Lucky Red Casino

Last Updated: July 11, 2005

3-Way Action

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Introduction

3-Way Action is a video poker variation in which the player makes up to three bets on three ways to win: (1) the 5-card hand on the deal, (2) the 5-card hand on the draw, and (3) a 7-card hand consisting of the 5-card draw hand plus two more cards from the remaining deck. The game is not to be confused with the table game of the same name, Three Way Action.

Rules

The first coin bet is applied to the 5-card deal bet, the second on the 5-card draw bet, and the third on the 7-card hand. Subsequent coins repeat this cycle. As with most video poker games the highest hands pay disproportionately higher with a max coin bet. The following pay tables are per coin based on max coins bet. The pay tables below are the highest I know to exist, others are indicated in the Return section.

5-Card Deal Hand Pay Table

Hand Pays
Royal flush 4000
Straight flush 500
Four aces + 2-4 1000
Four 2-4 + A-4 400
Four aces 400
Four 2-4 200
Four 5-K 100
Full house 25
Flush 15
Straight 9
Three of a kind 5
Two pair 4
Pair J-A 2
Pair 3-10 1
Nonpaying hand 0

5-Card Draw Hand Pay Table

Hand Pays
Royal Flush 800
Straight Flush 100
Four aces + 2-4 400
Four 2-4 + A-4 160
Four aces 160
Four 2-4 80
Four 5-K 50
Full House 9
Flush 6
Straight 4
Three of a kind 3
Two pair 1
Jacks or better 1
Nonpaying hand 0

7-Card Hand Pay Table

Hand Pays
Four aces + three 2-4 4000
Four 2-4 + Three A-4 2000
7-card straight flush 800
Four of a kind + three of a kind 400
Royal Flush 160
Straight Flush 25
Four aces 40
Four 2-4 20
Four 5-K 10
Full House 4
Flush 3
Straight 2
Three of a kind 1
Two pair J-A up 1
Nonpaying hand 0

Return

I am aware of five different sets of pay tables, which are listed below according to the combined return over the three bets. All 5-card draw and 7-card draw pay tables are based on optimal strategy.

99.291%

I have observed the following pay table at both the Oasis in Mesquite and the Santa Fe Station in Las Vegas. Be warned that the Santa Fe Station has lots of 3-Way Action games and not all follow this pay table.

5-Card Deal Hand Pay Table

Hand Pays Combinations Probability Return
Royal flush 4000 4 0.000002 0.006156
Straight flush 500 36 0.000014 0.006926
Four aces + 2-4 1000 12 0.000005 0.004617
Four 2-4 + A-4 400 36 0.000014 0.005541
Four aces 400 36 0.000014 0.005541
Four 2-4 200 108 0.000042 0.008311
Four 5-K 100 432 0.000166 0.016622
Full house 25 3744 0.001441 0.036014
Flush 15 5108 0.001965 0.029481
Straight 9 10200 0.003925 0.035322
Three of a kind 5 54912 0.021128 0.105642
Two pair 4 123552 0.047539 0.190156
Pair J-A 2 337920 0.130021 0.260042
Pair 3-10 1 675840 0.260042 0.260042
Other 0 1387020 0.533683 0
Total 2598960 1 0.970414

5-Card Draw Hand Pay Table

Hand Pays Combinations Probability Return
Royal Flush 800 455864388 0.000023 0.018296
Straight Flush 100 2924754012 0.000147 0.014673
Four aces + 2-4 400 1054172592 0.000053 0.021154
Four 2-4 + A-4 160 2848458900 0.000143 0.022864
Four aces 160 2864959896 0.000144 0.022996
Four 2-4 80 7616190864 0.000382 0.030567
Four 5-K 50 31176229800 0.001564 0.078202
Full House 9 220034894868 0.011039 0.099347
Flush 6 371536113900 0.018639 0.111834
Straight 4 252148866336 0.01265 0.050599
Three of a kind 3 1407242194968 0.070598 0.211793
Two pair 1 2447297042832 0.122775 0.122775
Jacks or better 1 3525969101724 0.176889 0.176889
Nonpaying hand 0 11660061672120 0.584956 0
Total 19933230517200 1 0.981989

7-Card Hand Pay Table

Hand Pays Combinations Probability Return
Four aces + three 2-4 4000 4681016040 0.000001 0.003273
Four 2-4 + Three A-4 2000 12980386932 0.000002 0.004538
7-card straight flush 800 14516920940 0.000003 0.00203
Four of a kind + three of a kind 400 200524463808 0.000035 0.014021
Royal Flush 160 945488968584 0.000165 0.026443
Straight Flush 25 5711953578324 0.000998 0.024961
Four aces 40 3427971195392 0.000599 0.023968
Four 2-4 20 8572402413276 0.001498 0.029969
Four 5-K 10 26081911438768 0.004559 0.045591
Full House 4 367933126611288 0.064315 0.257258
Flush 3 446552121004000 0.078057 0.234171
Straight 2 285165922600112 0.049847 0.099694
Three of a kind 1 468239964753232 0.081848 0.081848
Two pair J-A up 1 1021573023895800 0.178571 0.178571
Nonpaying hand 0 3086400569189906 0.539502 0
Total 5720837158436400 1 1.026337

Total Return by Bet

Bet Return
5-card deal 97.041%
5-card draw 98.199%
7-card draw 102.634%
Combined 99.291%

97.533%

5-Card Deal Hand Pay Table

Hand Pays Combinations Probability Return
Royal flush 4000 4 0.000002 0.006156
Straight flush 500 36 0.000014 0.006926
Four aces + 2-4 1000 12 0.000005 0.004617
Four 2-4 + A-4 400 36 0.000014 0.005541
Four aces 400 36 0.000014 0.005541
Four 2-4 200 108 0.000042 0.008311
Four 5-K 100 432 0.000166 0.016622
Full house 16 3744 0.001441 0.023049
Flush 12 5108 0.001965 0.023585
Straight 8 10200 0.003925 0.031397
Three of a kind 5 54912 0.021128 0.105642
Two pair 4 123552 0.047539 0.190156
Pair J-A 2 337920 0.130021 0.260042
Pair 3-10 1 675840 0.260042 0.260042
Other 0 1387020 0.533683 0
Total 2598960 1 0.947628

5-Card Draw Hand Pay Table

Hand Pays Combinations Probability Return
Royal Flush 800 470448636 0.000024 0.018881
Straight Flush 100 2951680848 0.000148 0.014808
Four aces + 2-4 400 1133663064 0.000057 0.022749
Four 2-4 + A-4 160 2853100872 0.000143 0.022901
Four aces 160 3089906328 0.000155 0.024802
Four 2-4 80 7628213628 0.000383 0.030615
Four 5-K 50 31206155220 0.001566 0.078277
Full House 9 211623404760 0.010617 0.09555
Flush 5 367429623216 0.018433 0.092165
Straight 4 283507091172 0.014223 0.056891
Three of a kind 3 1417755074436 0.071125 0.213376
Two pair 1 2353652942940 0.118077 0.118077
Jacks or better 1 3417934399920 0.171469 0.171469
Nonpaying hand 0 11831994812160 0.593581 0
Total 19933230517200 1 0.960561

7-Card Hand Pay Table

Hand Pays Combinations Probability Return
Four aces + three 2-4 4000 4902348360 0.000001 0.003428
Four 2-4 + Three A-4 2000 13127277552 0.000002 0.004589
7-card straight flush 800 14532875676 0.000003 0.002032
Four of a kind + three of a kind 400 193497507888 0.000034 0.013529
Royal Flush 160 937410577784 0.000164 0.026217
Straight Flush 25 5795889647772 0.001013 0.025328
Four aces 80 3619545377732 0.000633 0.050616
Four 2-4 40 8611680080084 0.001505 0.060213
Four 5-K 20 25958350489536 0.004538 0.09075
Full House 5 362387343671040 0.063345 0.316726
Flush 3 445303154285688 0.077839 0.233516
Straight 2 310385265719608 0.054255 0.10851
Three of a kind 1 471013321377908 0.082333 0.082333
Nonpaying hand 0 4086599137199772 0.714336 0
Total 5720837158436400 1 1.017788

Total Return by Bet

Bet Return
5-card deal 94.763%
5-card draw 96.056%
7-card draw 101.779%
Combined 97.533%

97.288%

5-Card Deal Hand Pay Table

Hand Pays Combinations Probability Return
Royal flush 4000 4 0.000002 0.006156
Straight flush 500 36 0.000014 0.006926
Four aces + 2-4 1000 12 0.000005 0.004617
Four 2-4 + A-4 400 36 0.000014 0.005541
Four aces 400 36 0.000014 0.005541
Four 2-4 200 108 0.000042 0.008311
Four 5-K 100 432 0.000166 0.016622
Full house 16 3744 0.001441 0.023049
Flush 10 5108 0.001965 0.019654
Straight 7 10200 0.003925 0.027473
Three of a kind 5 54912 0.021128 0.105642
Two pair 4 123552 0.047539 0.190156
Pair J-A 2 337920 0.130021 0.260042
Pair 3-10 1 675840 0.260042 0.260042
Other 0 1387020 0.533683 0
Total 2598960 1 0.939773

5-Card Draw Hand Pay Table

Hand Pays Combinations Probability Return
Royal Flush 800 475546284 0.000024 0.019086
Straight Flush 100 2949023136 0.000148 0.014795
Four aces + 2-4 400 1058864052 0.000053 0.021248
Four 2-4 + A-4 160 2849013120 0.000143 0.022868
Four aces 160 2880444552 0.000145 0.023121
Four 2-4 80 7618809012 0.000382 0.030577
Four 5-K 50 31182344400 0.001564 0.078217
Full House 8 220112902944 0.011043 0.08834
Flush 5 363280894980 0.018225 0.091124
Straight 4 258813730788 0.012984 0.051936
Three of a kind 3 1407926665128 0.070632 0.211896
Two pair 1 2447405889768 0.12278 0.12278
Jacks or better 1 3540751824636 0.177631 0.177631
Nonpaying hand 0 11645924564400 0.584247 0
Total 19933230517200 1 0.95362

7-Card Hand Pay Table

Hand Pays Combinations Probability Return
Four aces + three 2-4 4000 4690215180 0.000001 0.003279
Four 2-4 + Three A-4 2000 12984926712 0.000002 0.00454
7-card straight flush 800 14371446168 0.000003 0.00201
Four of a kind + three of a kind 400 200590676748 0.000035 0.014025
Royal Flush 160 959759193260 0.000168 0.026842
Straight Flush 25 5680521558444 0.000993 0.024824
Four aces 40 3447640529276 0.000603 0.024106
Four 2-4 20 8568894314828 0.001498 0.029957
Four 5-K 10 26083562233272 0.004559 0.045594
Full House 4 367999697065776 0.064326 0.257305
Flush 3 439410059102556 0.076809 0.230426
Straight 2 290446718221108 0.05077 0.10154
Three of a kind 1 468400665006428 0.081876 0.081876
Two pair J-A up 1 1023592314695412 0.178924 0.178924
Nonpaying hand 0 3086014689251232 0.539434 0
Total 5720837158436400 1 1.025247

Total Return by Bet

Bet Return
5-card deal 93.977%
5-card draw 95.362%
7-card draw 102.525%
Combined 97.288%

96.917%

5-Card Deal Hand Pay Table

Hand Pays Combinations Probability Return
Royal flush 4000 4 0.000002 0.006156
Straight flush 500 36 0.000014 0.006926
Four aces + 2-4 1000 12 0.000005 0.004617
Four 2-4 + A-4 400 36 0.000014 0.005541
Four aces 400 36 0.000014 0.005541
Four 2-4 200 108 0.000042 0.008311
Four 5-K 100 432 0.000166 0.016622
Full house 16 3744 0.001441 0.023049
Flush 10 5108 0.001965 0.019654
Straight 7 10200 0.003925 0.027473
Three of a kind 5 54912 0.021128 0.105642
Two pair 4 123552 0.047539 0.190156
Pair J-A 2 337920 0.130021 0.260042
Pair 3-10 1 675840 0.260042 0.260042
Other 0 1387020 0.533683 0
Total 2598960 1 0.939773

5-Card Draw Hand Pay Table

Hand Pays Combinations Probability Return
Royal Flush 800 470265456 0.000024 0.018874
Straight Flush 100 2953226784 0.000148 0.014816
Four aces + 2-4 400 1133479368 0.000057 0.022746
Four 2-4 + A-4 160 2853037404 0.000143 0.022901
Four aces 160 3089313960 0.000155 0.024797
Four 2-4 80 7628137260 0.000383 0.030615
Four 5-K 50 31197239772 0.001565 0.078254
Full House 8 211584953988 0.010615 0.084917
Flush 5 367614887340 0.018442 0.092212
Straight 4 283867481568 0.014241 0.056964
Three of a kind 3 1417337250660 0.071104 0.213313
Two pair 1 2353048340580 0.118047 0.118047
Jacks or better 1 3416666795352 0.171406 0.171406
Nonpaying hand 0 11833786107708 0.593671 0
Total 19933230517200 1 0.949859

7-Card Hand Pay Table

Hand Pays Combinations Probability Return
Four aces + three 2-4 4000 4901575920 0.000001 0.003427
Four 2-4 + Three A-4 2000 13126955292 0.000002 0.004589
7-card straight flush 800 14539119156 0.000003 0.002033
Four of a kind + three of a kind 400 193459318848 0.000034 0.013527
Royal Flush 160 936955409888 0.000164 0.026205
Straight Flush 25 5798927264628 0.001014 0.025341
Four aces 80 3618345921584 0.000632 0.050599
Four 2-4 40 8611880141552 0.001505 0.060214
Four 5-K 20 25949798433852 0.004536 0.09072
Full House 5 362300821945368 0.06333 0.31665
Flush 3 445544471072988 0.077881 0.233643
Straight 2 310674733231792 0.054306 0.108612
Three of a kind 1 470903758316108 0.082314 0.082314
Nonpaying hand 0 4086271439729424 0.714279 0
Total 5720837158436400 1 1.017874

Total Return by Bet

Bet Return
5-card deal 93.977%
5-card draw 94.986%
7-card draw 101.787%
Combined 96.917%

94.713%

5-Card Deal Hand Pay Table

Hand Pays Combinations Probability Return
Royal flush 4000 4 0.000002 0.006156
Straight flush 500 36 0.000014 0.006926
Four aces + 2-4 1000 12 0.000005 0.004617
Four 2-4 + A-4 400 36 0.000014 0.005541
Four aces 400 36 0.000014 0.005541
Four 2-4 200 108 0.000042 0.008311
Four 5-K 100 432 0.000166 0.016622
Full house 15 3744 0.001441 0.021609
Flush 9 5108 0.001965 0.017689
Straight 6 10200 0.003925 0.023548
Three of a kind 5 54912 0.021128 0.105642
Two pair 4 123552 0.047539 0.190156
Pair J-A 2 337920 0.130021 0.260042
Pair 3-10 1 675840 0.260042 0.260042
Other 0 1387020 0.533683 0
Total 2598960 1 0.932442

5-Card Draw Hand Pay Table

Hand Pays Combinations Probability Return
Royal Flush 800 475546284 0.000024 0.019086
Straight Flush 100 2949023136 0.000148 0.014795
Four aces + 2-4 400 1058864052 0.000053 0.021248
Four 2-4 + A-4 160 2849013120 0.000143 0.022868
Four aces 160 2880444552 0.000145 0.023121
Four 2-4 80 7618809012 0.000382 0.030577
Four 5-K 50 31182344400 0.001564 0.078217
Full House 8 220112902944 0.011043 0.08834
Flush 5 363280894980 0.018225 0.091124
Straight 4 258813730788 0.012984 0.051936
Three of a kind 3 1407926665128 0.070632 0.211896
Two pair 1 2447405889768 0.12278 0.12278
Jacks or better 1 3540751824636 0.177631 0.177631
Nonpaying hand 0 11645924564400 0.584247 0
Total 19933230517200 1 0.95362

7-Card Hand Pay Table

Hand Pays Combinations Probability Return
Four aces + three 2-4 4000 4893527520 0.000001 0.003422
Four 2-4 + Three A-4 2000 13121248812 0.000002 0.004587
7-card straight flush 800 14620858284 0.000003 0.002045
Four of a kind + three of a kind 400 193012594884 0.000034 0.013495
Royal Flush 160 935099549672 0.000163 0.026153
Straight Flush 25 5824832414268 0.001018 0.025454
Four aces 80 3606975937844 0.00063 0.05044
Four 2-4 40 8611914393584 0.001505 0.060214
Four 5-K 20 25873458282972 0.004523 0.090453
Full House 4 361367209535904 0.063167 0.252667
Flush 3 446851355039256 0.078109 0.234328
Straight 2 314468408942860 0.054969 0.109938
Three of a kind 1 469892097374240 0.082137 0.082137
Nonpaying hand 0 4083180158736300 0.713738 0
Total 5720837158436400 1 0.955334

Total Return by Bet

Bet Return
5-card deal 93.244%
5-card draw 95.362%
7-card draw 95.533%
Combined 94.713%

Strategy

The following strategy is based on the 99.291% combined return game and is not optimal. My program generated an optimal strategy but it was 76,045 lines long. This is my attempt to condense it. Note that there are plays which may seem strange to the video poker player, like 3 to a flush, 3 to a straight, two to a straight flush, and a single 4 or 10. Some common video poker terminology is used. If you are not familiar with some of the terms please see the key, my Jacks or Better optimal strategy.

  1. Pat royal
  2. Four aces + 2-4
  3. Four aces + 5-K
  4. Four 2-4 + A-4
  5. Pat straight flush
  6. Four 2-4 + 5-K
  7. Four 5-K
  8. Four to a royal
  9. Full house with no 5-K
  10. Three of a kind aces
  11. Full house, with at least one 5-K
  12. Three of a kind 2-4
  13. Four to an outside straight flush
  14. Flush
  15. Three of a kind 5-K
  16. Straight
  17. Four to an inside straight flush
  18. Two pair
  19. Pair of aces
  20. Three to a royal
  21. Four to a flush
  22. Pair J-K
  23. 9/10/J suited
  24. Three to a straight flush +0, -1
  25. Pair 2-4
  26. Four to an outside straight
  27. Three to a flush with two high cards
  28. Pair 5-K
  29. Two suited high cards
  30. Three to a straight flush -2
  31. Three to a flush with one high card
  32. Four to an inside straight with 2-3 high cards
  33. Two to a royal 10 low
  34. Four to an inside straight with 1 high card
  35. Three to a flush with zero high cards
  36. Two high cards
  37. One high card
  38. Three to a straight with two high cards
  39. Four to an inside straight with 0 high cards
  40. Two to a straight flush
  41. Three consecutive cards, zero high
  42. Ten
  43. Four
  44. Toss everything

Methodology

I've been toying with this game since I first saw it in the year 2001. The problem with it is that there are 3,432,502,295,061,840 possible outcomes of each hand. Most initial programs I created would have taken several years to cycle through. However, in 2005 I developed enough short cuts to cut down the analysis time to only 80 days. So after four years of off and on tinkering and almost three months of computer time, I finally cracked this game in August 2005. This section may interest few people but I consider it one of my proudest accomplishments.

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