Hi-Low Pai Gow Poker

Introduction

I came across a new game called Hi-Low Pai Gow Poker while visiting the Luxor on August 27, 2010. This game allows players to engage in typical pai gow poker or to place separate bets on their front and back hands. Below are the gameplay rules.

Rules

In this explanation, I will presume that the reader is already familiar with the rules of traditional pai gow poker. For those who aren’t, please follow my pai gow poker page . Hi-Low Pai Gow Poker operates similarly to standard pai gow poker but introduces extra betting opportunities. Here are the three types of bets a player can make:

• High Hand : This is a bet that the player’s high hand will outscore the dealer’s high hand.
• Low Hand : This is a wager that the player’s low hand will surpass the dealer’s low hand.
• Both : This functions like a typical wager in pai gow poker.

If a player places different amounts on the High Hand and Low Hand bets, they are required to set their hand in accordance with the house rules.

At the Luxor, where I first encountered this game, they adopted the conventional pai gow poker rule for banking, which involves alternating between the dealer and players. When a player’s turn to act as banker comes, the opportunity circulates around the table. Should a player choose not to bank, the chance passes to the next eligible player. Therefore, if 'p' players wish to act as the banker, each player would get their turn once every two times around.

Odds

The table below illustrates the expected returns for the Hi Hand, Low Hand, and Both wagers, differentiated by whether the player is the banker or not. The average column reflects the mean expected return when banking every second round on that wager. I operate under the assumption that when the player banks, the dealer's bets will mirror those of the player from the previous round against the dealer-banker.

A core inquiry to address in this analysis revolves around the likelihood of a tie for each hand. I demonstrate that the chance is 1 in 39.24 for the Low hand, 1 in 2,637 for the High hand, and strikingly, 1 in 78,200 for both occurring simultaneously.

Strategy

If you're willing to take on the banking role and feel confident doing so, I recommend that approach. Focus only on the Both wager, expecting the dealer to bet against you with the same amount you previously wagered. If you prefer not to bank—perhaps because other players are placing larger bets than you'd like to cover—then my suggestion is to stick with just the High Hand bet.

Prosperity Bonus

During my visit to Luxor on August 27, 2010, I noticed a side bet known as the Prosperity Bonus. The outcome depended on the player’s Low Hand combined with the last four cards remaining in the deck. After dedicating several hours to analyzing it, I was informed that it had been removed from play.

The complexity in the analysis arises from the strategic decisions players make with their cards, leading to combin (53,7) × combin(46,4) = 25,153,838,509,800 potential scoring combinations. Below is the pay table that was initially provided before the feature was taken out. Should I encounter it again, I will be encouraged to finalize my review. If you happen to find it before I do, my advice would be to refrain from engaging with it unless you're exclusively playing the Prosperity Bonus and prefer suited connectors. The game owner mentioned that the Prosperity Bonus has been approved for use in traditional pai gow poker as well.

Written by: Michael Shackleford