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Triple Play Keno Draw Poker

Introduction

Triple Play Keno Draw Poker is a video poker variant that combines video poker and keno. The keno game awards both instant wins and multipliers to be applied to the video poker win.

Rules

  1. The game is based on conventional Triple Play video poker, which I assume the reader already understands.
  2. The player may play Triple Play video poker with 0 to 15 credits bet. If the player bets 20 or 25 total credits, then he will enable the keno feature.
  3. With the keno feature enabled, the player will pick 2 to 10 numbers from the range of 1 to 80.
  4. After the player makes a bet, the game will deal the player five cards and draw 10 numbers from the same keno range of 1 to 80.
  5. The player will choose which cards to hold.
  6. After the player presses the "draw" button, his discarded cards will be replaced and 10 more keno balls will be drawn.
  7. According to how many balls chosen by the player match the 20-ball draw by the game will determine both an immediate keno win as well as a multiplier to be applied to the video poker win.
  8. Each hand will be scored according to it's poker value and the posted pay table.

The following table shows the immediate keno win with 20 total credits bet.

Immediate Keno Win with 20 Credits Bet

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
2 24 4 2 0 0 0 0 0 0
3   100 7 10 6 1 0 0 0
4     120 35 8 2 4 2 0
5       2100 150 30 25 10 10
6         3000 600 225 85 50
7           10000 3000 700 300
8             10000 10000 2000
9               20000 9000
10                 20000

The following table shows the immediate keno win with 25 total credits bet.

Immediate Keno Win with 25 Credits Bet

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
2 77 16 10 0 0 0 0 0 0
3   250 30 20 15 5 0 0 0
4     540 70 25 10 12 5 0
5       4500 400 135 75 25 25
6         8750 2475 575 250 125
7           30000 8400 2050 800
8             50000 25000 5000
9               50000 20000
10                 50000

The following table shows the video poker multiplier win with 20 total credits bet.

Video Poker Multiplier Win with 20 Credits Bet

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
2 5 2 2 1 1 1 1 1 1
3   6 2 2 2 2 1 1 1
4     4 7 3 2 2 2 1
5       7 9 4 7 3 3
6         9 4 9 7 9
7           4 9 7 9
8             9 7 9
9               7 9
10                 9

The following table shows the video poker multiplier win with 25 total credits bet.

Video Poker Multiplier Win with 25 Credits Bet

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
2 7 2 2 1 1 1 1 1 1
3   12 3 3 2 2 1 1 1
4     12 12 7 2 3 2 1
5       12 12 12 8 6 5
6         12 12 12 12 12
7           12 12 12 12
8             12 12 12
9               12 12
10                 12

Example

In the following image I am playing 9-5 Jacks or Better, betting 25 credits, and chosing 9 numbers (14,15,16,24,25,26,34,35 and 36). I caught five of the nine numbers chosen (14,15,24,25 and 36). For catching 5 out of 9, my immediate keno win is 25 credits. My video poker multiplier for catching 5 out of 9 is 6x.

Only the bottom hand won with a pair of jacks. The base win for a high pair is 5 credits. With the 6x multiplier, my video poker win is 6×5 = 30. My total win was thus 25 for keno + 30 for video poker = 55 credits.

Analysis

The following table shows the probability of all possible combinations of picks and catches in the keno portion of the game.

Keno Probabilities

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0.560127 0.416504 0.308321 0.227184 0.166602 0.121574 0.088266 0.063748 0.045791
1 0.379747 0.430867 0.432732 0.405686 0.363495 0.315193 0.266464 0.220666 0.179571
2 0.060127 0.138754 0.212635 0.270457 0.308321 0.326654 0.328146 0.316426 0.295257
3   0.013875 0.043248 0.083935 0.129820 0.174993 0.214786 0.246109 0.267402
4     0.003063 0.012092 0.028538 0.052191 0.081504 0.114105 0.147319
5       0.000645 0.003096 0.008639 0.018303 0.032601 0.051428
6         0.000129 0.000732 0.002367 0.005720 0.011479
7           0.000024 0.000160 0.000592 0.001611
8             0.000004 0.000033 0.000135
9               0.000001 0.000006
10                 0.000000
Total 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000

The following table shows the value of the immediate keno win (in credits), the average video poker multiplier, and the RTP multiplier (compared to the base game only) for a total bet of 20 credits. As an example of the RTP boost, if the base game was 8/5 Bonus Poker, then the RTP without the feature would be 0.991660. With the feature and piking four numbers, the RTP is 0.991660 × 1.003586 = 0.995673.

20 Credit Bet Summary

Pick Immediate
Keno
Win		 Video
Poker
Multiplier		 RTP
Boost
2 1.443038 1.240506 1.002532
3 1.942551 1.208130 1.003225
4 1.095613 1.265074 1.003586
5 2.616924 1.160359 1.001115
6 1.858521 1.212692 1.002445
7 1.221802 1.255369 1.002617
8 1.840912 1.211571 1.000724
9 1.794973 1.217375 1.002780
10 1.899758 1.208713 1.001523

The following table shows the value of the immediate keno win (in credits), the average video poker multiplier, and the RTP multiplier (compared to the base game only) for a total bet of 25 credits. As an example of the RTP boost, if the base game was 8/5 Bonus Poker, then the RTP without the feature would be 0.991660. With the feature and piking ten numbers, the RTP is 0.991660 × 1.003345 = 0.996583.

25 Credit Bet Summary

Pick Immediate
Keno
Win		 Video
Poker
Multiplier		 RTP
Boost
2 4.629747 1.360759 1.001646
3 5.688900 1.291383 1.002386
4 5.078023 1.332829 1.002818
5 5.427326 1.307980 1.001881
6 5.027615 1.336518 1.003015
7 5.107040 1.330529 1.002599
8 5.276705 1.318972 1.002452
9 4.879418 1.346903 1.003318
10 4.814651 1.351265 1.003345

The following table shows the overall Return to Player (RTP) for 20 credits bet under various popular games and pay tables according to the number of picks made in the keno portion. The right column shows the number of picks with the greatest RTP.

In general, to achieve the greatest RTP pick the following number of balls in keno according to the base RTP (without the feature) as follows:

  • Base RTP over 0.991561 — Pick 4
  • Base RTP under 0.991561 — Pick 3

20 Credit Bet ReturnsExpand

Game Pay Table Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10 Best Bet
Jacks or Better 9-6 0.998288 0.999093 0.988877 0.997146 0.998297 0.998323 0.996580 0.998616 0.997388 4
Jacks or Better 9-5 0.988109 0.989179 0.988336 0.987624 0.988346 0.988021 0.986638 0.988626 0.987469 3
Jacks or Better 8-6 0.987578 0.988662 0.977953 0.987127 0.987827 0.987484 0.986119 0.988105 0.986952 3
Jacks or Better 8-5 0.977397 0.978747 0.967030 0.977604 0.977874 0.977181 0.976176 0.978114 0.977032 3
Jacks or Better 7-5 0.966686 0.968315 0.956109 0.967585 0.967403 0.966342 0.965715 0.967603 0.966596 3
Jacks or Better 6-5 0.955976 0.957885 0.995673 0.957568 0.956934 0.955504 0.955255 0.957093 0.956160 3
Bonus Poker 8-5 0.994772 0.995669 0.984749 0.993857 0.994860 0.994765 0.993146 0.995166 0.993962 4
Bonus Poker 7-5 0.984061 0.985237 0.973876 0.983838 0.984389 0.983925 0.982684 0.984654 0.983525 3
Bonus Poker 6-5 0.973399 0.974853 1.000186 0.973864 0.973966 0.973135 0.972271 0.974190 0.973136 3
Bonus Poker Deluxe 9-6 0.999198 0.999979 0.989823 0.997997 0.999187 0.999243 0.997468 0.999509 0.998274 4
Bonus Poker Deluxe 9-5 0.989036 0.990082 0.989285 0.988492 0.989253 0.988960 0.987544 0.989537 0.988373 3
Bonus Poker Deluxe 8-6 0.988509 0.989569 0.978925 0.987998 0.988737 0.988426 0.987029 0.989019 0.987859 3
Bonus Poker Deluxe 8-5 0.978350 0.979675 0.968030 0.978496 0.978806 0.978146 0.977107 0.979050 0.977961 3
Bonus Poker Deluxe 7-5 0.967667 0.969270 0.959572 0.968503 0.968362 0.967334 0.966672 0.968565 0.967551 3
Bonus Poker Deluxe 6-5 0.959372 0.961192 0.995108 0.960744 0.960254 0.958940 0.958571 0.960426 0.959469 3
Double Bonus 9/7/5 0.994219 0.995129 0.982771 0.993339 0.994319 0.994204 0.992605 0.994622 0.993423 3
Double Bonus 9/6/5 0.982121 0.983347 0.979498 0.982023 0.982492 0.981962 0.980790 0.982750 0.981635 3
Double Bonus 10/6/4 0.978912 0.980222 0.969195 0.979022 0.979355 0.978714 0.977655 0.979601 0.978508 3
Double Bonus 9/6/4 0.968809 0.970383 0.958743 0.969571 0.969479 0.968490 0.967788 0.969686 0.968664 3
Double Bonus 9/5/4 0.958560 0.960401 0.993916 0.959985 0.959460 0.958119 0.957778 0.959629 0.958678 3
Double Double Bonus 9-6 0.993049 0.993990 0.983404 0.992245 0.993176 0.993021 0.991463 0.993475 0.992283 3
Double Double Bonus 9-5 0.982742 0.983952 0.973092 0.982604 0.983099 0.982590 0.981396 0.983359 0.982240 3
Double Double Bonus 8-5 0.972630 0.974104 0.962901 0.973146 0.973214 0.972357 0.971520 0.973436 0.972387 3
Double Double Bonus 7-5 0.962637 0.964372 0.996139 0.963798 0.963445 0.962244 0.961760 0.963629 0.962650 3
Triple Double Bonus 10-6 0.995229 0.996113 0.986071 0.994284 0.995307 0.995227 0.993592 0.995614 0.994407 4
Triple Double Bonus 9-6 0.985357 0.986499 0.975315 0.985050 0.985656 0.985236 0.983950 0.985926 0.984788 3
Triple Double Bonus 9-5 0.974810 0.976227 0.976154 0.975185 0.975345 0.974563 0.973649 0.975576 0.974511 3
Triple Double Bonus 8-6 0.975633 0.977028 0.965337 0.975954 0.976149 0.975396 0.974452 0.976383 0.975313 3
Triple Double Bonus 8-5 0.965025 0.966698 0.955366 0.966032 0.965780 0.964661 0.964093 0.965973 0.964977 3
Triple Double Bonus 7-5 0.955248 0.957176 1.001229 0.956886 0.956222 0.954767 0.954543 0.956378 0.955451 3
Triple Triple Bonus 9-6 1.000221 1.000975 0.990385 0.998953 1.000186 1.000278 0.998467 1.000512 0.999271 4
Triple Triple Bonus 9-5 0.989587 0.990619 0.980355 0.989007 0.989791 0.989518 0.988082 0.990077 0.988910 3
Triple Triple Bonus 8-5 0.979752 0.981041 0.970328 0.979808 0.980177 0.979565 0.978476 0.980426 0.979327 3
Triple Triple Bonus 7-5 0.969920 0.971465 0.960313 0.970611 0.970565 0.969615 0.968873 0.970777 0.969747 3
Triple Triple Bonus 6-5 0.960099 0.961900 0.985420 0.961424 0.960964 0.959676 0.959281 0.961139 0.960177 3
Joker Poker 50/17/7/5 0.984719 0.985877 0.977350 0.984453 0.985032 0.984590 0.983327 0.985299 0.984166 3
Joker Poker 50/16/7/5 0.976806 0.978171 0.969285 0.977051 0.977296 0.976583 0.975598 0.977534 0.976456 3
Joker Poker 50/15/7/5 0.968897 0.970468 0.960482 0.969653 0.969564 0.968579 0.967874 0.969772 0.968750 3
Joker Poker 40/20/5/4 0.960264 0.962061 0.998063 0.961579 0.961126 0.959843 0.959443 0.961301 0.960339 3
Deuces Wild 25/15/10/4/4/3 0.997116 0.997951 0.993273 0.996049 0.997151 0.997136 0.995435 0.997465 0.996246 4
Deuces Wild 25/15/9/4/4/3 0.992419 0.993377 0.980616 0.991656 0.992560 0.992384 0.990848 0.992856 0.991669 3
Deuces Wild 20/12/10/4/4/3 0.980008 0.981290 0.975930 0.980047 0.980427 0.979824 0.978726 0.980677 0.979576 3
Deuces Wild 25/16/13/4/3/2 0.975413 0.976814 0.965290 0.975749 0.975935 0.975173 0.974238 0.976167 0.975099 3
Deuces Wild 20/10/8/4/4/3 0.964980 0.966653 0.998369 0.965989 0.965735 0.964615 0.964048 0.965928 0.964933 3
Deuces Wild Bonus 9/4/4/3 0.997416 0.998244 0.994691 0.996330 0.997445 0.997440 0.995728 0.997760 0.996538 4
Deuces Wild Bonus 8/4/4/3 0.993809 0.994731 0.991110 0.992956 0.993919 0.993790 0.992205 0.994221 0.993024 3
Deuces Wild Bonus 7/4/4/3 0.990298 0.991311 0.992224 0.989672 0.990486 0.990237 0.988776 0.990775 0.989603 3
Deuces Wild Bonus 13/4/3/3 0.991390 0.992375 0.978579 0.990694 0.991554 0.991342 0.989843 0.991847 0.990667 3
Deuces Wild Bonus 10/4/3/3 0.978011 0.979344 0.967705 0.978178 0.978474 0.977802 0.976775 0.978716 0.977630 3
Deuces Wild Bonus 12/4/3/2 0.967347 0.968960 0.963386 0.968204 0.968050 0.967011 0.966361 0.968252 0.967240 3
Deuces Wild Bonus 11/4/3/2 0.963112 0.964835 0.959341 0.964243 0.963910 0.962725 0.962224 0.964096 0.963114 3
Deuces Wild Bonus 10/4/3/2 0.959146 0.960972 4.000000 0.960533 0.960033 0.958712 0.958351 0.960204 0.959249 3

The following table shows the overall Return to Player (RTP) for 25 credits bet under various popular games and pay tables according to the number of picks made in the keno portion. The right column shows the number of picks with the greatest RTP.

In general, to achieve the greatest RTP pick the following number of balls in keno according to the base RTP (without the feature) as follows:

  • RTP over 0.989829 — Pick 10
  • RTP between 0.971999 to 0.989829 — Pick 9
  • RTP under 0.971999 — Pick 3

25 Credit Bet ReturnsExpand

Game Pay Table Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10 Best Bet
Jacks or Better 9-6 0.997922 0.998852 0.990421 0.998302 0.999358 0.998958 0.998842 0.999632 0.999647  
Jacks or Better 9-5 0.988989 0.990374 0.989965 0.989715 0.990584 0.990224 0.990183 0.990791 0.990777  
Jacks or Better 8-6 0.988523 0.989932 0.981214 0.989267 0.990126 0.989768 0.989732 0.990329 0.990314  
Jacks or Better 8-5 0.979588 0.981453 0.972007 0.980679 0.981351 0.981032 0.981072 0.981486 0.981442  
Jacks or Better 7-5 0.970189 0.972533 0.962802 0.971645 0.972119 0.971841 0.971961 0.972182 0.972108  
Jacks or Better 6-5 0.960791 0.963614 0.996149 0.962611 0.962889 0.962652 0.962851 0.962880 0.962775  
Bonus Poker 8-5 0.994836 0.995924 0.986942 0.995336 0.996327 0.995941 0.995851 0.996578 0.996583  
Bonus Poker 7-5 0.985436 0.987003 0.977777 0.986301 0.987095 0.986750 0.986740 0.987274 0.987249  
Bonus Poker 6-5 0.976080 0.978123 0.999953 0.977307 0.977905 0.977601 0.977671 0.978013 0.977958  
Bonus Poker Deluxe 9-6 0.998720 0.999609 0.991218 0.999069 1.000142 0.999739 0.999616 1.000423 1.000440  
Bonus Poker Deluxe 9-5 0.989803 0.991147 0.990765 0.990498 0.991384 0.991019 0.990972 0.991596 0.991585  
Bonus Poker Deluxe 8-6 0.989340 0.990707 0.982033 0.990053 0.990929 0.990567 0.990524 0.991138 0.991125  
Bonus Poker Deluxe 8-5 0.980425 0.982247 0.972850 0.981484 0.982173 0.981850 0.981883 0.982314 0.982273  
Bonus Poker Deluxe 7-5 0.971050 0.973350 0.965721 0.972472 0.972965 0.972683 0.972795 0.973034 0.972963  
Bonus Poker Deluxe 6-5 0.963771 0.966442 0.995673 0.965475 0.965816 0.965566 0.965740 0.965829 0.965735  
Double Bonus 9/7/5 0.994351 0.995462 0.985274 0.994869 0.995850 0.995466 0.995380 0.996098 0.996101  
Double Bonus 9/6/5 0.983734 0.985387 0.982516 0.984664 0.985423 0.985086 0.985090 0.985589 0.985559  
Double Bonus 10/6/4 0.980918 0.982715 0.973832 0.981958 0.982657 0.982332 0.982361 0.982802 0.982762  
Double Bonus 9/6/4 0.972052 0.974301 0.965023 0.973436 0.973949 0.973663 0.973767 0.974026 0.973958  
Double Bonus 9/5/4 0.963058 0.965766 0.994668 0.964790 0.965115 0.964869 0.965049 0.965124 0.965027  
Double Double Bonus 9-6 0.993324 0.994489 0.985808 0.993882 0.994842 0.994463 0.994386 0.995082 0.995082  
Double Double Bonus 9-5 0.984279 0.985904 0.977117 0.985188 0.985958 0.985618 0.985618 0.986128 0.986099  
Double Double Bonus 8-5 0.975406 0.977483 0.968527 0.976659 0.977243 0.976942 0.977017 0.977345 0.977288  
Double Double Bonus 7-5 0.966636 0.969161 0.996541 0.968229 0.968629 0.968367 0.968517 0.968665 0.968580  
Triple Double Bonus 10-6 0.995237 0.996304 0.988056 0.995721 0.996721 0.996333 0.996240 0.996975 0.996981  
Triple Double Bonus 9-6 0.986574 0.988082 0.978990 0.987394 0.988212 0.987862 0.987843 0.988400 0.988378  
Triple Double Bonus 9-5 0.977318 0.979299 0.979697 0.978497 0.979122 0.978812 0.978871 0.979239 0.979188  
Triple Double Bonus 8-6 0.978040 0.979984 0.970580 0.979191 0.979830 0.979518 0.979571 0.979953 0.979904  
Triple Double Bonus 8-5 0.968732 0.971150 0.962176 0.970244 0.970688 0.970416 0.970548 0.970740 0.970661  
Triple Double Bonus 7-5 0.960152 0.963007 1.000832 0.961997 0.962261 0.962027 0.962232 0.962247 0.962141  
Triple Triple Bonus 9-6 0.999617 1.000461 0.991692 0.999932 1.001023 1.000616 1.000486 1.001311 1.001331  
Triple Triple Bonus 9-5 0.990286 0.991605 0.983238 0.990962 0.991858 0.991492 0.991441 0.992075 0.992065  
Triple Triple Bonus 8-5 0.981655 0.983415 0.974787 0.982666 0.983381 0.983053 0.983075 0.983532 0.983494  
Triple Triple Bonus 7-5 0.973027 0.975226 0.966345 0.974373 0.974907 0.974616 0.974712 0.974991 0.974926  
Triple Triple Bonus 6-5 0.964409 0.967047 0.987507 0.966088 0.966442 0.966189 0.966358 0.966461 0.966368  
Joker Poker 50/17/7/5 0.986014 0.987551 0.980706 0.986855 0.987662 0.987314 0.987300 0.987846 0.987822  
Joker Poker 50/16/7/5 0.979070 0.980961 0.973907 0.980181 0.980842 0.980525 0.980569 0.980972 0.980927  
Joker Poker 50/15/7/5 0.972129 0.974374 0.966488 0.973509 0.974025 0.973738 0.973841 0.974102 0.974034  
Joker Poker 40/20/5/4 0.964554 0.967185 0.998163 0.966228 0.966585 0.966331 0.966499 0.966604 0.966512  
Deuces Wild 25/15/10/4/4/3 0.996893 0.997875 0.994126 0.997313 0.998347 0.997952 0.997845 0.998614 0.998626  
Deuces Wild 25/15/9/4/4/3 0.992772 0.993964 0.983458 0.993351 0.994299 0.993922 0.993850 0.994535 0.994533  
Deuces Wild 20/12/10/4/4/3 0.981880 0.983628 0.979508 0.982882 0.983602 0.983273 0.983293 0.983754 0.983717  
Deuces Wild 25/16/13/4/3/2 0.977848 0.979801 0.970541 0.979006 0.979641 0.979330 0.979384 0.979763 0.979713  
Deuces Wild 20/10/8/4/4/3 0.968692 0.971112 0.998421 0.970205 0.970649 0.970377 0.970510 0.970700 0.970621  
Deuces Wild Bonus 9/4/4/3 0.997157 0.998126 0.995321 0.997566 0.998606 0.998210 0.998100 0.998875 0.998887  
Deuces Wild Bonus 8/4/4/3 0.993991 0.995122 0.992303 0.994524 0.995497 0.995115 0.995032 0.995742 0.995744  
Deuces Wild Bonus 7/4/4/3 0.990910 0.992197 0.993242 0.991562 0.992471 0.992102 0.992046 0.992692 0.992684  
Deuces Wild Bonus 13/4/3/3 0.991869 0.993107 0.981741 0.992483 0.993412 0.993039 0.992975 0.993641 0.993636  
Deuces Wild Bonus 10/4/3/3 0.980127 0.981964 0.972576 0.981197 0.981880 0.981559 0.981594 0.982019 0.981977  
Deuces Wild Bonus 12/4/3/2 0.970770 0.973084 0.968936 0.972203 0.972689 0.972409 0.972524 0.972757 0.972684  
Deuces Wild Bonus 11/4/3/2 0.967053 0.969557 0.965527 0.968630 0.969039 0.968775 0.968921 0.969078 0.968994  
Deuces Wild Bonus 10/4/3/2 0.963573 0.966254 4.000000 0.965285 0.965621 0.965372 0.965548 0.965633 0.965538  

Acknowledgements

I would like to thank VideoPoker.com for the Gold Level membership and permission to use screenshots from their web site.

Written by: Michael Shackleford