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Q Poker

Last Update: Aug 13, 2007

Introduction

Q Poker is a game I noticed at the Lisboa in Macau in August 2007. It is very similar to Three Card Poker. The first difference is that instead of having the choice to raise or fold, the player may surrender or call. In both games the player will win half his total bet if the dealer does not qualify, in this case half the Ante bet. The dealer must qualify, and the player must beat the dealer, to be paid premium odds for a straight or higher.

The Pairplus bet is exactly the same in both games. The strategy is also exactly the same.

Rules

Player makes an Ante and/or Pairplus bet.
The dealer gives each player three cards and himself three cards. The player may examine his own cards. The dealer's cards are dealt face down.
If the player made the Ante bet, then he may surrender his hand for half the Ante bet.
The dealer will turn over his cards.
The dealer needs a queen high or better to qualify.
If the dealer does not qualify, then the player's Ante bet will pay 1 to 2 (win of half the bet amount).
If the dealer qualifies, then the player's hand will be compared to the dealer's hand, and the higher hand wins. The order of poker hands is indicated below.
If the player has the higher poker hand then the Ante bet will pay 3 to 1 for a straight flush, 2 to 1 for a three of a kind, 3 to 2 for a straight, and 1 to 1 for all other hands.
If the dealer has the higher poker hand then the Ante bet will lose.
If the player and dealer tie then the Ante bet will push.
The Pairplus bet will pay entirely based on the poker value of the player's hand, as shown in the Pairplus section below.

Analysis

The following table shows the possible outcomes of the Ante bet, assuming optimal player strategy. The lower right cell shows a house edge of 2.76%.

Ante Return Table
Event	Pays	Combinations	Probability	Return
Straight flush win	3	617044	0.001515	0.004546
Three of a kind win	2	665776	0.001635	0.00327
Straight win	1.5	8975484	0.022044	0.033065
All other wins	1	87096380	0.213906	0.213906
Dealer doesn't qualify	0.5	85493652	0.20997	0.104985
Push	0	267648	0.000657	0
Fold	-0.5	132652800	0.325792	-0.162896
Dealer wins	-1	91401616	0.22448	-0.22448
Total		407170400	1	-0.027602

There is no raising in Q Poker, so the element of risk is the same as the house edge at 2.76%. To compare Q Poker to Three Card Poker, the element of risk for the common 1-4-5 Ante Bonus pay table is 2.01%, making Three Card Poker the marginally better bet.

Following is the return table for the Pairplus bet offered at the Lisboa. The lower right cell shows a house edge of 2.32%.

Event	Pays	Combinations	Probability	Return
Pairplus Return Table
Straight flush	40	48	0.002172	0.086878
Three of a kind	30	52	0.002353	0.070588
Straight	6	720	0.032579	0.195475
Flush	4	1096	0.049593	0.198371
Pair	1	3744	0.169412	0.169412
Loser	-1	16440	0.743891	-0.743891
Total		22100	1	-0.023167

Strategy

The player should raise with a poker value hand of Q64 or higher.

I'm often asked what is the optimal mix of Ante and Pairplus bet. The house edge on the Pairplus is less, so the optimal mix is 100% Pairplus and 0% Ante.