Pyramid Poker

Introduction

Pyramid Poker is a video poker variant by IGT. It features a triangular pyramid of cards with five at the base. For the five-card base, the game plays like standard video poker. The four top levels are random and pay credits and multipliers according to the posted pay tables.
 

Rules

 

Following are the rules for the full Pyramid Poker game, including the multiplier feature. It should be noted the player can also play without the multiplier feature, without having double the bet to invoke the feature. However, this analysis is on the full version with the multiplier feature only.

1. Five 52-card decks are used, one for each level.
2. The player may bet 2 to 10 credits per level, in increments of 2. There is an economy of scale incentive to bet the maximum 10 credits per line, for a total bet of 50 credits.
3. After pressing the "deal" button, the player shall get five cards on the bottom row face up, and the top four rows face down.
4. The player may discard cards he doesn't want, as in conventional video poker.
5. Replacements cards will be dealt to the bottom hand.
6. A multiplier shall start at 1.
7. The top, level 1, card shall be revealed in the pyramid.
8. The player shall be paid according to the level 1 pay table.
9. If the player had a paying hand in level 1, then the multiplier shall be incremented by 1.
10. The level 2 cards shall be revealed in the pyramid.
11. The player shall be paid according to the level 2 pay table and the multiplier at that point.
12. If the player had a paying hand in level 2, then the multiplier shall be incremented by 1.
13. The level 3 cards shall be revealed in the pyramid.
14. The player shall be paid according to the level 3 pay table and the multiplier at that point.
15. If the player had a paying hand in level 3, then the multiplier shall be incremented by 1.
16. The level 4 cards shall be revealed in the pyramid.
17. The player shall be paid according to the level 4 pay table and the multiplier at that point.
18. If the player had a paying hand in level 4, then the multiplier shall be incremented by 1.
19. The player shall be paid for his level 5 hand and the multiplier at that point.

 

The following pay tables show the win per two coins bet, based on a maximum 10 coins bet per level, for 7-5 Bonus Poker. Please note that these tables vary from game to game.

Example

 

In this example I bet ten credits in Bonus Poker. Wins are based on one credit bet per line, with the other five credits being a fee.

 

• Level 1: The top hand was a queen, which pays 4. The multiplier is always 1x on the top hand. So my win for level 1 is 1×4 = 4. Because I had a winning hand, my multiplier increases to 2 for the next hand.
• Level 2: The second level is a flush, which pays 2. The multiplier was 2 also, so my win for level 2 is 2 × 2 = 4. Because I won, my multiplier going into hand 3 increases by one to 3.
• Level 3: A pair in level 3 pays 3. The multiplier was also 3, so my win is 3 × 3 = 9. My multiplier increases to 4 because I won the hand.
• Level 4: I had garbage which pays 0. My big multiplier of 4 was wasted: 4 × 0 = 0. Because I didn't win anything in level 4, my multiplier remains at 4 in the next level.
• Level 5: My pair of jacks in the bottom level pays 1. With a multiplier of 4, my win in level 4 is 1 × 4 = 4.

 

My total win for that game is 4 + 4 + 9 + 0 + 4 = 21.

Analysis — 7-5 Bonus Poker

 

The following tables show the probability and contribution to the return for each hand at each level in 7-5 Bonus Poker. In each case, the return is the product of the pay, probability, and 0.5. The reason for dividing by 2 is the pays are per two credits bet.

The probability of a paying hand in level 1 is 30.76%, for an average multiplier going into level 2 of 1.3076.

The probability of a paying hand in level 2 is 41.18%, for an average multiplier going into level 3 of 1.3076+0.4118 = 1.7195.

The probability of a paying hand in level 3 is 25.61%, for an average multiplier going into level 4 of 1.7195 + 0.2561 = 1.975566.

The probability of a paying hand in level 3 is 34.47%, for an average multiplier going into level 5 of 1.9756 + 0.3447 = 2.320259.

The following table shows the probability and contribution to the return for 7-5 Bonus Poker, a game observed at the Palace Station. As before, the returns have been divided by two because wins are paid in coins based on every two coins bet.

We're ready to summarize each level. The following table shows the average win and multiplier for each level. The product column shows the overall contribution to the return. The bottom right cell shows an overall return of 98.05%. In case you were wondering, the return for this pay table in conventional video poker is 98.01%.

Analysis of Other Games

 

To prevent this page from running to long, I will present just the summary table of some other games and pay tables. I'm adding a column for the pay table, which varies from game to game at all levels.

Other Games

 

Here are a couple pay tables I haven't analyzed yet. Click on either version for a larger version.

Bonus Deuces

Bonus Deuces

 

External Links

 

• Wizard of Vegas — Discussion about Pyramid Poker.

Written by: Michael Shackleford