Mathematical Analysis 

RULES

Following are the rules for Casino Omaha™

1.                  Players make an Ante wager and an optional side bet 2-Pair Bonus.

2.                  3 cards are dealt face down to each player and the dealer, In addition 3 flop (community) cards are dealt face up.
The players may examine their own 3 cards but sharing information should be discouraged. 
All players and dealer may use the 3 flop (community) cards as part of their hand. 

3.                  Each player must decide to either fold or call.
If the player folds he gives up his cards and his Ante.
If the player calls the Call bet must be double the Ante.

4.                  The dealer will then deals 2 more community cards, form a total of 5. The dealer will also turn over his own 3 cards.

5.                  Each player and the dealer will form the best 5-card poker hand by using Exactly 2 of his own 3 cards and 3 of the 5 flop (community) cards.

6.                  Each player will compare his best hand against the dealer’s best hand. 

7.                  The dealer must have a pair of 7s or better to qualify.
If the dealer does not qualify then the ante will pay according to the AnteWin® pay table below and the call bet will push.

If the dealer qualifies:
(a) Dealer beats the player, then the player will lose both the Ante and Call.
(b) Player beats the dealer, then the ante will pay according to the AnteWin® pay table shown below, and the call bet will pay 1 to 1.
(c)  if the Dealer and Player have exactly the same hand the bet is a 'push', it neither wins nor loses;

8.                   If the dealer qualifies and the player ties the dealer then both ante and call bets will push.

ANALYSIS

Table 3 shows a breakdown of every significant outcome, the number of combinations, the probability, and contribution to the total return – based on optimal player strategy.
The number in the lower right cell of table 3 shows a house edge of 2.33%

The total number of combinations equals the number of ways to choose sets of 3, 3, 2, and 3 out of 52.  In other words combin(52,3)*combin(49,3)*combin(46,2)*combin(44,3) = 5,581,304,544,816,000.

The number in the lower right cell of table 3 shows the player can expect to lose 2.33% for each initial wager made. In other words the house edge is 2.33%, defined as the ratio of expected player loss to the initial wager.
The average wager in this game is 2.52 units. The ratio of expected player loss to total amount bet, what I define as the “element of risk” is 0.93%.

As in most poker based games the optimal strategy in this game is complex. It would also be difficult to put a basic strategy into words.
According to table 3 the player should fold 23.92% of the time, so the player should fold on about the weakest 24% of hands.

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Conclusion

This analysis was conducted using a combinational approach that analyzed every possible combination of player cards, community cards, and dealer cards.
This was a very difficult and time consuming analysis. A random simulation, although slow, showed the house edge of 2.33% was reasonable.

Thank you for choosing me to analyze Casino Omaha™ and I wish you success with it.

Regards,

Michael Shackleford, A.S.A.

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