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Last Updated: June 3, 2017

Flip & Pay Poker

Introduction



Flip & Pay Poker is a video poker variant that is placed on top of conventional three-play, five-play, and ten-play video poker machines. The player can play those games normally or pay a fee equal to the maximum bet amount of five coins per line to invoke the Flip & Pay feature. If the feature is active, cards may flip a card one rank in either direction, leaving the suit the same, if it improves the hand to at least a two pair.

Rules



  1. Flip & Pay can play like conventional three-, five-, or ten-play video poker. In addition, if the player pays a fee equal to the total bet amount if playing without the feature, then he will invoke the Flip & Pay feature.
  2. With the feature active, at most one card will flip one position in rank, but not suit, on the deal if these conditions are bet:
    • The flip results in a hand of two pair or higher.
    • The flip results in a hand of greater expected value than with the original card.
    • The flip results in a card not already in the player's hand.

  3. If more than one card meet these requirements, the game will chose the flip that results in a hand of the greatest expected value.
  4. Cards of rank three to king can flip one rank in either direction. For example, the seven of hearts can flip to the six of hearts or eight of hearts.
  5. The deuce can flip to a three or ace.
  6. The ace can flip to a deuce or king.
  7. The player can choose to un-flip the card if he wants, but he never should.
  8. If a card gets flipped, the old card will be put back in the deck, available to get on the draw.
  9. In addition to the enabling the feature, the additional fee pumps up the pay table, generally on the straight, flush, and full house.


Example



The example below shows a game based on 3-play Bonus Poker. On the deal I was dealt the five of clubs, five of hearts, the four of diamonds, and two junk cards. The four of diamonds flipped up to the five of diamonds, giving me a three of a kind. You can tell is was formerly the four of diamonds from the box on lower right.



I threw away the two junk cards and improved to a four of a kind on one of my hands on the draw.



Analysis



The following tables show my analysis of games and pay tables I'm aware of. The return column is the product of the win, probability and 0.5. The reason for dividing by two is the player must double his bet to invoke the feature, thus any win should be divided by two if comparing it to the total amount bet.

13-10-7 Jacks or Better

Event Pays Combinations Probability Return
Royal flush 800 521,357,448 0.000026 0.010462
Straight flush 50 2,690,768,748 0.000135 0.003375
Four of a kind 25 153,997,920,828 0.007726 0.096571
Full house 13 670,186,134,612 0.033622 0.218540
Flush 10 338,467,524,204 0.016980 0.084900
Straight 7 675,700,173,072 0.033898 0.118644
Three of a kind 3 2,662,719,968,052 0.133582 0.200373
Two pair 2 3,572,194,567,428 0.179208 0.179208
Jacks or better 1 2,574,912,836,736 0.129177 0.064588
Nothing 0 9,281,839,266,072 0.465647 0.000000
Total 19,933,230,517,200 1.000000 0.976661


12-9-8 Jacks or Better

Event Pays Combinations Probability Return
Royal flush 800 522,833,868 0.000026 0.010492
Straight flush 50 2,552,206,332 0.000128 0.003201
Four of a kind 25 154,030,102,716 0.007727 0.096591
Full house 12 670,277,661,444 0.033626 0.201757
Flush 9 314,434,550,220 0.015774 0.070985
Straight 8 702,030,676,812 0.035219 0.140876
Three of a kind 3 2,661,931,750,404 0.133542 0.200314
Two pair 2 3,567,705,909,876 0.178983 0.178983
Jacks or better 1 2,630,225,949,444 0.131952 0.065976
Nothing 0 9,229,518,876,084 0.463022 0.000000
Total 19,933,230,517,200 1.000000 0.969174


12-9-7 Bonus Poker

Event Pays Combinations Probability Return
Royal flush 800 505,817,256 0.000025 0.010150
Straight flush 50 2,561,493,324 0.000129 0.003213
Four aces 80 12,700,415,844 0.000637 0.025486
Four 2-4 40 35,535,300,792 0.001783 0.035654
Four 5-K 25 105,942,557,544 0.005315 0.066436
Full house 12 670,974,672,780 0.033661 0.201967
Flush 9 317,843,280,300 0.015945 0.071754
Straight 7 689,679,088,800 0.034599 0.121098
Three of a kind 3 2,669,307,415,104 0.133912 0.200869
Two pair 2 3,580,053,587,352 0.179602 0.179602
Jacks or better 1 2,643,732,119,268 0.132629 0.066315
Nothing 0 9,204,394,768,836 0.461761 0.000000
Total 19,933,230,517,200 1.000000 0.982544


11-10-7 Bonus Poker

Event Pays Combinations Probability Return
Royal flush 800 516,780,156 0.000026 0.010370
Straight flush 50 2,684,255,892 0.000135 0.003367
Four aces 80 12,711,938,124 0.000638 0.025509
Four 2-4 40 35,519,125,224 0.001782 0.035638
Four 5-K 25 105,795,529,536 0.005307 0.066344
Full house 11 670,223,812,716 0.033623 0.184929
Flush 10 339,614,801,712 0.017038 0.085188
Straight 7 676,165,474,020 0.033922 0.118725
Three of a kind 3 2,663,378,406,972 0.133615 0.200422
Two pair 2 3,572,277,528,492 0.179212 0.179212
Jacks or better 1 2,558,099,223,828 0.128333 0.064167
Nothing 0 9,296,243,640,528 0.466369 0.000000
Total 19,933,230,517,200 1.000000 0.973871


11-10-7 Bonus Poker

Event Pays Combinations Probability Return
Royal flush 800 516,780,156 0.000026 0.010370
Straight flush 50 2,684,255,892 0.000135 0.003367
Four aces 80 12,711,938,124 0.000638 0.025509
Four 2-4 40 35,519,125,224 0.001782 0.035638
Four 5-K 25 105,795,529,536 0.005307 0.066344
Full house 11 670,223,812,716 0.033623 0.184929
Flush 10 339,614,801,712 0.017038 0.085188
Straight 7 676,165,474,020 0.033922 0.118725
Three of a kind 3 2,663,378,406,972 0.133615 0.200422
Two pair 2 3,572,277,528,492 0.179212 0.179212
Jacks or better 1 2,558,099,223,828 0.128333 0.064167
Nothing 0 9,296,243,640,528 0.466369 0.000000
Total 19,933,230,517,200 1.000000 0.973871


9-6-5 Bonus Poker Deluxe

Event Pays Combinations Probability Return
Royal flush 800 570,086,412 0.000029 0.011440
Straight flush 50 2,417,623,560 0.000121 0.003032
Four of a kind 80 158,767,693,248 0.007965 0.318599
Full house 9 680,958,866,952 0.034162 0.153729
Flush 6 213,983,057,388 0.010735 0.032205
Straight 5 572,679,063,744 0.028730 0.071825
Three of a kind 3 2,794,572,629,544 0.140197 0.210295
Two pair 1 3,663,491,309,784 0.183788 0.091894
Jacks or better 1 3,140,556,504,480 0.157554 0.078777
Nothing 0 8,705,233,682,088 0.436720 0.000000
Total 19,933,230,517,200 1.000000 0.971796


9-6-5 Bonus Poker Deluxe

Event Pays Combinations Probability Return
Royal flush 800 498,265,416 0.000025 0.009999
Straight flush 50 2,541,044,892 0.000127 0.003187
Four of a kind 80 158,140,902,888 0.007934 0.317341
Full house 9 677,342,999,232 0.033981 0.152913
Flush 8 325,906,728,432 0.016350 0.065400
Straight 5 553,423,780,656 0.027764 0.069410
Three of a kind 3 2,761,898,734,296 0.138558 0.207836
Two pair 1 3,606,837,787,800 0.180946 0.090473
Jacks or better 1 2,765,318,689,980 0.138729 0.069365
Nothing 0 9,081,321,583,608 0.455587 0.000000
Total 19,933,230,517,200 1.000000 0.985923


11-6-4 Double Double Bonus

Event Pays Combinations Probability Return
Royal flush 800 585,802,740 0.000029 0.011755
Straight flush 50 2,466,484,632 0.000124 0.003093
Four aces + 2-4 400 4,603,499,724 0.000231 0.046189
Four aces + 5-K 160 11,246,976,408 0.000564 0.045139
Four 2-4 + A-4 160 11,028,548,448 0.000553 0.044262
Four 2-4 + 5-K 80 25,294,427,376 0.001269 0.050758
Four 5-K 50 109,589,693,532 0.005498 0.137446
Full house 11 614,491,141,716 0.030827 0.169551
Flush 6 220,368,113,628 0.011055 0.033166
Straight 4 529,565,789,016 0.026567 0.053134
Three of a kind 3 2,905,018,133,328 0.145737 0.218606
Two pair 1 3,190,670,661,924 0.160068 0.080034
Jacks or better 1 3,604,714,562,916 0.180839 0.090420
Nothing 0 8,703,586,681,812 0.436637 0.000000
Total 19,933,230,517,200 1.000000 0.983554


10-6-4 Double Double Bonus

Event Pays Combinations Probability Return
Royal flush 800 588,926,604 0.000030 0.011818
Straight flush 50 2,472,863,940 0.000124 0.003101
Four aces + 2-4 400 4,603,208,700 0.000231 0.046186
Four aces + 5-K 160 11,246,109,528 0.000564 0.045135
Four 2-4 + A-4 160 11,028,494,268 0.000553 0.044262
Four 2-4 + 5-K 80 25,294,427,376 0.001269 0.050758
Four 5-K 50 109,580,410,176 0.005497 0.137434
Full house 10 614,453,184,756 0.030826 0.154128
Flush 6 220,503,170,436 0.011062 0.033186
Straight 4 529,768,853,076 0.026577 0.053154
Three of a kind 3 2,904,613,097,580 0.145717 0.218576
Two pair 1 3,190,148,253,720 0.160042 0.080021
Jacks or better 1 3,603,141,928,044 0.180761 0.090380
Nothing 0 8,705,787,588,996 0.436747 0.000000
Total 19,933,230,517,200 1.000000 0.968140


7-5-4 Triple Double Bonus

Event Pays Combinations Probability Return
Royal flush 800 628,368,096 0.000032 0.012609
Straight flush 50 2,424,642,192 0.000122 0.003041
Four aces + 2-4 800 5,704,958,484 0.000286 0.114481
Four aces + 5-K 160 8,063,956,104 0.000405 0.032364
Four 2-4 + A-4 400 14,343,875,796 0.000720 0.143919
Four 2-4 + 5-K 80 18,972,342,744 0.000952 0.038072
Four 5-K 50 109,467,189,972 0.005492 0.137292
Full house 7 564,601,982,544 0.028325 0.099136
Flush 5 214,593,010,152 0.010766 0.026914
Straight 4 541,499,118,228 0.027166 0.054331
Three of a kind 2 2,954,480,356,680 0.148219 0.148219
Two pair 1 3,181,724,163,108 0.159619 0.079810
Jacks or better 1 3,581,375,418,000 0.179669 0.089834
Nothing 0 8,735,351,135,100 0.438231 0.000000
Total 19,933,230,517,200 1.000000 0.980023


6-5-4 Triple Double Bonus

Event Pays Combinations Probability Return
Royal flush 800 628,812,372 0.000032 0.012618
Straight flush 50 2,429,960,088 0.000122 0.003048
Four aces + 2-4 800 5,704,701,000 0.000286 0.114476
Four aces + 5-K 160 8,062,912,236 0.000404 0.032360
Four 2-4 + A-4 400 14,343,850,512 0.000720 0.143919
Four 2-4 + 5-K 80 18,971,968,128 0.000952 0.038071
Four 5-K 50 109,457,502,072 0.005491 0.137280
Full house 6 564,542,204,976 0.028322 0.084965
Flush 5 214,729,509,180 0.010772 0.026931
Straight 4 543,916,355,832 0.027287 0.054574
Three of a kind 2 2,953,690,029,408 0.148179 0.148179
Two pair 1 3,180,104,865,324 0.159538 0.079769
Jacks or better 1 3,574,888,232,976 0.179343 0.089672
Nothing 0 8,741,759,613,096 0.438552 0.000000
Total 19,933,230,517,200 1.000000 0.965862


Summary



The following table summarizes known games and pay tables thus far and the associated return of each.

Flip & Pay Summary

Game Pay Table Return
Bonus Poker 12-9-7 98.25%
Bonus Poker 11-10-7 97.39%
Bonus Poker Deluxe 9-8-5 98.59%
Bonus Poker Deluxe 9-6-5 97.18%
Double Bonus Poker 12-7-6 98.81%
Double Bonus Poker 12-7-5 97.26%
Double Double Bonus 11-6-4 98.36%
Double Double Bonus 10-6-4 96.81%
Jacks or Better 13-10-7 97.67%
Jacks or Better 12-9-8 96.92%
Triple Double Bonus 7-5-4 98.00%
Triple Double Bonus 6-5-4 96.59%






Acknowledgements



I would like to thank Gary J. Koehler for verifying the returns in the tables above.


Written by: Michael Shackleford

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