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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
- The game is played with a standard 52-card deck.
- Except as noted, conventional video poker rules are followed.
- The player must bet in increments of three coins. In particular, the total bet amount can be 3, 6, 9, 12, or 15 coins.
- 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.