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Last Updated: October 18, 2020

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Reversible Royals

Introduction

A "reversible royal" is one that pays a premium for a sequential royal flush in EITHER direction. This is not to be confused with a Sequential Royal, which pays in the 10-J-Q-K-A direction only. To make matters more confusing, sometimes Reversible Royal games refer to one in either direction as a Sequential Royal. Whatever the terminology, this page refers to the game that pays a jackpot for a royal flush in sequence in either direction.

Overview

The following table shows returns for some common games and pay tables that pay 50,000 coins, based on a five-coin bet, for a reversible royal. As usual, this assumes optimal player strategy, including card order.

Reversible Royal Game Summary

Game Pay Table Return
Jacks or Better 9-6 100.01%
Jacks or Better 9-5 98.92%
Jacks or Better 8-6 98.86%
Jacks or Better 8-5 97.77%
Jacks or Better 7-5 96.62%
Jacks or Better 6-5 95.47%
Bonus Poker 8-5 99.64%
Bonus Poker 7-5 98.48%
Bonus Poker 6-5 97.34%
Bonus Poker 10-8-5-1 94.62%
Bonus Poker Deluxe 8-6 98.96%
Bonus Poker Deluxe 8-5 97.87%
Bonus Poker Deluxe 7-5 96.72%
Bonus Poker Deluxe 6-5 95.83%
Double Bonus 9-7-5 99.56%
Double Bonus 9-6-5 98.27%
Double Bonus 9-6-4 96.85%
Double Bonus 9-5-4 95.74%
Double Bonus 7-5-4 93.57%
Double Double Bonus 9-5 98.34%
Double Double Bonus 8-5 97.26%
Double Double Bonus 7-5 96.18%
Double Double Bonus 6-5 95.13%
Triple Double Bonus 9-6 98.62%
Triple Double Bonus 8-6 97.57%
Triple Double Bonus 8-5 96.44%
Triple Double Bonus 7-5 95.38%
Triple Double Bonus 6-5 94.34%

The bottom line is if a reversible royal pays 50,000 coins, for a five-coin bet, it adds 0.45% to 0.50% to the return, depending on the particular game and pay table. A fair average to assume is 0.466%. If the player does not make strategy adjustments for card order, and follows the strategy if all royals pay 4,000 coins, then the player will realize an increase in return of 0.263% only. In other words, 0.203% of the value of the reversible royal win comes from strategy adjustments.

On average, with optimal strategy, a reversible royal occurs once in about 1.9 million hands. Assuming a playing rate of 1,000 hands per hour, playing 24 hours a day, a reversible royal will occur on average once every 78 days.

There is often a progressive jackpot on reversible royal games. On average, every additional 100,000 coins in the jackpot, above the usual 50,000 is worth an additional 1.065% in return. This figure assumes optimal strategy for a 50,000 coin jackpot, not that actual jackpot amount.

The next six sections of this page show return tables for six popular forms of video poker. I do not claim these pay tables are available in reversible royal games, but chose otherwise popular pay tables.

Jacks or Better

9-6 Jacks or Better

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 52,880,588 0.000001 0.005306
Royal Flush 800 2,450,503,473 0.000025 0.019670
Straight Flush 50 10,851,975,695 0.000109 0.005444
Four of a Kind 25 235,415,094,090 0.002362 0.059051
Full House 9 1,147,171,398,690 0.011510 0.103591
Flush 6 1,099,179,417,749 0.011029 0.066172
Straight 4 1,115,571,100,812 0.011193 0.044772
Three of a Kind 3 7,419,111,667,662 0.074440 0.223319
Two Pair 2 12,884,050,953,846 0.129272 0.258544
Jacks or Better 1 21,356,192,145,867 0.214277 0.214277
All Other 0 54,396,105,447,528 0.545783 0.000000
Totals   99,666,152,586,000 1.000000 1.000146

9-5 Jacks or Better

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 53,468,398 0.000001 0.005365
Royal Flush 800 2,464,965,319 0.000025 0.019786
Straight Flush 50 10,642,308,641 0.000107 0.005339
Four of a Kind 25 235,444,952,946 0.002362 0.059058
Full House 9 1,147,321,288,434 0.011512 0.103605
Flush 5 1,085,735,125,727 0.010894 0.054469
Straight 4 1,116,106,524,858 0.011198 0.044794
Three of a Kind 3 7,420,441,870,512 0.074453 0.223359
Two Pair 2 12,886,070,877,900 0.129292 0.258585
Jacks or Better 1 21,412,156,019,271 0.214839 0.214839
All Other 0 54,349,715,183,994 0.545318 0.000000
Totals   99,666,152,586,000 1.000000 0.989198

8-6 Jacks or Better

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 52,867,344 0.000001 0.005304
Royal Flush 800 2,450,207,375 0.000025 0.019667
Straight Flush 50 10,851,436,475 0.000109 0.005444
Four of a Kind 25 235,414,475,406 0.002362 0.059051
Full House 8 1,147,165,830,534 0.011510 0.092081
Flush 6 1,099,132,800,761 0.011028 0.066169
Straight 4 1,115,961,822,462 0.011197 0.044788
Three of a Kind 3 7,419,024,742,560 0.074439 0.223316
Two Pair 2 12,883,831,011,684 0.129270 0.258540
Jacks or Better 1 21,356,068,130,943 0.214276 0.214276
All Other 0 54,396,199,260,456 0.545784 0.000000
Totals   99,666,152,586,000 1.000000 0.988636

8-5 Jacks or Better

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 53,467,882 0.000001 0.005365
Royal Flush 800 2,464,907,269 0.000025 0.019785
Straight Flush 50 10,684,459,907 0.000107 0.005360
Four of a Kind 25 235,441,141,254 0.002362 0.059057
Full House 8 1,147,292,927,526 0.011511 0.092091
Flush 5 1,086,627,274,247 0.010903 0.054513
Straight 4 1,116,553,509,342 0.011203 0.044812
Three of a Kind 3 7,420,202,552,292 0.074451 0.223352
Two Pair 2 12,885,604,494,912 0.129288 0.258575
Jacks or Better 1 21,405,846,854,247 0.214775 0.214775
All Other 0 54,355,380,997,122 0.545375 0.000000
Totals   99,666,152,586,000 1.000000 0.977686

7-5 Jacks or Better

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 53,466,635 0.000001 0.005365
Royal Flush 800 2,464,760,424 0.000025 0.019784
Straight Flush 50 10,698,431,639 0.000107 0.005367
Four of a Kind 25 235,365,578,214 0.002362 0.059038
Full House 7 1,147,011,067,686 0.011509 0.080560
Flush 5 1,086,910,248,647 0.010906 0.054528
Straight 4 1,121,239,190,790 0.011250 0.045000
Three of a Kind 3 7,417,062,617,988 0.074419 0.223257
Two Pair 2 12,881,171,852,640 0.129243 0.258486
Jacks or Better 1 21,407,412,485,967 0.214791 0.214791
All Other 0 54,356,762,885,370 0.545388 0.000000
Totals   99,666,152,586,000 1.000000 0.966176

6-5 Jacks or Better

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 53,464,571 0.000001 0.005364
Royal Flush 800 2,464,717,596 0.000025 0.019784
Straight Flush 50 10,722,771,359 0.000108 0.005379
Four of a Kind 25 235,361,995,110 0.002362 0.059038
Full House 6 1,146,985,878,630 0.011508 0.069050
Flush 5 1,087,674,265,079 0.010913 0.054566
Straight 4 1,121,423,444,586 0.011252 0.045007
Three of a Kind 3 7,416,846,520,800 0.074417 0.223251
Two Pair 2 12,880,760,045,940 0.129239 0.258478
Jacks or Better 1 21,403,423,854,987 0.214751 0.214751
All Other 0 54,360,435,627,342 0.545425 0.000000
Totals   99,666,152,586,000 1.000000 0.954668

Bonus Poker

8-5 Bonus Poker

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 53,428,537 0.000001 0.005361
Royal Flush 800 2,461,367,638 0.000025 0.019757
Straight Flush 50 10,600,767,545 0.000106 0.005318
Four Aces 80 19,499,584,788 0.000196 0.015652
Four 2s, 3s, 4s 40 52,548,720,180 0.000527 0.021090
Four 5s thru Ks 25 163,407,353,430 0.001640 0.040989
Full House 8 1,147,360,794,942 0.011512 0.092096
Flush 5 1,084,498,138,535 0.010881 0.054407
Straight 4 1,115,196,110,712 0.011189 0.044757
Three of a Kind 3 7,420,841,207,556 0.074457 0.223371
Two Pair 2 12,886,573,567,680 0.129297 0.258595
Jacks or Better 1 21,423,989,869,359 0.214958 0.214958
All Other 0 54,339,121,675,098 0.545211 0.000000
Totals   99,666,152,586,000 1.000000 0.996350

7-5 Bonus Poker

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 53,426,774 0.000001 0.005361
Royal Flush 800 2,461,292,517 0.000025 0.019756
Straight Flush 50 10,620,310,013 0.000107 0.005328
Four Aces 80 19,498,560,012 0.000196 0.015651
Four 2s, 3s, 4s 40 52,548,638,652 0.000527 0.021090
Four 5s thru Ks 25 163,331,491,110 0.001639 0.040970
Full House 7 1,147,071,857,646 0.011509 0.080564
Flush 5 1,084,939,961,471 0.010886 0.054429
Straight 4 1,119,943,106,376 0.011237 0.044948
Three of a Kind 3 7,417,635,167,460 0.074425 0.223274
Two Pair 2 12,882,035,376,576 0.129252 0.258504
Jacks or Better 1 21,424,740,962,055 0.214965 0.214965
All Other 0 54,341,272,435,338 0.545233 0.000000
Totals   99,666,152,586,000 1.000000 0.984839

6-5 Bonus Poker

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 53,424,538 0.000001 0.005360
Royal Flush 800 2,461,199,293 0.000025 0.019756
Straight Flush 50 10,676,615,933 0.000107 0.005356
Four Aces 80 19,965,269,628 0.000200 0.016026
Four 2s, 3s, 4s 40 52,548,542,676 0.000527 0.021090
Four 5s thru Ks 25 163,327,615,950 0.001639 0.040969
Full House 6 1,136,663,074,686 0.011405 0.068428
Flush 5 1,086,367,315,511 0.010900 0.054500
Straight 4 1,120,499,476,668 0.011243 0.044970
Three of a Kind 3 7,427,102,013,576 0.074520 0.223559
Two Pair 2 12,881,243,792,844 0.129244 0.258488
Jacks or Better 1 21,416,201,418,507 0.214879 0.214879
All Other 0 54,349,042,826,190 0.545311 0.000000
Totals   99,666,152,586,000 1.000000 0.973382

10-8-5-1 Bonus Poker

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 51,687,491 0.000001 0.005186
Royal Flush 800 2,127,709,350 0.000021 0.017079
Straight Flush 50 12,134,512,451 0.000122 0.006088
Four Aces 80 18,536,614,752 0.000186 0.014879
Four 2s, 3s, 4s 40 52,095,499,836 0.000523 0.020908
Four 5s thru Ks 25 158,116,429,782 0.001586 0.039662
Full House 10 1,113,719,398,050 0.011174 0.111745
Flush 8 1,657,997,019,293 0.016636 0.133084
Straight 5 1,459,915,102,140 0.014648 0.073240
Three of a Kind 3 7,065,241,180,686 0.070889 0.212667
Two Pair 1 12,262,443,012,918 0.123035 0.123035
Jacks or Better 1 18,801,094,521,795 0.188641 0.188641
All Other 0 57,062,679,897,456 0.572538 0.000000
Totals   99,666,152,586,000 1.000000 0.946213

Bonus Poker Deluxe

8-6 Bonus Poker Deluxe

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 52,419,392 0.000001 0.005259
Royal Flush 800 2,354,768,367 0.000024 0.018901
Straight Flush 50 10,828,072,073 0.000109 0.005432
Four of a Kind 80 235,081,870,062 0.002359 0.188695
Full House 8 1,144,692,758,478 0.011485 0.091882
Flush 6 1,109,534,138,933 0.011133 0.066795
Straight 4 1,273,874,692,440 0.012781 0.051126
Three of a Kind 3 7,381,101,976,230 0.074058 0.222175
Two Pair 1 12,792,070,857,798 0.128349 0.128349
Jacks or Better 1 21,029,643,289,293 0.211001 0.211001
All Other 0 54,686,917,742,934 0.548701 0.000000
Totals   99,666,152,586,000 1.000000 0.989616

8-5 Bonus Poker Deluxe

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 53,088,859 0.000001 0.005327
Royal Flush 800 2,444,347,042 0.000025 0.019620
Straight Flush 50 10,733,256,557 0.000108 0.005385
Four of a Kind 80 234,999,452,994 0.002358 0.188629
Full House 8 1,144,304,924,106 0.011481 0.091851
Flush 5 1,083,069,949,667 0.010867 0.054335
Straight 4 1,294,875,833,358 0.012992 0.051969
Three of a Kind 3 7,376,254,098,438 0.074010 0.222029
Two Pair 1 12,782,966,750,910 0.128258 0.128258
Jacks or Better 1 21,057,861,472,467 0.211284 0.211284
All Other 0 54,678,589,411,602 0.548617 0.000000
Totals   99,666,152,586,000 1.000000 0.978686

7-5 Bonus Poker Deluxe

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 53,088,859 0.000001 0.005327
Royal Flush 800 2,444,343,946 0.000025 0.019620
Straight Flush 50 10,734,268,949 0.000108 0.005385
Four of a Kind 80 234,999,292,002 0.002358 0.188629
Full House 7 1,144,304,032,458 0.011481 0.080370
Flush 5 1,083,090,395,651 0.010867 0.054336
Straight 4 1,294,885,115,166 0.012992 0.051969
Three of a Kind 3 7,376,245,996,206 0.074010 0.222029
Two Pair 1 12,782,953,069,686 0.128258 0.128258
Jacks or Better 1 21,057,731,468,331 0.211283 0.211283
All Other 0 54,678,711,514,746 0.548619 0.000000
Totals   99,666,152,586,000 1.000000 0.967205

6-5 Bonus Poker Deluxe

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 53,062,629 0.000001 0.005324
Royal Flush 800 2,444,047,160 0.000025 0.019618
Straight Flush 50 10,734,662,141 0.000108 0.005385
Four of a Kind 80 248,178,428,910 0.002490 0.199208
Full House 6 819,169,556,790 0.008219 0.049315
Flush 5 1,082,994,798,395 0.010866 0.054331
Straight 4 1,294,964,352,126 0.012993 0.051972
Three of a Kind 3 7,795,789,221,462 0.078219 0.234657
Two Pair 1 10,863,196,782,966 0.108996 0.108996
Jacks or Better 1 22,871,725,546,731 0.229483 0.229483
All Other 0 54,676,902,126,690 0.548601 0.000000
Totals   99,666,152,586,000 1.000000 0.958289

Double Bonus

9-7-5 Double Bonus

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 51,739,714 0.000001 0.005191
Royal Flush 800 2,078,745,457 0.000021 0.016686
Straight Flush 50 11,264,353,295 0.000113 0.005651
Four Aces 160 21,878,268,420 0.000220 0.035122
Four 2s, 3s, 4s 80 52,234,038,612 0.000524 0.041927
Four 5s thru Ks 50 159,843,002,934 0.001604 0.080189
Full House 9 1,059,767,682,750 0.010633 0.095699
Flush 7 1,506,508,911,569 0.015116 0.105809
Straight 5 1,491,400,136,766 0.014964 0.074820
Three of a Kind 3 7,267,411,507,938 0.072918 0.218753
Two Pair 1 11,862,201,454,650 0.119019 0.119019
Jacks or Better 1 19,608,905,871,783 0.196746 0.196746
All Other 0 56,622,606,872,112 0.568123 0.000000
Totals   99,666,152,586,000 1.000000 0.995612

9-6-5 Double Bonus

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 52,257,841 0.000001 0.005243
Royal Flush 800 2,421,847,894 0.000024 0.019440
Straight Flush 50 10,788,353,489 0.000108 0.005412
Four Aces 160 22,329,573,372 0.000224 0.035847
Four 2s, 3s, 4s 80 52,285,738,974 0.000525 0.041969
Four 5s thru Ks 50 161,479,672,116 0.001620 0.081010
Full House 9 1,072,643,026,254 0.010762 0.096861
Flush 6 1,106,248,469,201 0.011100 0.066597
Straight 5 1,538,264,063,472 0.015434 0.077171
Three of a Kind 3 7,383,238,417,728 0.074080 0.222239
Two Pair 1 12,068,463,667,284 0.121089 0.121089
Jacks or Better 1 20,910,218,657,691 0.209803 0.209803
All Other 0 55,337,718,840,684 0.555231 0.000000
Totals   99,666,152,586,000 1.000000 0.982681

9-6-4 Double Bonus

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 52,926,276 0.000001 0.005310
Royal Flush 800 2,416,989,797 0.000024 0.019401
Straight Flush 50 10,894,938,191 0.000109 0.005466
Four Aces 160 22,664,266,968 0.000227 0.036384
Four 2s, 3s, 4s 80 52,541,788,494 0.000527 0.042174
Four 5s thru Ks 50 162,613,149,966 0.001632 0.081579
Full House 9 1,080,357,294,108 0.010840 0.097558
Flush 6 1,126,610,885,711 0.011304 0.067823
Straight 4 1,277,988,336,288 0.012823 0.051291
Three of a Kind 3 7,479,661,620,738 0.075047 0.225141
Two Pair 1 12,243,934,692,558 0.122849 0.122849
Jacks or Better 1 21,276,711,104,829 0.213480 0.213480
All Other 0 54,929,704,592,076 0.551137 0.000000
Totals   99,666,152,586,000 1.000000 0.968457

9-5-4 Double Bonus

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 53,538,682 0.000001 0.005372
Royal Flush 800 2,455,567,591 0.000025 0.019710
Straight Flush 50 10,693,916,459 0.000107 0.005365
Four Aces 160 22,512,961,578 0.000226 0.036141
Four 2s, 3s, 4s 80 52,534,127,184 0.000527 0.042168
Four 5s thru Ks 50 162,826,915,608 0.001634 0.081686
Full House 9 1,080,657,216,786 0.010843 0.097585
Flush 5 1,089,486,323,753 0.010931 0.054657
Straight 4 1,296,022,256,100 0.013004 0.052015
Three of a Kind 3 7,481,643,767,916 0.075067 0.225201
Two Pair 1 12,246,264,403,920 0.122873 0.122873
Jacks or Better 1 21,393,895,974,963 0.214656 0.214656
All Other 0 54,827,105,615,460 0.550108 0.000000
Totals   99,666,152,586,000 1.000000 0.957428

7-5-4 Double Bonus

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 53,512,538 0.000001 0.005369
Royal Flush 800 2,478,051,603 0.000025 0.019891
Straight Flush 50 10,759,499,285 0.000108 0.005398
Four Aces 160 22,394,923,482 0.000225 0.035952
Four 2s, 3s, 4s 80 52,528,246,848 0.000527 0.042163
Four 5s thru Ks 50 162,763,921,038 0.001633 0.081655
Full House 7 1,080,027,701,688 0.010836 0.075855
Flush 5 1,089,875,999,729 0.010935 0.054676
Straight 4 1,298,483,056,230 0.013028 0.052113
Three of a Kind 3 7,474,832,096,034 0.074999 0.224996
Two Pair 1 12,238,165,646,406 0.122792 0.122792
Jacks or Better 1 21,417,101,980,269 0.214888 0.214888
All Other 0 54,816,687,950,850 0.550003 0.000000
Totals   99,666,152,586,000 1.000000 0.935749

9-5 Double Double Bonus

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 53,866,944 0.000001 0.005405
Royal Flush 800 2,473,137,047 0.000025 0.019851
Straight Flush 50 10,549,396,985 0.000106 0.005292
Four Aces with any 2,3,4 400 6,132,735,576 0.000062 0.024613
Four 2s, 3s, 4s with any A,2,3,4 160 14,270,992,668 0.000143 0.022910
Four Aces 160 17,283,042,048 0.000173 0.027745
Four 2s, 3s, 4s 80 38,314,060,104 0.000384 0.030754
Four 5s thru Ks 50 162,650,700,318 0.001632 0.081598
Full House 9 1,083,061,619,922 0.010867 0.097802
Flush 5 1,093,223,996,069 0.010969 0.054844
Straight 4 1,283,381,914,008 0.012877 0.051507
Three of a Kind 3 7,508,316,853,590 0.075335 0.226004
Two Pair 1 12,274,966,922,238 0.123161 0.123161
Jacks or Better 1 21,122,961,140,319 0.211937 0.211937
All Other 0 55,048,512,208,164 0.552329 0.000000
Totals   99,666,152,586,000 1.000000 0.983424

8-5 Double Double Bonus

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 53,856,968 0.000001 0.005404
Royal Flush 800 2,472,982,677 0.000025 0.019850
Straight Flush 50 10,597,084,157 0.000106 0.005316
Four Aces with any 2,3,4 400 6,127,699,158 0.000061 0.024593
Four 2s, 3s, 4s with any A,2,3,4 160 14,270,214,798 0.000143 0.022909
Four Aces 160 17,267,258,898 0.000173 0.027720
Four 2s, 3s, 4s 80 38,314,060,104 0.000384 0.030754
Four 5s thru Ks 50 162,654,254,268 0.001632 0.081600
Full House 8 1,082,984,399,490 0.010866 0.086929
Flush 5 1,094,358,069,383 0.010980 0.054901
Straight 4 1,284,286,339,974 0.012886 0.051544
Three of a Kind 3 7,507,557,548,754 0.075327 0.225981
Two Pair 1 12,273,879,877,938 0.123150 0.123150
Jacks or Better 1 21,120,025,626,897 0.211908 0.211908
All Other 0 55,051,303,312,536 0.552357 0.000000
Totals   99,666,152,586,000 1.000000 0.972558

7-5 Double Double Bonus

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 53,852,195 0.000001 0.005403
Royal Flush 800 2,498,763,972 0.000025 0.020057
Straight Flush 50 10,656,333,083 0.000107 0.005346
Four Aces with any 2,3,4 400 6,126,111,942 0.000061 0.024587
Four 2s, 3s, 4s with any A,2,3,4 160 14,622,486,450 0.000147 0.023474
Four Aces 160 17,262,103,026 0.000173 0.027712
Four 2s, 3s, 4s 80 39,371,498,904 0.000395 0.031603
Four 5s thru Ks 50 162,575,460,810 0.001631 0.081560
Full House 7 1,051,575,580,884 0.010551 0.073857
Flush 5 1,096,531,935,845 0.011002 0.055010
Straight 4 1,285,435,223,262 0.012897 0.051590
Three of a Kind 3 7,533,803,205,312 0.075590 0.226771
Two Pair 1 12,269,267,222,616 0.123104 0.123104
Jacks or Better 1 21,103,768,962,015 0.211745 0.211745
All Other 0 55,072,603,845,684 0.552571 0.000000
Totals   99,666,152,586,000 1.000000 0.961818

6-5 Double Double Bonus

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 53,835,941 0.000001 0.005402
Royal Flush 800 2,512,744,734 0.000025 0.020169
Straight Flush 50 10,711,737,551 0.000107 0.005374
Four Aces with any 2,3,4 400 6,121,060,818 0.000061 0.024566
Four 2s, 3s, 4s with any A,2,3,4 160 14,621,559,198 0.000147 0.023473
Four Aces 160 17,246,992,998 0.000173 0.027688
Four 2s, 3s, 4s 80 39,371,498,904 0.000395 0.031603
Four 5s thru Ks 50 162,535,260,798 0.001631 0.081540
Full House 6 1,051,343,492,340 0.010549 0.063292
Flush 5 1,097,578,682,609 0.011013 0.055063
Straight 4 1,287,479,637,966 0.012918 0.051672
Three of a Kind 3 7,531,312,807,680 0.075565 0.226696
Two Pair 1 12,265,841,065,176 0.123069 0.123069
Jacks or Better 1 21,095,610,136,683 0.211663 0.211663
All Other 0 55,083,812,072,604 0.552683 0.000000
Totals   99,666,152,586,000 1.000000 0.951269

Triple Double Bonus

9-6 Triple Double Bonus

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 53,587,562 0.000001 0.005377
Royal Flush 800 2,499,180,939 0.000025 0.020060
Straight Flush 50 11,026,749,221 0.000111 0.005532
Four Aces with any 2,3,4 800 7,003,677,240 0.000070 0.056217
Four 2s, 3s, 4s with any A,2,3,4 400 17,194,855,764 0.000173 0.069010
Four Aces 160 14,800,979,394 0.000149 0.023761
Four 2s, 3s, 4s 80 31,888,251,552 0.000320 0.025596
Four 5s thru Ks 50 160,221,811,434 0.001608 0.080379
Full House 9 1,041,337,956,072 0.010448 0.094034
Flush 6 1,262,549,179,403 0.012668 0.076007
Straight 4 1,341,804,899,790 0.013463 0.053852
Three of a Kind 2 7,431,156,785,934 0.074560 0.149121
Two Pair 1 12,098,520,959,850 0.121390 0.121390
Jacks or Better 1 20,516,273,403,099 0.205850 0.205850
All Other 0 55,729,820,308,746 0.559165 0.000000
Totals   99,666,152,586,000 1.000000 0.986186

8-6 Triple Double Bonus

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 53,826,943 0.000001 0.005401
Royal Flush 800 2,502,376,828 0.000025 0.020086
Straight Flush 50 11,052,472,079 0.000111 0.005545
Four Aces with any 2,3,4 800 7,003,417,176 0.000070 0.056215
Four 2s, 3s, 4s with any A,2,3,4 400 17,194,800,036 0.000173 0.069010
Four Aces 160 14,800,817,886 0.000149 0.023761
Four 2s, 3s, 4s 80 31,887,246,900 0.000320 0.025595
Four 5s thru Ks 50 160,071,825,456 0.001606 0.080304
Full House 8 1,040,698,032,222 0.010442 0.083535
Flush 6 1,270,232,199,845 0.012745 0.076469
Straight 4 1,341,379,254,486 0.013459 0.053835
Three of a Kind 2 7,424,814,847,944 0.074497 0.148994
Two Pair 1 12,089,492,029,260 0.121300 0.121300
Jacks or Better 1 20,500,630,428,885 0.205693 0.205693
All Other 0 55,754,339,010,054 0.559411 0.000000
Totals   99,666,152,586,000 1.000000 0.975741

8-5 Triple Double Bonus

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 54,543,506 0.000001 0.005473
Royal Flush 800 2,613,844,485 0.000026 0.020981
Straight Flush 50 10,614,778,571 0.000107 0.005325
Four Aces with any 2,3,4 800 7,021,937,736 0.000070 0.056364
Four 2s, 3s, 4s with any A,2,3,4 400 17,201,392,272 0.000173 0.069036
Four Aces 160 14,895,821,454 0.000149 0.023913
Four 2s, 3s, 4s 80 31,921,173,048 0.000320 0.025622
Four 5s thru Ks 50 161,104,441,302 0.001616 0.080822
Full House 8 1,047,068,228,004 0.010506 0.084046
Flush 5 1,096,827,601,523 0.011005 0.055025
Straight 4 1,360,404,648,606 0.013650 0.054598
Three of a Kind 2 7,483,353,067,710 0.075084 0.150168
Two Pair 1 12,186,787,236,930 0.122276 0.122276
Jacks or Better 1 20,999,640,471,357 0.210700 0.210700
All Other 0 55,246,643,399,496 0.554317 0.000000
Totals   99,666,152,586,000 1.000000 0.964350

7-5 Triple Double Bonus

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 54,822,920 0.000001 0.005501
Royal Flush 800 2,649,587,031 0.000027 0.021268
Straight Flush 50 10,665,502,661 0.000107 0.005351
Four Aces with any 2,3,4 800 7,020,344,844 0.000070 0.056351
Four 2s, 3s, 4s with any A,2,3,4 400 17,201,164,716 0.000173 0.069035
Four Aces 160 14,892,014,148 0.000149 0.023907
Four 2s, 3s, 4s 80 31,920,945,492 0.000320 0.025622
Four 5s thru Ks 50 160,921,722,348 0.001615 0.080730
Full House 7 1,046,377,383,468 0.010499 0.073492
Flush 5 1,099,151,091,473 0.011028 0.055142
Straight 4 1,363,235,275,740 0.013678 0.054712
Three of a Kind 2 7,475,946,271,614 0.075010 0.150020
Two Pair 1 12,177,012,750,066 0.122178 0.122178
Jacks or Better 1 20,983,860,430,257 0.210541 0.210541
All Other 0 55,275,243,279,222 0.554604 0.000000
Totals   99,666,152,586,000 1.000000 0.953849

6-5 Triple Double Bonus

Hand Pays Permutations Probability Return
Reversible Royal Flush 10000 54,857,363 0.000001 0.005504
Royal Flush 800 2,674,246,284 0.000027 0.021466
Straight Flush 50 10,696,301,411 0.000107 0.005366
Four Aces with any 2,3,4 800 7,019,241,120 0.000070 0.056342
Four 2s, 3s, 4s with any A,2,3,4 400 17,201,059,452 0.000173 0.069035
Four Aces 160 14,887,857,252 0.000149 0.023900
Four 2s, 3s, 4s 80 31,919,369,628 0.000320 0.025621
Four 5s thru Ks 50 160,796,998,440 0.001613 0.080668
Full House 6 1,045,821,097,284 0.010493 0.062959
Flush 5 1,100,760,047,327 0.011044 0.055222
Straight 4 1,373,972,975,934 0.013786 0.055143
Three of a Kind 2 7,469,374,773,996 0.074944 0.149888
Two Pair 1 12,165,988,190,508 0.122067 0.122067
Jacks or Better 1 20,947,006,165,611 0.210172 0.210172
All Other 0 55,317,979,404,390 0.555033 0.000000
Totals   99,666,152,586,000 1.000000 0.943354

Strategy

The following table shows the average value of a royal flush according to how many cards towards a reversible royal you are already holding. It is based on a win of 10,000 for a reversible royal and 800 for all others. Average wins are rounded to the nearest whole number.

  • 4 Cards: 3100
  • 3 Cards: 964
  • 2 Cards: 807
  • 1 Cards: 800
  • 0 Cards: 800

In my opinion, it's not worth worrying about strategy changes with 2 cards or less to a sequential royal.

Next, put whatever is the appropriate average royal into my video poker strategy maker along with all the other pays. That will generate an appropriate strategy. On a practical level, I would print out the strategy for average royals of 800 and 964 only. Only use the 964 strategy when you have three cards already towards a sequential royal. Otherwise use the 800 strategy.

If you have four to reversible royal, always go for it, even sacrificing a pat straight flush.

External Links

VIDEO POKER OPPORTUNITY WITH 105% RETURN -- My article at Wizard of Vegas on a reversible royal game with 807,782 coin jackpot.


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