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Last Updated: February 13, 2019

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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.

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