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Sequential Royal
Introduction
For purposes of this page, a sequential royal is a royal flush that is sequential in the low to high (10-J-Q-K-A) order only. If a royal flush pays in both directions (10-J-Q-K-A and A-K-Q-J-10) it is known as a reversible royal. To make matters more confusing, a reversible royal game may refer to a royal flush in either direction a "sequential royal." This page refers to those games that do not make use of the word "reversible" anywhere on the machine, in which case I assume sequential royals to count low to high only.
Generally, a game that pays for a sequential royal will pay 50,000 coins for one, based on a five-coin bet. In other words, 10,000 time the total amount bet. On average, that jackpot adds 0.23% to the return of the game, assuming optimal strategy, including strategy adjustments for card order.
If there is a progressive jackpot on the game, the return will go up by about 0.526% for every 100,000 coins in the jackpot above the usual 50,000.
Assuming a playing speed of 1,000 hands per hour and playing 24 hours a day, a sequential royal will occur, on average, once every 167 days.
The rest of this page shows some return tables for various games and pay tables that pay 50,000 coins for a sequential royal.
If you desire to know the return of a game and/or pay table not listed, please refer to my video poker analyzer.
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 sequential royal. As usual, this assumes optimal player strategy, including card order.
Sequential Royal Game Summary
| Game | Pay Table | Return |
|---|---|---|
| Jacks or Better | 9-6 | 99.78% |
| Jacks or Better | 9-5 | 98.68% |
| Jacks or Better | 8-6 | 98.63% |
| Jacks or Better | 8-5 | 97.53% |
| Jacks or Better | 7-5 | 96.38% |
| Jacks or Better | 6-5 | 95.23% |
| Bonus Poker | 8-5 | 99.40% |
| Bonus Poker | 7-5 | 98.25% |
| Bonus Poker | 6-5 | 97.10% |
| Bonus Poker | 10-8-5-1 | 94.40% |
| Bonus Poker Deluxe | 8-6 | 98.73% |
| Bonus Poker Deluxe | 8-5 | 97.63% |
| Bonus Poker Deluxe | 7-5 | 96.72% |
| Bonus Poker Deluxe | 6-5 | 95.59% |
| Double Bonus | 9-7-5 | 99.33% |
| Double Bonus | 9-6-5 | 98.04% |
| Double Bonus | 9-6-4 | 96.61% |
| Double Bonus | 9-5-4 | 47.87% |
| Double Bonus | 7-5-4 | 95.51% |
| Double Double Bonus | 9-5 | 98.11% |
| Double Double Bonus | 8-5 | 97.02% |
| Double Double Bonus | 7-5 | 95.95% |
| Double Double Bonus | 6-5 | 94.89% |
| Triple Double Bonus | 9-6 | 98.39% |
| Triple Double Bonus | 8-6 | 97.34% |
| Triple Double Bonus | 8-5 | 97.34% |
| Triple Double Bonus | 7-5 | 95.15% |
| Triple Double Bonus | 6-5 | 94.10% |
| Deuces Wild | 25-15-10 | 99.63% |
| Deuces Wild | 25-15-9 | 99.12% |
| Deuces Wild | 20-12-10 | 97.79% |
| Deuces Wild | 20-12-9 | 97.26% |
| Deuces Wild | 25-16-13 | 96.97% |
The bottom line is if a sequential royal pays 50,000 coins, for a five-coin bet, it adds 0.209% to 0.235% to the return, depending on the particular game and pay table. A fair average to assume is 0.233% for games with no wild cards and 0.209% for deuces wild games. 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 0.189% only. In other words, of the increased return for the sequential royal, about 81% of the benefit comes from the average royal (4,383 coins) paying more and 19% from strategy changes.
On average, with optimal strategy, a sequential royal occurs once in about 3.8 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 158 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 0.526% in return. This figure assumes optimal strategy for a 50,000 coin jackpot, not that actual jackpot amount.
The next seven sections of this page show return tables for seven popular forms of video poker. I do not claim these pay tables are available in sequential royal games, but chose otherwise popular pay tables.
Jacks or Better
Sequential Royal - "9/6" Jacks or Better
| Hand | Payoff | Permutations | Probability | Return |
|---|---|---|---|---|
| Sequential Royal | 10000 | 71980892640 | 0.00000025 | 0.00250771 |
| Royal Flush | 800 | 7064703256320 | 0.00002461 | 0.01968991 |
| Straight Flush | 50 | 31366951279200 | 0.00010928 | 0.00546389 |
| Four of a Kind | 25 | 678079613943360 | 0.00236233 | 0.05905824 |
| Full House | 9 | 3304062075839040 | 0.01151087 | 0.10359780 |
| Flush | 6 | 3163031130817440 | 0.01101954 | 0.06611721 |
| Straight | 4 | 3223217230902720 | 0.01122921 | 0.04491686 |
| Three of a Kind | 3 | 21367430247709400 | 0.07444099 | 0.22332296 |
| Two Pair | 2 | 37103658035794500 | 0.12926369 | 0.25852738 |
| Jacks or Better | 1 | 61574649363747300 | 0.21451703 | 0.21451703 |
| Nothing | 0 | 156585888113497000 | 0.54552221 | 0.00000000 |
| Total | 287038519447680000 | 1.00000000 | 0.99771898 |
Sequential Royal - "9/5" Jacks or Better
| Hand | Payoff | Permutations | Probability | Return |
|---|---|---|---|---|
| Sequential Royal | 10000 | 71695627200 | 0.00000025 | 0.00249777 |
| Royal Flush | 800 | 7103504371680 | 0.00002475 | 0.01979805 |
| Straight Flush | 50 | 30761443153440 | 0.00010717 | 0.00535842 |
| Four of a Kind | 25 | 678186947557440 | 0.00236270 | 0.05906759 |
| Full House | 9 | 3304563908708160 | 0.01151261 | 0.10361353 |
| Flush | 5 | 3127862766005280 | 0.01089701 | 0.05448507 |
| Straight | 4 | 3224050650573120 | 0.01123212 | 0.04492847 |
| Three of a Kind | 3 | 21372054322348800 | 0.07445710 | 0.22337129 |
| Two Pair | 2 | 37110446241183300 | 0.12928734 | 0.25857468 |
| Jacks or Better | 1 | 61733316811281100 | 0.21506980 | 0.21506980 |
| Nothing | 0 | 156450101156870000 | 0.54504915 | 0.00000000 |
| Total | 287038519447680000 | 1.00000000 | 0.98676467 |
Sequential Royal - "8/5" Jacks or Better
| Hand | Payoff | Permutations | Probability | Return |
|---|---|---|---|---|
| Sequential Royal | 10000 | 71693398080 | 0.00000025 | 0.00249769 |
| Royal Flush | 800 | 7103316754080 | 0.00002475 | 0.01979753 |
| Straight Flush | 50 | 30886118949600 | 0.00010760 | 0.00538013 |
| Four of a Kind | 25 | 678175481707200 | 0.00236266 | 0.05906659 |
| Full House | 8 | 3304479440664000 | 0.01151232 | 0.09209856 |
| Flush | 5 | 3130498900283040 | 0.01090620 | 0.05453099 |
| Straight | 4 | 3225366841907520 | 0.01123670 | 0.04494682 |
| Three of a Kind | 3 | 21371339961463600 | 0.07445461 | 0.22336382 |
| Two Pair | 2 | 37109059904643800 | 0.12928251 | 0.25856502 |
| Jacks or Better | 1 | 61714736498676900 | 0.21500507 | 0.21500507 |
| Nothing | 0 | 156466801289232000 | 0.54510733 | 0.00000000 |
| Total | 287038519447680000 | 1.00000000 | 0.97525222 |
Sequential Royal - "7/5" Jacks or Better
| Hand | Payoff | Permutations | Probability | Return |
|---|---|---|---|---|
| Sequential Royal | 10000 | 71691912000 | 0.00000025 | 0.00249764 |
| Royal Flush | 800 | 7102906967520 | 0.00002475 | 0.01979639 |
| Straight Flush | 50 | 30915956463840 | 0.00010771 | 0.00538533 |
| Four of a Kind | 25 | 677959608525120 | 0.00236191 | 0.05904779 |
| Full House | 7 | 3303676999817280 | 0.01150952 | 0.08056667 |
| Flush | 5 | 3131105653743840 | 0.01090831 | 0.05454156 |
| Straight | 4 | 3238752800759040 | 0.01128334 | 0.04513335 |
| Three of a Kind | 3 | 21362382531786200 | 0.07442340 | 0.22327020 |
| Two Pair | 2 | 37096435245628800 | 0.12923853 | 0.25847705 |
| Jacks or Better | 1 | 61720545139572900 | 0.21502530 | 0.21502530 |
| Nothing | 0 | 156469570912503000 | 0.54511698 | 0.00000000 |
| Total | 287038519447680000 | 1.00000000 | 0.96374129 |
Sequential Royal - "7/5" Super Double Bonus
| Hand | Payoff | Permutations | Probability | Return |
|---|---|---|---|---|
| Sequential Royal | 10000 | 71065137840 | 0.00000025 | 0.00247580 |
| Royal Flush | 800 | 7023807493680 | 0.00002447 | 0.01957593 |
| Straight Flush | 80 | 32291334131040 | 0.00011250 | 0.00899986 |
| Four Aces | 160 | 63427690327680 | 0.00022097 | 0.03535564 |
| Four J-K | 120 | 186623870935680 | 0.00065017 | 0.07802042 |
| Four 2-4 | 80 | 151223819564160 | 0.00052684 | 0.04214732 |
| Four 5-10 | 50 | 301174476868800 | 0.00104925 | 0.05246238 |
| Full House | 7 | 2627231812246080 | 0.00915289 | 0.06407023 |
| Flush | 5 | 3134920594033440 | 0.01092160 | 0.05460801 |
| Straight | 4 | 3682502013147840 | 0.01282930 | 0.05131718 |
| Three of a Kind | 3 | 22194113507144600 | 0.07732103 | 0.23196309 |
| Two Pair | 1 | 31289840806852800 | 0.10900920 | 0.10900920 |
| Jacks or Better | 1 | 66003029507754700 | 0.22994485 | 0.22994485 |
| Nothing | 0 | 157365045142041000 | 0.54823668 | 0.00000000 |
| Total | 287038519447680000 | 1.00000000 | 0.97994992 |
Sequential Royal - "6/5" Super Double Bonus
| Hand | Payoff | Permutations | Probability | Return |
|---|---|---|---|---|
| Sequential Royal | 10000 | 70996747200 | 0.00000025 | 0.00247342 |
| Royal Flush | 800 | 6982374871200 | 0.00002433 | 0.01946045 |
| Straight Flush | 80 | 32296691449440 | 0.00011252 | 0.00900135 |
| Four Aces | 160 | 63286853783040 | 0.00022048 | 0.03527714 |
| Four J-K | 120 | 186608675767680 | 0.00065012 | 0.07801406 |
| Four 2-4 | 80 | 155275718480640 | 0.00054096 | 0.04327662 |
| Four 5-10 | 50 | 301141439824320 | 0.00104913 | 0.05245663 |
| Full House | 6 | 2536654623981120 | 0.00883733 | 0.05302399 |
| Flush | 5 | 3127638157817760 | 0.01089623 | 0.05448116 |
| Straight | 4 | 3734643854675520 | 0.01301095 | 0.05204380 |
| Three of a Kind | 3 | 22264590975975300 | 0.07756656 | 0.23269968 |
| Two Pair | 1 | 31257978478891200 | 0.10889820 | 0.10889820 |
| Jacks or Better | 1 | 65974196163777100 | 0.22984440 | 0.22984440 |
| Nothing | 0 | 157397154441638000 | 0.54834854 | 0.00000000 |
| Total | 287038519447680000 | 1.00000000 | 0.97095091 |
Sequential Royal - "7/5" Triple Bonus
| Hand | Payoff | Permutations | Probability | Return |
|---|---|---|---|---|
| Sequential Royal | 10000 | 71837589840 | 0.00000025 | 0.00250272 |
| Royal Flush | 800 | 7387908177360 | 0.00002574 | 0.02059071 |
| Straight Flush | 100 | 34340267674080 | 0.00011964 | 0.01196364 |
| Four Aces | 240 | 67492342782720 | 0.00023513 | 0.05643202 |
| Four 2-4 | 120 | 155508286656960 | 0.00054177 | 0.06501216 |
| Four 5-K | 50 | 467512515797760 | 0.00162874 | 0.08143724 |
| Full House | 7 | 3025941230750400 | 0.01054193 | 0.07379354 |
| Flush | 5 | 3180196497042720 | 0.01107934 | 0.05539669 |
| Straight | 4 | 3642351028289280 | 0.01268942 | 0.05075766 |
| Three of a Kind | 3 | 21679239640694400 | 0.07552728 | 0.22658185 |
| Two Pair | 1 | 35314930400624600 | 0.12303203 | 0.12303203 |
| Jacks or Better | 1 | 60708416331373900 | 0.21149920 | 0.21149920 |
| Nothing | 0 | 158755131160225000 | 0.55307954 | 0.00000000 |
| Total | 287038519447680000 | 1.00000000 | 0.97899945 |
Sequential Royal - "6/5" Triple Bonus
| Hand | Payoff | Permutations | Probability | Return |
|---|---|---|---|---|
| Sequential Royal | 10000 | 71830082040 | 0.00000025 | 0.00250245 |
| Royal Flush | 800 | 7414649892840 | 0.00002583 | 0.02066524 |
| Straight Flush | 100 | 34403666819040 | 0.00011986 | 0.01198573 |
| Four Aces | 240 | 67487773458240 | 0.00023512 | 0.05642820 |
| Four 2-4 | 120 | 155507343739200 | 0.00054176 | 0.06501177 |
| Four 5-K | 50 | 467464823403840 | 0.00162858 | 0.08142894 |
| Full House | 6 | 3024206725728960 | 0.01053589 | 0.06321535 |
| Flush | 5 | 3182346105446880 | 0.01108683 | 0.05543413 |
| Straight | 4 | 3644368049378880 | 0.01269644 | 0.05078577 |
| Three of a Kind | 3 | 21677407671859200 | 0.07552090 | 0.22656270 |
| Two Pair | 1 | 35296230007555200 | 0.12296688 | 0.12296688 |
| Jacks or Better | 1 | 60700705059653200 | 0.21147233 | 0.21147233 |
| Nothing | 0 | 158780905740662000 | 0.55316933 | 0.00000000 |
| Total | 287038519447680000 | 1.00000000 | 0.96845948 |
Deuces Wild
Sequential Royal - "25-15-10" Deuces Wild
| Hand | Payoff | Permutations | Probability | Return |
|---|---|---|---|---|
| Sequential Natural Royal Flush | 10000 | 194,830,757 | 0.00000024 | 0.00244354 |
| Natural Royal Flush | 800 | 18,295,678,555 | 0.00002295 | 0.01835696 |
| Four Deuces | 200 | 148,506,848,520 | 0.00018626 | 0.03725107 |
| Wild Royal Flush | 25 | 1,523,602,070,048 | 0.00191088 | 0.04777205 |
| Five of a Kind | 15 | 2,472,853,618,800 | 0.00310142 | 0.04652132 |
| Straight Flush | 10 | 4,105,667,219,480 | 0.00514927 | 0.05149275 |
| Four of a Kind | 4 | 48,589,685,697,864 | 0.06094056 | 0.24376222 |
| Full House | 4 | 20,819,433,561,408 | 0.02611146 | 0.10444586 |
| Flush | 3 | 16,574,917,176,200 | 0.02078805 | 0.06236414 |
| Straight | 2 | 45,764,206,459,896 | 0.05739688 | 0.11479375 |
| Three of a Kind | 1 | 212,938,657,276,224 | 0.26706491 | 0.26706491 |
| All Other | 0 | 444,373,200,250,248 | 0.55732712 | 0.00000000 |
| Totals | 797,329,220,688,000 | 1.00000000 | 0.99626858 |
Sequential Royal - "25-15-9" Deuces Wild
| Hand | Payoff | Permutations | Probability | Return |
|---|---|---|---|---|
| Sequential Natural Royal Flush | 10000 | 195,340,695 | 0.00000024 | 0.00244994 |
| Natural Royal Flush | 800 | 18,310,203,945 | 0.00002296 | 0.01837154 |
| Four Deuces | 200 | 149,068,462,920 | 0.00018696 | 0.03739195 |
| Wild Royal Flush | 25 | 1,522,009,125,440 | 0.00190888 | 0.04772210 |
| Five of a Kind | 15 | 2,489,624,928,240 | 0.00312246 | 0.04683683 |
| Straight Flush | 9 | 3,930,128,743,520 | 0.00492912 | 0.04436205 |
| Four of a Kind | 4 | 48,886,762,370,184 | 0.06131315 | 0.24525258 |
| Full House | 4 | 20,881,225,618,368 | 0.02618896 | 0.10475585 |
| Flush | 3 | 16,309,152,077,216 | 0.02045473 | 0.06136418 |
| Straight | 2 | 45,741,036,609,600 | 0.05736782 | 0.11473563 |
| Three of a Kind | 1 | 213,669,495,768,048 | 0.26798152 | 0.26798152 |
| All Other | 0 | 443,732,211,439,824 | 0.55652320 | 0.00000000 |
| Totals | 797,329,220,688,000 | 1.00000000 | 0.99122418 |
Sequential Royal - "20-12-10" Deuces Wild
| Hand | Payoff | Permutations | Probability | Return |
|---|---|---|---|---|
| Sequential Natural Royal Flush | 10000 | 194,768,749 | 0.00000024 | 0.00244276 |
| Natural Royal Flush | 800 | 18,045,434,915 | 0.00002263 | 0.01810588 |
| Four Deuces | 200 | 147,212,343,840 | 0.00018463 | 0.03692636 |
| Wild Royal Flush | 20 | 1,420,983,845,936 | 0.00178218 | 0.03564359 |
| Five of a Kind | 12 | 2,377,646,086,560 | 0.00298201 | 0.03578416 |
| Straight Flush | 10 | 4,363,825,246,400 | 0.00547305 | 0.05473053 |
| Four of a Kind | 4 | 48,527,742,132,432 | 0.06086287 | 0.24345147 |
| Full House | 4 | 20,817,589,877,424 | 0.02610915 | 0.10443661 |
| Flush | 3 | 16,825,926,645,824 | 0.02110286 | 0.06330858 |
| Straight | 2 | 46,348,148,541,216 | 0.05812925 | 0.11625850 |
| Three of a Kind | 1 | 212,724,226,407,600 | 0.26679597 | 0.26679597 |
| All Other | 0 | 443,757,679,357,104 | 0.55655514 | 0.00000000 |
| Totals | 797,329,220,688,000 | 1.00000000 | 0.97788441 |
Sequential Royal - "20-12-9" Deuces Wild
| Hand | Payoff | Permutations | Probability | Return |
|---|---|---|---|---|
| Sequential Natural Royal Flush | 10000 | 97,445,383 | 0.00000024 | 0.00244429 |
| Natural Royal Flush | 800 | 9,025,124,489 | 0.00002264 | 0.01811071 |
| Four Deuces | 200 | 76,031,013,300 | 0.00019071 | 0.03814285 |
| Wild Royal Flush | 20 | 722,491,928,008 | 0.00181228 | 0.03624560 |
| Five of a Kind | 12 | 1,202,785,684,440 | 0.00301704 | 0.03620444 |
| Straight Flush | 9 | 1,989,825,546,700 | 0.00499123 | 0.04492104 |
| Four of a Kind | 4 | 24,459,554,709,972 | 0.06135371 | 0.24541486 |
| Full House | 4 | 10,441,147,675,584 | 0.02619030 | 0.10476122 |
| Flush | 3 | 8,398,696,126,444 | 0.02106707 | 0.06320122 |
| Straight | 2 | 22,999,592,255,052 | 0.05769158 | 0.11538316 |
| Three of a Kind | 1 | 106,770,555,502,860 | 0.26782050 | 0.26782050 |
| All Other | 0 | 221,594,807,331,768 | 0.55584268 | 0.00000000 |
| Totals | 398,664,610,344,000 | 1.00000000 | 0.97264989 |
Sequential Royal - "25-16-13" Deuces Wild
| Hand | Payoff | Permutations | Probability | Return |
|---|---|---|---|---|
| Sequential Natural Royal Flush | 10000 | 24,359,202 | 0.00000024 | 0.00244408 |
| Natural Royal Flush | 800 | 2,253,842,175 | 0.00002261 | 0.01809113 |
| Four Deuces | 200 | 17,840,785,140 | 0.00017901 | 0.03580109 |
| Wild Royal Flush | 25 | 183,030,987,238 | 0.00183644 | 0.04591102 |
| Five of a Kind | 16 | 311,864,120,700 | 0.00312909 | 0.05006540 |
| Straight Flush | 13 | 574,041,697,480 | 0.00575965 | 0.07487539 |
| Four of a Kind | 4 | 6,206,184,808,788 | 0.06226973 | 0.24907894 |
| Full House | 3 | 2,090,172,843,576 | 0.02097174 | 0.06291523 |
| Flush | 2 | 1,762,204,947,061 | 0.01768108 | 0.03536215 |
| Straight | 2 | 5,771,466,458,955 | 0.05790799 | 0.11581598 |
| Three of a Kind | 1 | 27,842,590,867,644 | 0.27935854 | 0.27935854 |
| All Other | 0 | 54,904,476,868,041 | 0.55088388 | 0.00000000 |
| Total | 99,666,152,586,000 | 1.00000000 | 0.96971895 |
Strategy
The following table shows the average value of a royal flush according to how many cards towards a sequential royal you are already holding. It is based on a win of 10,000 for a sequential 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 sequential royal, always go for it, even sacrificing a pat straight flush.
Internal Links
My video poker analyzer can calculate the return of sequential royal games. In all fairness, for the same pay table the return is off by about 0.007% of this page. Why, I am not sure.