HOME

BACKGROUND

INSTALLATIONS (Land)

INSTALLATIONS (Online)

CASINO REPORTS

 


 
Mathematical Analysis

Of The Following Casino Game

 
Casino Hold'em Poker™ 

 September 1, 2005

Prepared By
Michael Shackleford, ASA

The Wizard of Odds Gaming Consulting, Inc.
 9200 Sienna Vista Drive, Las Vegas, NV 89117
Tel: (702) 804-0015
E-mail: mail@gamingmath.com
 

 
www.wizardofodds.com / www.gamingmath.com


RULES

Following are the rules of Casino Lo-Ball Baccarat™

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.
 

(1) Play starts with the player making a Double-deck Baccarat wager, and such other side bets (as described below).

(2) Both player and dealer receive three cards. Each of the players’ hands is then compared in turn with the dealer’s hand.

(3) The sum of all singleton numbers shall be taken of both hands. In other words any number that appears two or more times shall be ignored.
For example if a hand has the 1-2, 2-3, and 4-5 cards the point value is 1+3+4+5 = 13.

(4) If the player’s hand has fewer points than the dealer’s hand then the player shall win.
A winning player hand of one or more points shall be paid 1 to 1.
A winning player hand of zero points shall be paid (win-bonus), 3 to2.

(5) If the dealer has fewer or equal points then the player shall lose.
However, if the player has exactly 27 points (the highest possible) the player will Lose his bet, but be paid a bonus (Play-bonus) of 2 to1.

 

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 3 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 3 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.

--------------------------------------------------------------------------------------------------------------------------------------------

 ANALYSIS

Table 1 shows the possible outcomes of the Main Wager
The lower right cell shows a house edge of 2.56%

Table 1:  Outcomes of the Main Wager
 

Event

Pays

Combinations

Probability

Return

Player wins with 0

1.5

204050

0.027081

0.0406215

Player has 27

1

34500

0.004579

0.004579

Player wins

1

3381218

0.448747

0.448747

Dealer wins

-1

3915032

0.519593

-0.519593

Total

 

7534800

1.000000

-0.0256455


Table 2 shows the possible outcomes of the
Lo-Card side bet
The lower right cell shows a house edge of 3.57%

Table 2:  Outcomes of the Lo-Card side bet
 

Event

Pays

Combinations

Probability

Return

Player has 1/1 card

8

351

0.107143

0.857143

Other

-1

2925

0.892857

-0.892857

Total

 

3276

1.000000

-0.035714


Table 3 shows the possible outcomes of
the Hi-Card side bet
he lower right cell shows a house edge of 3.57%

Table 3:  Outcomes of the Hi-Card side bet
 

Event

Pays

Combinations

Probability

Return

Player has 7/7 card

8

351

0.107143

0.857143

Other

-1

2925

0.892857

-0.892857

Total

 

3276

1.000000

-0.035714

--------------------------------------------------------------------------------------------------------------------------------------------


Conclusion

Double-Deck Baccarat was analyzed using a combinatorial program in C++. In addition my assistant Eric Wikman confirmed the results using his own independent analysis.
 

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-Deck Baccarat™ 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 on the Internet.
The Game can also be played with a deck of Au-Yeung's designed dual-symbol cards (Registered Design application: DNEW 3022679).
The game itself is protected by UK Patent Application No: 0514851.5; the Game-cloth is protected by a Registered Design application: DNEW 3022672.
The rules are copyright.

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