Jacks or Better

Last update: July 7, 2008

Jacks or Better

Betfair Zero Lounge Pay Table
Hand	Payoff	Combinations	Probability	Return
Royal flush	976	554,637,108	0.000028	0.027157
Straight flush	50	2,218,146,252	0.000111	0.005564
4 of a kind	25	46,944,834,792	0.002355	0.058878
Full house	9	228,938,634,648	0.011485	0.103367
Flush	6	221,687,899,200	0.011122	0.066729
Straight	4	225,414,163,536	0.011308	0.045234
3 of a kind	3	1,478,350,617,468	0.074165	0.222495
Two pair	2	2,569,778,781,732	0.128919	0.257839
Jacks or better	1	4,240,539,117,972	0.212737	0.212737
Nothing	0	10,918,803,684,492	0.547769	0.000000
Total		19,933,230,517,200	1.000000	1.000000

Jacks or Better

Hand Payoff Combinations Probability Return

Royal Flush 940 523487220 0.000026 0.024686

Straight Flush 50 2210097684 0.000111 0.005544

4 of a Kind 25 47036519220 0.002360 0.058993

Full House 9 229274750340 0.011502 0.103519

Flush 6 220266691236 0.011050 0.066301

Straight 4 224836698648 0.011279 0.045118

3 of a Kind 3 1481912846688 0.074344 0.223032

Two Pair 2 2574414297144 0.129152 0.258304

Jacks or Better 1 4256413692336 0.213534 0.213534

Nothing 0 10896341436684 0.546642 0.000000

Total 19933230517200 1.000000 0.999030

"Full Pay" Jacks or Better

Hand Payoff Combinations Probability Return

Royal flush 800 493512264 0.00002476 0.01980661

Straight flush 50 2178883296 0.00010931 0.00546545

Four of a kind 25 47093167764 0.00236255 0.05906364

Full house 9 229475482596 0.01151221 0.10360987

Flush 6 219554786160 0.01101451 0.06608707

Straight 4 223837565784 0.01122937 0.04491747

Three of a kind 3 1484003070324 0.07444870 0.22334610

Two pair 2 2576946164148 0.12927890 0.25855780

Pair 1 4277372890968 0.21458503 0.21458503

Nothing 0 10872274993896 0.54543467 0

Total 19933230517200 1 0.99543904

The standard deviation of Full Pay 9/6 Jacks or Better is 4.42.

"8/6" Jacks or Better, Paying 26 for a Four of a Kind
Hand	Payoff	Combinations	Probability	Return
Royal flush	800	493,461,180	0.000025	0.019805
Straight flush	50	2,178,781,128	0.000109	0.005465
4 of a kind	26	47,093,065,596	0.002363	0.061426
Full house	8	229,474,563,084	0.011512	0.092097
Flush	6	219,546,510,552	0.011014	0.066085
Straight	4	223,901,471,868	0.011233	0.044930
3 of a kind	3	1,483,988,715,720	0.074448	0.223344
Two pair	2	2,576,909,843,424	0.129277	0.258554
Jacks or better	1	4,277,338,869,024	0.214583	0.214583
Nothing	0	10,872,305,235,624	0.545436	0.000000
Total		19,933,230,517,200	1.000000	0.986289

"9/5" Jacks or Better

Hand Payoff Combinations Probability Return

Royal flush 800 496237776 0.000025 0.019916

Straight flush 50 2137447980 0.000107 0.005362

4 of a kind 25 47100799404 0.002363 0.059073

Full house 9 229510637676 0.011514 0.103626

Flush 5 217120426644 0.010892 0.054462

Straight 4 223861063908 0.011231 0.044922

3 of a kind 3 1484332642620 0.074465 0.223396

Two pair 2 2577431192796 0.129303 0.258606

Jacks or better 1 4288342040640 0.215135 0.215135

Nothing 0 10862898027756 0.544964 0.000000

Total 0 1.000000 0.984498

"8/6" Jacks or Better

Hand Payoff Combinations Probability Return

Royal flush 800 493461180 0.000025 0.019805

Straight flush 50 2178781128 0.000109 0.005465

4 of a kind 25 47093065596 0.002363 0.059064

Full house 8 229474563084 0.011512 0.092097

Flush 6 219546510552 0.011014 0.066085

Straight 4 223901471868 0.011233 0.044930

3 of a kind 3 1483988715720 0.074448 0.223344

Two pair 2 2576909843424 0.129277 0.258554

Jacks or better 1 4277338869024 0.214583 0.214583

Nothing 0 10872305235624 0.545436 0.000000

Total 19933230517200 1.000000 0.983927

"8/5" Jacks or Better
Hand	Payoff	Combinations	Probability	Return
Royal flush	800	496224876	0.00002489	0.01991548
Straight flush	50	2146096656	0.00010766	0.00538321
Four of a kind	25	47100003732	0.00236289	0.05907222
Full house	8	229504776948	0.01151368	0.09210942
Flush	5	217303355868	0.01090156	0.05450781
Straight	4	223952329860	0.01123512	0.04494050
Three of a kind	3	1484283075660	0.07446275	0.22338824
Two pair	2	2577335006268	0.12929841	0.25859682
Pair	1	4287052708344	0.21507064	0.21507064
Nothing	0	10864056938988	0.54502239	0
Total		19933230517200	1	0.97298434

"7/5" Jacks or Better

Hand Payoff Combinations Probability Return

Royal Flush 800 496195464 0.000025 0.019914

Straight Flush 50 2148216384 0.000108 0.005389

4 of a Kind 25 47085010836 0.002362 0.059053

Full House 7 229449036564 0.011511 0.080576

Flush 5 217345878912 0.010904 0.054518

Straight 4 224882540088 0.011282 0.045127

3 of a Kind 3 1483660907628 0.074432 0.223295

Two Pair 2 2576458033308 0.129254 0.258509

Jacks or Better 1 4287450841560 0.215091 0.215091

Nothing 0 10864253856456 0.545032 0.000000

Total 19933230517200 1.000000 0.961472

"6/5" Jacks or Better

Hand Payoff Combinations Probability Return

Royal Flush 800 496188240 0.000025 0.019914

Straight Flush 50 2152883604 0.000108 0.005400

4 of a Kind 25 47084328684 0.002362 0.059053

Full House 6 229444197516 0.011511 0.069064

Flush 5 217494726336 0.010911 0.054556

Straight 4 224915292156 0.011283 0.045134

3 of a Kind 3 1483619627628 0.074429 0.223288

Two Pair 2 2576379215340 0.129250 0.258501

Jacks or Better 1 4286678700708 0.215052 0.215052

Nothing 0 10864965356988 0.545068 0.000000

Total 19933230517200 1.000000 0.949961

Jacks or Better

Hand Payoff Combinations Probability Return

Royal Flush 1000 584850156 0.000029 0.029340

Straight Flush 125 2767415496 0.000139 0.017354

4 of a Kind 30 46557578340 0.002336 0.070070

Full House 9 227393352180 0.011408 0.102670

Flush 6 230950967928 0.011586 0.069517

Straight 4 234429994332 0.011761 0.047043

3 of a Kind 2 1461920711760 0.073341 0.146682

Two Pair 2 2546047990440 0.127729 0.255458

Jacks or Better 1 4178517979140 0.209626 0.209626

Nothing 0 11004059677428 0.552046 0.000000

Total 19933230517200 1.000000 0.947760

Jacks or Better

Hand Payoff Combinations Probability Return

Royal Flush 1000 583259868 0.000029 0.029261

Straight Flush 100 2605479636 0.000131 0.013071

4 of a Kind 30 46627381272 0.002339 0.070175

Full House 9 227648604168 0.011421 0.102785

Flush 6 230293442256 0.011553 0.069319

Straight 4 235552505568 0.011817 0.047268

3 of a Kind 2 1464439288980 0.073467 0.146934

Two Pair 2 2548996728588 0.127877 0.255753

Jacks or Better 1 4181746030488 0.209788 0.209788

Nothing 0 10994737796376 0.551578 0.000000

Total 19933230517200 1.000000 0.944355

Jacks or Better

Hand Payoff Combinations Probability Return

Royal flush 1000 553557120 0.000028 0.027771

Straight flush 50 2182888488 0.000110 0.005476

4 of a kind 25 46926826392 0.002354 0.058855

Full house 6 228885971688 0.011483 0.068896

Flush 5 220272599952 0.011051 0.055253

Straight 4 226192098552 0.011347 0.045390

3 of a kind 3 1477676746236 0.074131 0.222394

Two pair 2 2568945722436 0.128878 0.257755

Jacks or better 1 4252314431988 0.213328 0.213328

Nothing 0 10909279674348 0.547291 0.000000

Total 19933230517200 1.000000 0.955116

Jacks or Better

Hand Payoff Combinations Probability Return

Royal Flush 500 411240468 0.000021 0.010315

Straight Flush 100 2532907488 0.000127 0.012707

4 of a Kind 30 46803703116 0.002348 0.070441

Full House 9 228016506204 0.011439 0.102951

Flush 6 247464811524 0.012415 0.074488

Straight 4 238469512044 0.011963 0.047854

3 of a Kind 2 1468138588212 0.073653 0.147306

Two Pair 2 2548457384580 0.127850 0.255699

Jacks or Better 1 4191669903384 0.210286 0.210286

Nothing 0 10961265960180 0.549899 0.000000

Total 19933230517200 1.000000 0.932047

Jacks or Better

Hand Payoff Combinations Probability Return

Royal flush 1000 553693344 0.000028 0.027777

Straight flush 50 2181883836 0.000109 0.005473

4 of a kind 20 46927098840 0.002354 0.047084

Full house 7 228888423720 0.011483 0.080379

Flush 5 220234644540 0.011049 0.055243

Straight 4 226131938628 0.011344 0.045378

3 of a kind 3 1477703531280 0.074133 0.222398

Two pair 2 2569008096000 0.128881 0.257761

Jacks or better 1 4252431465432 0.213334 0.213334

Nothing 0 10909169741580 0.547286 0.000000

Total 19933230517200 1.000000 0.954828

Methodology of Expected Return Tables

I have personally developed the above tables for jacks or better, bonus poker, double bonus, double double bonus, triple bonus, and triple double bonus and deuces wild. In general the wide tables that show the exact Combinations of combinations were done by me. The determination of said tables was done by testing all 32 ways to play any given hand. For each possible play I looped through every possible set of cards on the second deal and averaging the payoffs. Finally the decision that yielded the greatest overall expected return was defined as the best way to play that hand. The determination of the overall expected return was done by systematically analyzing all 2,598,960 possible five card poker hands, testing all 32 ways to play each one, adding the average results of the best way to play each hand, and finally dividing by the total Combinations of hands to yield the average results.

All other forms of video poker were analyzed with the help of WinPoker 5. This software allows the user to specify the payoff table to most forms of video poker and it evidently uses the same methodology as mine to determine the tables above. You can also play video poker with this software and it will tell you if and when you make a mistake and show you the reason why. To develop your own strategy you can enter any hand you like and the program will give you the expected return of all 32 ways to play it on one screen. The cost of this software is $30 and the web page has a stripped down version for free. For anyone serious about playing video poker properly I give WinPoker an A.

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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.

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