Hi-Low Pai Gow Poker

Introduction

Hi-Low Pai Gow Poker is a new table game I noticed at the Luxor on August 27, 2010. The player may play the game like typical pai gow poker and/or may bet individually on his front or back bet. Following are the rules.

Rules

I am going to assume the reader already knows the rules for conventional pai gow poker. If not, please see my pai gow poker page. Hi-Low Pai Gow Poker plays like regular pai gow poker, but with additional betting options. Following are the three bets the player may make:

• High Hand: Bet that the player's high hand will beat the dealer's high hand.
• Low Hand: Bet that the player's low hand will beat the dealer's low hand.
• Both: The same as a conventional pai gow poker wager.

If the player bets any unequal amounts on the High Hand and Low Hand wagers, then the player must set his hand by the house way.

At the Luxor, where I saw the game, they followed the standard pai gow poker banking rule where the dealer and players alternate banking. When it was a player's turn to bank, the option would rotate around the table. If a player declined to bank, then it would be offered to the next player in turn. So, if p players wished to bank, then each would have the turn to bank once every 2×p turns.

Odds

The following table shows the expected return of the Hi Hand, Low Hand, and Both wagers, crossed by whether or not the player is banking. The average column shows the average expected return, if banking every other hand on that wager. I assume that when the player is banking, the dealer will bet the same way and amount the player bet his previous turn betting against the dealer-banker.

The fundamental question to answer in the analysis is what is the probability of a tie in each hand. I show the probability is 1 in 39.24 in the Low hand, 1 in 2,637 in the High hand, and 1 in 78,200 at the same time.

Strategy

If you're able to bank and comfortable with banking, then I would do so. Play the Both wager only, assuming the dealer will bet against you the same amount you bet against him the last time he banked. If you don't wish to bank, perhaps because other players are betting more than you are comfortable covering, then I recommend betting the High Hand only.

Prosperity Bonus

When I saw the game at the Luxor on August 27, 2010, there was a side wager called the Prosperity Bonus. The win was based on the player's Low Hand and the last four cards in the deck. After spending hours analyzing it, I was informed that they removed it from the felt.

The reason the analysis is complicated is it depends on how the player plays his cards, resulting in combin(53,7)×combin(46,4)=25,153,838,509,800 possible combinations to score. Here is the pay table that was offered before they removed it. If I ever see it again, I will be motivated to complete my analysis. If you should find it before I do, my advice would be to leave it alone unless you play the Prosperity Bonus only, favoring playing suited connectors. The game owner told me the Prosperity Bonus is approved for use in conventional pai gow poker as well.