Share this

Wizard Recommends

Last Updated: June 4, 2017

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.

Level 1 Pay Table

Event Pays
Ace of spades 15
Ace of diamonds 12
Ace of hearts 10
Ace of clubs 8
Any king 5
Any queen 4
Any jack 3

Level 2 Pay Table

Event Pays
Royal flush 20
Straight flush 10
Any pair 5
Straight 3
Flush 2

Level 3 Pay Table

Event Pays
Royal flush 250
Straight flush 50
Three of a kind 28
Straight 6
Flush 4
Pair 3

Level 4 Pay Table

Event Pays
Royal flush 1000
Straight flush 150
Four aces 150
Four 2-4 100
Four 5-K 50
Flush 10
Straight 9
Three of a kind 8
Two pair 5
Pair 2

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.

Level 1 Analysis

Event Pays Combinations Probability Return
Ace of spades 15 1 0.019231 0.144231
Ace of diamonds 12 1 0.019231 0.115385
Ace of hearts 10 1 0.019231 0.096154
Ace of clubs 8 1 0.019231 0.076923
Any king 5 4 0.076923 0.192308
Any queen 4 4 0.076923 0.153846
Any jack 3 4 0.076923 0.115385
Other 0 36 0.692308 0.000000
Total 0 52 1.000000 0.894231

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

Level 2 Analysis

Event Pays Combinations Probability Return
Royal flush 20 4 0.003017 0.030166
Straight flush 10 48 0.036199 0.180995
Any pair 5 78 0.058824 0.147059
Straight 3 156 0.117647 0.176471
Flush 2 260 0.196078 0.196078
Other 0 780 0.588235 0.000000
Total 40 1326 1.000000 0.730769

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.

Level 3 Analysis

Event Pays Combinations Probability Return
Royal flush 250 4 0.000181 0.022624
Straight flush 50 44 0.001991 0.049774
Three of a kind 28 52 0.002353 0.032941
Straight 6 720 0.032579 0.097738
Flush 4 1,096 0.049593 0.099186
Pair 3 3,744 0.169412 0.254118
Other 0 16,440 0.743891 0.000000
Total 22,100 1.000000 0.556380

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.

Level 4 Analysis

Event Pays Combinations Probability Return
Royal flush 1000 4 0.000015 0.007388
Straight flush 150 40 0.000148 0.011081
Four aces 150 1 0.000004 0.000277
Four 2-4 100 3 0.000011 0.000554
Four 5-K 50 9 0.000033 0.000831
Flush 10 2,816 0.010402 0.052008
Straight 9 2,772 0.010239 0.046076
Three of a kind 8 2,496 0.009220 0.036879
Two pair 5 2,808 0.010372 0.025930
Pair 2 82,368 0.304250 0.304250
Other 0 177,408 0.655307 0.000000
Total 1484 270,725 1.000000 0.485275

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.

Level 5 Analysis

Event Pays Combinations Probability Return
Royal flush 800 495,430,236 0.000025 0.009942
Straight flush 50 2,132,733,288 0.000107 0.002675
4 aces 80 3,903,635,460 0.000196 0.007833
4 2-4 40 10,509,856,008 0.000527 0.010545
4 5-K 25 32,673,298,536 0.001639 0.020489
Full house 7 229,459,754,916 0.011511 0.040290
Flush 5 216,946,473,756 0.010884 0.027209
Straight 4 224,617,025,580 0.011268 0.022537
3 of a kind 3 1,483,756,110,144 0.074436 0.111654
Two pair 2 2,576,626,215,768 0.129263 0.129263
Jacks or better 1 4,291,056,995,796 0.215272 0.107636
Nothing 0 10,861,052,987,712 0.544872 0.000000
Total 19,933,230,517,200 1.000000 0.490073

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%.

Pyramid Poker Summary — 7-5 Bonus Poker

Level Average
Win
Average
Multiplier
Product
1 0.894231 1.000000 0.178846
2 0.730769 1.307692 0.191124
3 0.556380 1.719457 0.191334
4 0.485275 1.975566 0.191738
5 0.490073 2.320259 0.227419
Total 0.980463

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.

Pyramid Poker Summary — 9-5 Double Double Bonus

Level Pay
Table
Average
Win
Average
Multiplier
Product
1 3,4,5,8,10,12,15 0.894231 1.000000 0.178846
2 2,3,5,10,20 0.730769 1.307692 0.191124
3 3,4,6,27,50,250 0.555204 1.719457 0.190930
4 3,4,6,27,50,250 0.483055 1.975566 0.190861
5 2,5,7,8,11,100,250,500,150,1000 0.489365 2.320259 0.227091
Total 1,1,3,4,5,9,50,80,160,160,400,50,800 0.978852

Pyramid Poker Summary — 7-5 Super Double Bonus

Level Pay
Table
Average
Win
Average
Multiplier
Product
1 3,4,5,8,10,12,15 0.894231 1.000000 0.178846
2 2,3,5,10,20 0.730769 1.307692 0.191124
3 3,4,6,28,50,250 0.556380 1.719457 0.191334
4 2,5,8,9,10,50,100,150,150,1000 0.485275 1.975566 0.191738
5 1,1,3,4,5,7,50,80,120,160,80,800 0.488855 2.320259 0.226854
Total 0.979897

Pyramid Poker Summary — 7-5 Super Aces

Level Pay
Table
Average
Win
Average
Multiplier
Product
1 3,4,5,8,10,12,15 0.894231 1.000000 0.178846
2 2,3,5,10,20 0.730769 1.307692 0.191124
3 3,4,6,30,50,250 0.558733 1.719457 0.192143
4 2,6,7,9,12,50,100,500,180,1000 0.499115 1.975566 0.197207
5 1,1,3,4,5,7,50,80,400,60,800 0.494258 2.320259 0.229361
Total 0.988682

Pyramid Poker Summary — 8-6 Bonus Poker Deluxe

Level Pay
Table
Average
Win
Average
Multiplier
Product
1 3,4,5,8,10,12,15 0.894231 1.000000 0.178846
2 2,3,5,10,20 0.730769 1.307692 0.191124
3 3,4,6,29,50,250 0.557557 1.719457 0.191739
4 2,6,8,9,10,200,200,200,150,1000 0.493601 1.975566 0.195028
5 1,1,3,4,6,8,80,50,800 0.492464 2.320259 0.228529
Total 0.985266

Pyramid Poker Summary — 9-6-5 Double Bonus

Level Pay
Table
Average
Win
Average
Multiplier
Product
1 3,4,5,8,10,12,15 0.894231 1.000000 0.178846
2 2,3,5,10,20 0.730769 1.307692 0.191124
3 3,4,6,27,50,250 0.555204 1.719457 0.190930
4 2,4,8,9,10,100,200,300,150,1000 0.481751 1.975566 0.190346
5 1,1,3,5,6,9,50,80,160,50,800 0.489031 2.320259 0.226936
Total 0.978182

Pyramid Poker Summary — 9-6 Triple Double Bonus

Level Pay
Table
Average
Win
Average
Multiplier
Product
1 3,4,5,8,8,8,15 0.836538 1.000000 0.167308
2 2,3,5,10,20 0.730769 1.307692 0.191124
3 3,4,6,27,50,250 0.555204 1.719457 0.190930
4 2,5,8,9,10,100,250,500,150,1000 0.487583 1.975566 0.192651
5 1,1,2,4,6,9,50,80,160,400,800,50,800 0.490770 2.320259 0.227743
Total 0.969755

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







Written by: Michael Shackleford

Wizard Recommends