Mathematical Analysis
Of The
Following
Casino
Game
January 28, 2006
| INSTALLATIONS (Land) |
|
RULES
1. A single 52-card deck shall be used.
2. The highest type of hand is a Pair, followed by a Straight (Two Adjacent Cards), and finally No Hand (Two Odd Cards).
3.
Ace/Two 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 seven shall pay 5 to 1.
5. A straight shall pay 2 to 1.
6. All other hands shall lose.
--------------------------------------------------------------------------------------------------------------------------------------------
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 |
--------------------------------------------------------------------------------------------------------------------------------------------
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.
Patent Pending
South Africa Patent:
2006/09262
Registered Design: DNEW
3022672
© 2005-2011 Stephen Au-Yeung.
All rights reserved
Stephen@CasinoHoldemPoker.com
