Sequential Royal Video Poker

Last update: Dec. 1, 2004

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

Super Double Bonus

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

Triple Bonus

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

My Video Poker Offerings

Analyzer

Analyze the return for almost any video poker pay table.

My Strategies

Jacks or Better:

Simple Strategy (return of 99.46%)
Intermediate strategy (return of 99.52%)
Optimal Strategy (return of 99.54%)

Full Pay Deuces Wild:

Simple Strategy (return of 100.71%)
Optimal Strategy (return of 100.77%)
When to play two to a royal, king high, with no penalty cards
When to play two suited high cards, ace high, with a deuce
When to play two to a royal, king high, with a straight penalty card

Other Strategies:

Other Stuff

Jacks or better quiz.
Probability distribution for each hand by number of cards held in full pay Deuces Wild.
Programming video poker tips.
San Diego County video poker survey.

The Wizard's other sites: Wizard of Vegas, Wizard of Macau, Math Problems The Wizard recommends: The Bear Growls, Casinomeister, Online Casino Suite