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Q Poker
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%.
Pairplus Return Table
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 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.