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Mathematical Analysis

Of The Following Casino Game


Casino Hold'em Poker™

January 28, 2006

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

There are various bets available to the player, described individually below.
The following rules apply to all bets.

1.                  A single 52-card deck shall be used.

2.                  The highest type of hand is a pair, followed by a straight (two consecutive cards), and finally two singletons.

3.                  Ace/2 is the lowest straight.
 

Entry Bet

1.                  If the player’s hand has a higher level than the dealer’s hand then the player shall win 1 to 1.

2.                  If the player’s hand has a lower level than the dealer’s hand then the player shall lose.

3.                  If the player and dealer both have a straight or pair, and both are the same level, then the highest rank of both hands shall be used to determine the winner.  If the player has the higher rank the bet shall pay 1 to 1.  If the dealer has the higher rank, or there is a tie, the bet shall lose.

4.                  If neither the player nor dealer have at least a straight the individual ranks shall be used to determine the winner.  The player’s high card shall be compared to the dealer’s high card.  Likewise the player’s low card shall be compared to the dealer’s low card. 

A          If both of the player’s cards are greater than the corresponding dealer’s cards then the player’s bet shall pay 1 to 1.

B          If one of the player’s cards are greater than the corresponding dealer card, and the other player card is less than or equal to the corresponding dealer card then the bet shall push.

C         If both the player’s cards are less than the corresponding dealer’s cards then the bet shall lose.

D         If one player is less than the corresponding dealer card and the other card is equal to the corresponding dealer card then the bet shall lose.

E          If there is a tie of both ranks then the bet shall lose.

5                    If the player wins with a pair of tens or higher the player shall win 2 to 1.
 

Set Bonus

1.                  The Set Bonus shall pay based only the value of the player’s hand.

2.                  A pair of tens to aces shall pay 10 to 1.

3.                  A pair of eights or nines shall pay 8 to 1

4.                  A pair of twos to tens shall pay 5 to 1.

5.                  A straight shall pay 2 to 1.

6.                  All other hands shall lose.
 

Dealer-High

1.                  If the dealer’s hole card is higher than the dealer’s exposed card then the Dealer High bet shall win.

2.                  If the dealer’s hole card is lower than the dealer’s exposed card then the Dealer High bet shall lose.

3.                  If both dealer’s cards are the same rank then if both cards form a pair of twos, threes, kings, or aces then the bet shall win.  Any other pair shall result in a loss.

Dealer-Low

1.                  If the dealer’s hole card is lower than the dealer’s exposed card then the Dealer Low bet shall win.       

2.                  If the dealer’s hole card is higher than the dealer’s exposed card then the Dealer Low bet shall lose.       

3.                  If both dealer’s cards are the same rank then if both cards form a pair of twos, threes, kings, or aces then the bet shall win.  Any other pair shall result in a loss.

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ANALYSIS

Table 1 shows the return table for the Entry Bet
The lower right cell shows a house edge of 3.42%

Table 1:  Entry Bet
 

Event

Combinations

Probability

Pays

Return

Win with Tens or Better

36360

0.022384

2

0.044769

All other Wins

574320

0.353569

1

0.353569

Loss

702630

0.432561

-1

-0.432561

Tie

311040

0.191486

0

0.000000

Total

1624350

1.000000

 

-0.034223


Table 2 shows the return table for the Set Bonus
The lower right cell shows a house edge of 3.62%

Table 2:  Set Bonus
 

Event

Combinations

Probability

Pays

Return

Pair 10 - Aces

30

0.022624

10

0.226244

Pair 8-9

12

0.009050

8

0.072398

Pair 2-7

36

0.027149

5

0.135747

Straight

208

0.156863

2

0.313725

All other

1040

0.784314

-1

-0.784314

Total

1326

1.000000

 

-0.036199


Table 3 shows the return table for both the Dealer High and Dealer Low bets
The lower right cell shows a house edge of 2.26%

Table 3:  Dealer High/Low
 

Event

Combinations

Probability

Pays

Return

Win

648

0.488688

1

0.488688

Loss

678

0.511312

-1

-0.511312

Total

1326

1.000000

 

-0.022624

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Conclusion

This analysis was performed in both Excel and C++.  An independent analysis was also performed by Cindy Liu, which agrees with mine.

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 2-Card Action!™ and I wish you success with it.

Regards,

Michael Shackleford, A.S.A.

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