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Last Updated: June 14, 2016

Sequential Royal

Introduction

I'm proud to present my analysis of sequential royal video poker. This is a project I worked at off and on for years and to analyze a pay table within a reasonable period of time. My program analyzed over 287 quadrillion possible hands, the number of ways to deal and draw any 5 cards and in any order on both the deal and the draw. A "sequential royal" is only one way, from 10 to ace going from left to right. There is another game called "Reversable Royals", which goes both ways, however that game I have yet to analyze.

A sequential royal that pays 10,000 adds about 0.23% to the return of any non-wild card game. Sequential royals will constitute about 1.01% of all royals, as opposed to 1 in 120 in a non-sequential game. Other sources may say sequential royals add 0.46% or so, but I believe they count sequentials in both directions.

A sequential royal can be added to any base game. The following tables are categorized according to the base game.

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

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Written by: Michael Shackleford

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