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Last Updated: June 3, 2014

Power Quads

Introduction

Power Quads is a form of video poker bonusing by slot maker IGT. It plays like conventional video poker with a free bonus feature. As the player achieves a four of a kind on the draw, the game keeps track of the progress. When the player has made a four of a kind in all 13 ranks, the player will win a bonus of 500, 1000, or 2000 coins, depending on the game setting.

Rules

Power Quads plays like conventional single-hand video poker, except as follows.

  1. The player must first establish an account for the purpose of recording his progress. How this is done, I'm not sure.
  2. If the player makes a four of a kind on the draw, with a max five-coin bet, in a rank that he hasn't achieved before, then the game will record that the player achieved that particular four of a kind.
  3. When the player has achieved a four of a kind in all 13 ranks, the game will awards the player a bonus. This bonus can be 500, 1000, or 2000 coins, depending on how the game is configured.

Analysis

This analysis assumes optimal player strategy for the given game and pay table. It does not assume strategy deviations for purposes of achieving the bonus faster. That said, the following table shows the expected number of hands between bonuses for various games and pay tables, as well as the increase in expected value due to the bonus feature.

Power Quads — Additional Return

Game Pay Table Cycle* 500 Coin
Increase
1,000 Coin
Increase
2,000 Coin
Increase
Bonus Deuces Wild 9/4/4/3 19,891 0.50% 1.01% 2.01%
Bonus Poker 8/5 17,578 0.57% 1.14% 2.28%
Bonus Poker Deluxe 8/6 17,606 0.57% 1.14% 2.27%
Deuces Wild 25/16/10/4/4/3 20,054 0.50% 1.00% 1.99%
Double Bonus 9/7/5 17,748 0.56% 1.13% 2.25%
Double Double Bonus 9/6 17,481 0.57% 1.14% 2.29%
Double Double Bonus Plus 9/5 17,467 0.57% 1.15% 2.29%
Jacks or Better 9/6 17,580 0.57% 1.14% 2.28%
Super Aces 60/7/5 17,470 0.57% 1.14% 2.29%
Super Double Bonus 8/5 17,205 0.58% 1.16% 2.32%
Super Double Double Bonus 7/5 17,671 0.57% 1.13% 2.26%
Triple Bonus Plus 8/5 17,376 0.58% 1.15% 2.30%
Triple Double Bonus 9/6 18,006 0.56% 1.11% 2.22%
White Hot Aces 8/5 17,374 0.58% 1.15% 2.30%


* Cycle = Average number of hands between bonuses.

The table above shows that the average number of hands between bonuses among all these games is 17,893 hands. The average increase in expected value is 0.56% for a 500 coin bonus, 1.12% for 1,000, and 2.24% for 2,000.

The next table shows the total expected value for various games and pay tables according to the bonus amount.

Power Quads Return Table

Game Pay Table Base
Return
500 Coin
Return
1,000 Coin
Return
2,000 Coin
Return
Bonus Deuces Wild 9/4/4/3 99.45% 99.95% 100.46% 101.46%
Bonus Poker 8/5 99.17% 99.73% 100.30% 101.44%
Bonus Poker Deluxe 8/6 98.49% 99.06% 99.63% 100.76%
Deuces Wild 25/16/10/4/4/3 99.73% 100.23% 100.73% 101.72%
Double Bonus 9/7/5 99.11% 99.67% 100.23% 101.36%
Double Double Bonus 9/6 98.98% 99.55% 100.12% 101.27%
Double Double Bonus Plus 9/5 98.33% 98.91% 99.48% 100.62%
Jacks or Better 9/6 99.54% 100.11% 100.68% 101.82%
Super Aces 60/7/5 98.85% 99.42% 100.00% 101.14%
Super Double Bonus 8/5 98.69% 99.27% 99.85% 101.01%
Super Double Double Bonus 7/5 98.61% 99.18% 99.74% 100.87%
Triple Bonus Plus 8/5 98.73% 99.30% 99.88% 101.03%
Triple Double Bonus 9/6 98.15% 98.71% 99.26% 100.38%
White Hot Aces 8/5 99.24% 99.82% 100.39% 101.54%

Methodology

If each four of a kind were equally likely, then the math on this would have been easy. The expected number of four of a kinds required would be (13/13) + (13/12) + (13/11) + ... + (13/1) = 41.341739. Then, divide by the probability of any four of a kind to get the cycle length.

However, each four of a kind isn't equally likely. The following table shows the probability of each four of kind in 9-6 Jacks or Better, in order, assuming optimal strategy.

Four of a Kind Probability

Rank Probability
Kings 0.000195881
Aces 0.000195666
Queens 0.000195571
Jacks 0.000194995
Fives 0.000175832
Sixes 0.000175830
Sevens 0.000175828
Eights 0.000175793
Fours 0.000175788
Nines 0.000175748
Threes 0.000175746
Deuces 0.000175702
Tens 0.000174166

Given this uneven distribution, all 13! = 6,227,020,800 possible orders of ranks had to be considered. In general, the more skewed the probabilities, the longer it will take to get all of them at least once. To do this analysis, I wrote a recursive program to loop through all of them. It took about ten minutes to complete.

Conclusion

I haven't seen this game in Vegas yet but will keep an eye peeled out for it. With up to 2.3% in additional return, it could turn some negative games positive. The additional return would be even higher with appropriate strategy deviations to go after the four of a kinds you need. However, you're on your own with that.

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Written by: Michael Shackleford

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