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Last Updated: April 8, 2015

Pyramid Bonus Poker

Introduction





Pyramid Bonus Poker is a video poker game by BetSoft that pays three ways: the full five card hand, the left three cards, and the right three cards. If you're looking for a challenging video poker game in terms of strategy, it doesn't get much more complicated than this.

Rules



  1. The game is played with a standard 52-card deck.
  2. Except as noted, conventional video poker rules are followed.
  3. The player must bet in increments of three coins. In particular, the total bet amount can be 3, 6, 9, 12, or 15 coins.
  4. The player will be paid according the the left three cards, the full five-card hand, and the right three cards.

The following three tables show the three pay tables according to the amount bet on that hand alone.

Left Three Cards

Hand 1 coin 2 coins 3 coins 4 coins 5 coins
Mini Royal 50 100 150 200 250
Straight Flush 20 40 60 80 100
Three of a Kind 10 20 30 40 50
Straight 5 10 15 20 25
Flush 1 2 3 4 5
Jacks or Better 1 2 3 4 5
All Other 0 0 0 0 0


Right Three Cards

Hand 1 coin 2 coins 3 coins 4 coins 5 coins
Mini Royal 100 200 300 400 500
Straight Flush 15 30 45 60 75
Three of a Kind 5 10 15 20 25
Straight 3 6 9 12 15
Flush 2 4 6 8 10
Jacks or Better 1 2 3 4 5
All Other 0 0 0 0 0


All Five Cards

Hand 1 coin 2 coins 3 coins 4 coins 5 coins
Royal Flush 800 1600 2400 3200 4000
Straight Flush 50 100 150 200 250
Four Aces 80 160 240 320 400
Four 2s, 3s, 4s 40 80 120 160 200
Four 5s through Ks 25 50 75 100 125
Full House 8 16 24 32 40
Flush 5 10 15 20 25
Straight 4 8 12 16 20
Three of a Kind 3 6 9 12 15
Two Pair 2 4 6 8 10
Jacks or Better 1 2 3 4 5
All Other 0 0 0 0 0


What is a Wild Royal?



The game says the highest pay in the three-card hands is a "wild royal." However, after much play, I can say with a probability of 99.54% that what they mean is a "mini royal." A mini royal is a suited ace-king-queen. As evidence, I present the following screenshot:



What is the Greatest Possible Total Win?



The game says "Win up to 4,200 credits!" However, the greatest possible win is actually 4,600 credits. It can be achieved with any of the following suited hands: AKQJT, KAQJT, AKQTJ, KAQJT.

Analysis



The following three tables show the probability and return of all possible outcomes for all three hands. As usual, optimal strategy is assumed.

Left Three Cards

Hand Pays Permutations Probability Return
Mini Royal 100 48,483,738,306,432 0.000845 0.084455
Straight Flush 15 359,053,407,884,160 0.006254 0.093817
Three of a Kind 5 433,686,550,480,128 0.007555 0.037773
Straight 3 4,190,948,742,454,848 0.073003 0.219010
Flush 2 6,607,480,668,883,776 0.115097 0.230195
Jacks or Better 1 5,692,161,308,220,288 0.099153 0.099153
All Other 0 40,075,889,473,306,368 0.698093 0.000000
Totals 57,407,703,889,536,000 1.000000 0.764402


Right Three Cards

Hand Pays Permutations Probability Return
Mini Royal 50 42,542,925,752,448 0.000741 0.037053
Straight Flush 20 385,961,990,977,728 0.006723 0.134463
Three of a Kind 10 468,256,589,836,992 0.008157 0.081567
Straight 5 5,167,552,229,028,288 0.090015 0.450075
Flush 1 4,519,462,081,698,432 0.078726 0.078726
Jacks or Better 1 5,694,073,798,368,384 0.099187 0.099187
All Other 0 41,129,854,273,873,728 0.716452 0.000000
Totals 57,407,703,889,536,000 1.000000 0.881071


All Five Cards

Hand Pays Permutations Probability Return
Royal Flush 800 1,217,101,514,112 0.000021 0.016961
Straight Flush 50 6,994,469,916,288 0.000122 0.006092
Four Aces 80 9,361,668,056,832 0.000163 0.013046
Four 2s, 3s, 4s 40 21,308,513,500,800 0.000371 0.014847
Four 5s through Ks 25 65,418,413,819,904 0.001140 0.028489
Full House 8 537,667,682,454,144 0.009366 0.074926
Flush 5 732,583,590,427,584 0.012761 0.063805
Straight 4 771,591,717,616,896 0.013441 0.053762
Three of a Kind 3 3,244,715,958,044,736 0.056521 0.169562
Two Pair 2 6,506,767,231,171,776 0.113343 0.226686
Jacks or Better 1 11,189,814,579,115,776 0.194918 0.194918
All Other 0 34,320,262,963,897,152 0.597834 0.000000
Totals 57,407,703,889,536,000 1.000000 0.863094


To summarize, the three returns are as follows:

  • Left three cards: 0.764402
  • Right three cards: 0.881071
  • All five cards: 0.863094

The average of these returns is 0.836189.

Strategy



Sorry, you're on your own with that. At a return of 83.62%, I don't think there would be much demand for one anyway.

Other Games



Here are some other Pyramid Poker games. These have not been analyzed yet.


Aces & Faces

Bonus Poker Deluxe

Deuces Wild

Double Bonus

Double Jackpot

Jacks or Better

Joker Poker


Acknowledgement



I've seen a lot of games in my 18 years analyzing casino games, and this one is one of the hardest to analyze. It ranks up there with Lunar Poker. Because card order matters in this game, the amount of permutations to loop through is a very large number. In this case, 57,407,703,889,536,000. This is 14,400 times as many as conventional video poker. It takes a lot of creative short cuts for the computer to cycle through all the permutations in a matter of days, as opposed to centuries.

With that daunting task ahead of me, I felt it had the name of JB, otherwise known as the "video poker genius," all over it. When I showed him the game, I knew he would rise to the occasion, and he did.

It took JB about three weeks to write the program, and the program itself took about a week to run. The output is what you see above. So, all due credit and praise to JB on this one.

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Strategies

Full-Pay Jacks or Better:

Full-Pay Deuces Wild:

Quick Quads:

Other Strategies:



Written by: Michael Shackleford

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