Last Updated: July 24, 2004

Pyramid Poker

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Introduction

On July 22, 2004, I spotted Pyramid Poker at the Bellagio. It is a simplified version of Pai Gow Poker, using three cards instead of seven. If you are looking for a game of skill that is easy to play and strategy is usually obvious then you may like Pyramid Poker.

Rules

  1. Game is played with a single ordinary 52-card deck.
  2. All cards are ranked as in poker except aces are always high.
  3. After bets are made each player and dealer get three cards each, dealt face down.
  4. Player must arrange his three cards into a 2-card and a 1-card hand. The 1-card hand must be less than the 2-card hand.
  5. A pair shall beat any two singletons in the 2-card hand. There are no straights or flushes. Otherwise hands are scored according to poker value.
  6. After players have arranged their hands the dealer will arrange his hand according to the house way below.
  7. Player's 1-card hand will be compared to the dealer's 1-card hand and player's 2-card hand compared to dealer's 2-card hand. The highest hands shall win. All copies shall go to the dealer (thus the house advantage).
  8. If player wins both ways then he shall win 1 to 1.
  9. If player wins one way and loses one way then his bet shall push.
  10. If dealer wins both ways then the player shall lose his bet.

House Way

  1. With three singletons play middle card in the 1-card hand.
  2. With a pair of 2's to 8's always play the pair in the 2-card hand.
  3. With a pair of 9's play the pair in the 2-card hand if the singleton is a 6 or more, otherwise play a 9 in the 1-card hand.
  4. With a pair of 10's play the pair in the 2-card hand if the singleton is a 7 or more, otherwise play a 10 in the 1-card hand.
  5. With a pair of jacks play the pair in the 2-card hand if the singleton is an 8 or more, otherwise play a jack in the 1-card hand.
  6. With a pair of queens play the pair in the 2-card hand if the singleton is a 9 or more, otherwise play a queen in the 1-card hand.
  7. With a pair of kings play the pair in the 2-card hand if the singleton is a 10 or more, otherwise play a king in the 1-card hand.
  8. With a pair of aces play the pair in the 2-card hand if the singleton is a jack or more, otherwise play a ace in the 1-card hand.

Strategy

Following is the optimal player strategy.

With three singletons play the middle card in the 1-card hand, except play the lowest card in the 1-card hand with any of the following.

  1. 2, 3, and any card 5 or greater.
  2. 2, 4, and any card queen or greater.

With a pair and a singleton normally play the pair in the 2-card hand except with any of the following.

  1. 2 to 4 singleton and a pair of jacks or higher.
  2. 5 to 7 singleton and a pair of queens or higher.
  3. 8 or 9 singleton and a pair of kings or higher.
  4. 10 or jack singleton and a pair of aces.

House Edge

The following table shows the possible outcomes in Pyramid Poker. The lower right cell shows a house edge of 3.53%.

Return Table for Pyramid Poker

Event Combinations Probability Pays Return
Win 130992144 0.321713 1 0.321713
Tie 130801752 0.321246 0 0
Loss 145376504 0.357041 -1 -0.357041
Total hands= 407170400 1 -0.035328

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