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.
Written by:
Michael Shackleford
Gambling Guide
