands are higher than the dealer’s hands then the wager shall be paid 1 to 1 less a 5% commission.

12.              If both of the player’s hands are lower than the dealer’s hands the wager shall lose.

13.              If the player has one winning hand and one losing hand the wager shall push.
 

Following are the rules of the Super Bonus side bet.

1.                  The outcome of the Super Bonus bet shall be based only on the player’s hand. If a winning hand exists it will be paid regardless of how the player sets his hand.

2.                  Two 3 of a kinds shall pay 50 to 1.

3.                  A six-tile/card straight shall pay 30 to 1.

4.                  3 pairs shall pay 15 to 1.

5.                  All other hands shall lose.
 

Following are the rules of the Lo-Card side bet.

1.                  The Lo-Card side bet shall win if the player’s hand contains the 1-1 tile/card.

2.                  If no player has the 1-1 tile/card then either 2 or 3 (according to the preference of casino management) tiles/cards shall be exposed from the unused tiles/cards.

3.                  If one of the exposed tiles/cards is the 1-1 tile/card then the Lo bet shall push.

4.                  Otherwise the Lo bet shall lose.
 

Following are the rules of the Hi-Card side bet.

5.                  The Hi-Card side bet shall win if the player’s hand contains the 7-7 tile/card.

6.                  If no player has the 7-7 tile/card then either 2 or 3 (according to the preference of casino management) tiles/cards shall be exposed from the unused tiles/cards.

7.                  If one of the exposed tiles/cards is the 7-7 tile/card then the Hi bet shall push.

8.         Otherwise the Hi bet shall lose.
 

Following are the rules of the Dice-Lo side bet.
Wins on Dice (3 dice) total of 4-10 except for a three of a kind. Pays 1 to 1.

Following are the rules of the Dice-Hi side bet.
Wins on Dice (3 dice) total of 11-17 except for a three of a kind. Pays 1 to 1.

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ANALYSIS

Table 1 shows the probability and contribution to the return of the possible outcomes of the Casino Double-Hand Poker bet, assuming optimal player strategy.
The lower right cell of table shows a house edge of 2.27%

Table 2 shows the distribution of the dealer’s High hand.

Table 3 shows the distribution of the dealer’s Low hand.

Table 4 shows the return table for the Super Bonus side bet.
The lower right cell shows a house edge of 4.73%.

Table 5 shows the return table for both the Hi-Card and Lo-Card side bets exposing two unused tiles/cards.
The lower right cell shows a house edge of 7.14%.

Table 6 shows the return table for both the Hi-Card and Lo-Card side bets exposing 3 unused tiles/cards.
The lower right cell shows a house edge of 3.57%.

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Conclusion

Casino Double-Hand Poker™ was analyzed using a combinatorial program in C++.   In addition I retained Cindy Liu to do an independent analysis and she confirmed my results of the primary game.

My program determined the optimal player hand for every situation by analyzing the expected return for all possible plays and selected that play with the highest expected value.  Therefore an optimal player strategy did not need to be quantified.  However after experimenting with several other house ways it was found the one in this report was the strongest for the dealer.  Likewise I expect the optimal strategy for the player to be very similar to the dealer house way.

If you or any interested party have any questions about this analysis please contact me by any of the means below.

E-mail:             mail@gamingmath.com

Phone:             702-804-0015

Postal mail:     9200 Sienna Vista Dr., Las Vegas, NV 89117
 

Thank you for choosing me to analyze Casino Double-Hand Poker™ and I wish you success with it.

Regards,

Michael Shackleford, A.S.A.

The Game can be played as a live table game or in electronic form or on the Internet.
The Game can also be played with a deck of Au-Yeung's designed dual-symbol cards (Registered Design Number: DNEW 3022679).
The Game-cloth is protected by a Registered Design Number: DNEW 3022672).
The game itself is protected by UK Patent Application No: 0514851.5 & The rules are copyright.

Patents Pending
UK Patent Application No: 0514851.5
© 2005-2010 Stephen Au-Yeung, All rights reserved