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Jackpot Party Keno

Introduction

Jackpot Party Keno is a keno variant I noticed at the Red Rock casino on March 14, 2009. It is based on the concept of the bonus round in the slot machine "Jackpot Party," in which the player keeps picking prizes until a dreaded "Party Poopers" is picked, ending the bonus. In regular keno, the game always picks 20 balls. In Jackpot Party Keno four to seven "Pooper Balls" are added to the hopper, and game keeps picking balls until a Pooper Ball is chosen. The player is then paid based on the number of hits among the balls drawn before the Pooper Ball.

Unlike regular keno, the player picks 2 to 10 numbers from a range of 1 to 40, instead of 1 to 80. The player also decides how many Pooper Balls will be in the hopper. The greater the number of Pooper Balls, the fewer balls are likely to be drawn, so the larger the prizes.

Number of Balls Drawn

 

 

Probabilities for Number of Balls Drawn before Pooper Ball

Balls Drawn 4 Pooper Balls 5 Pooper Balls 6 Pooper Balls 7 Pooper Balls
40 0.00000737 0.00000082 0.00000011 0.00000002
39 0.00002947 0.00000409 0.00000064 0.00000011
38 0.00007366 0.00001228 0.00000224 0.00000045
37 0.00014733 0.00002865 0.00000598 0.00000134
36 0.00025782 0.00005729 0.00001345 0.00000334
35 0.00041252 0.00010313 0.00002690 0.00000735
34 0.00061878 0.00017188 0.00004932 0.00001469
33 0.00088397 0.00027010 0.00008455 0.00002729
32 0.00121546 0.00040515 0.0001374 0.00004775
31 0.00162061 0.00058522 0.00021373 0.00007958
30 0.00210680 0.00081931 0.0003206 0.00012733
29 0.00268138 0.00111724 0.00046633 0.00019678
28 0.00335172 0.00148966 0.00066063 0.00029518
27 0.00412520 0.00194801 0.00091472 0.00043141
26 0.00500917 0.00250459 0.0012414 0.0006163
25 0.00601101 0.00317248 0.0016552 0.00086282
24 0.00713807 0.00396559 0.00217246 0.00118638
23 0.00839773 0.00489867 0.00281141 0.0016051
22 0.00979735 0.00598727 0.00359236 0.00214013
21 0.0113443 0.00724775 0.00453772 0.00281596
20 0.01304594 0.00869730 0.00567215 0.00366075
19 0.01490965 0.01035392 0.00702266 0.00470668
18 0.01694278 0.01223646 0.00861872 0.00599032
17 0.01915271 0.01436454 0.01049236 0.00755301
16 0.0215468 0.01675862 0.01267826 0.00944126
15 0.02413242 0.01944000 0.01521392 0.01170716
14 0.02691693 0.02243077 0.01813967 0.01440882
13 0.02990770 0.02575385 0.02149887 0.01761077
12 0.03311209 0.02943297 0.02533795 0.02138451
11 0.03653748 0.03349269 0.02970656 0.02580889
10 0.04019123 0.03795839 0.03465766 0.03097067
9 0.04408071 0.04285624 0.04024760 0.03696500
8 0.04821327 0.04821327 0.04653629 0.04389593
7 0.0525963 0.05405731 0.05358724 0.05187701
6 0.05723715 0.06041699 0.06146772 0.06103178
5 0.06214319 0.06732179 0.07024882 0.07149437
4 0.06732179 0.07480199 0.0800056 0.08341010
3 0.07278031 0.08288869 0.09081717 0.09693606
2 0.07852613 0.09161381 0.10276680 0.11224175
1 0.08456660 0.1010101 0.11594203 0.12950971
0 0.09090909 0.11111111 0.13043478 0.14893617
Total 1 1 1 1

 

The following table shows the expected number of balls drawn before a Pooper Ball, according to the number of Pooper Balls in the hopper.

 

 

Expected Balls Drawn before Pooper Ball

Pooper Balls Expected Draw
4 8.00
5 6.67
6 5.71
7 5.00

 

Four Pooper Balls

The following pay table shows the win with four Pooper Balls, according to the number of picks the player makes, from 2 to 10, and the number of matching balls drawn.

 

 

Pay Table for Four Pooper Balls

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
10                 275
9               172 55
8             240 40 20
7           140 25 10 5
6         105 12 4 5 2
5       82 12 4 2 2 1
4     46 6 2 2 1 1 0
3   24 2 1 1 1 0 0 0
2 13 2 1 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0

 

The following pay table shows the probability of winning with four Pooper Balls, according to the number of picks the player makes, from 2 to 10, and number of catches.

 

 

Probabilities of Winning for Four Pooper BallsExpand

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
10                 0.000999
9               0.001399 0.003996
8             0.00202 0.005594 0.00999
7           0.00303 0.008081 0.013986 0.01998
6         0.004762 0.012121 0.020202 0.027972 0.034965
5       0.007937 0.019048 0.030303 0.040404 0.048951 0.055944
4     0.014286 0.031746 0.047619 0.060606 0.070707 0.078322 0.083916
3   0.028571 0.057143 0.079365 0.095238 0.106061 0.113131 0.117483 0.11988
2 0.066667 0.114286 0.142857 0.15873 0.166667 0.169697 0.169697 0.167832 0.164835
1 0.266667 0.285714 0.285714 0.277778 0.266667 0.254545 0.242424 0.230769 0.219780
0 0.666667 0.571429 0.5 0.444444 0.4 0.363636 0.333333 0.307692 0.285714
Total 1 1 1 1 1 1 1 1 1

 

The following pay table shows the expected return with four Pooper Balls, according to the number of picks the player makes, from 2 to 10, and number of catches. The bottom row shows the overall return according to number of picks. The greatest return is for the pick 5 at 92.0635%.

 

 

Probabilities of Winning for Four Pooper BallsExpand

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
10                 0.274725
9               0.240559 0.21978
8             0.484848 0.223776 0.1998
7           0.424242 0.20202 0.13986 0.0999
6         0.5 0.145455 0.080808 0.13986 0.06993
5       0.650794 0.228571 0.121212 0.080808 0.097902 0.055944
4     0.657143 0.190476 0.095238 0.121212 0.070707 0.078322 0
3   0.685714 0.114286 0.079365 0.095238 0.106061 0 0 0
2 0.866667 0.228571 0.142857 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
Total 0.866667 0.914286 0.914286 0.920635 0.919048 0.918182 0.919192 0.920280 0.920080

 

Five Pooper Balls

The following pay table shows the win with five Pooper Balls, according to the number of picks the player makes, from 2 to 10, and the number of matching balls drawn.

 

 

Pay Table for Five Pooper Balls

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
10                 838
9               350 100
8             520 72 40
7           320 60 25 10
6         220 30 8 12 5
5       132 18 8 3 3 1
4     65 11 3 2 2 1 0
3   36 4 3 2 1 0 0 0
2 19 3 2 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0

 

The following pay table shows the probability of winning with five Pooper Balls, according to the number of picks the player makes, from 2 to 10, and number of catches.

 

 

Probabilities of Winning for Five Pooper BallsExpand

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
10                 0.000333
9               0.0005 0.001665
8             0.000777 0.002498 0.004995
7           0.001263 0.003885 0.007493 0.011655
6         0.002165 0.006313 0.011655 0.017483 0.02331
5       0.003968 0.010823 0.018939 0.027195 0.034965 0.041958
4     0.007937 0.019841 0.032468 0.044192 0.05439 0.062937 0.06993
3   0.017857 0.039683 0.059524 0.075758 0.088384 0.097902 0.104895 0.10989
2 0.047619 0.089286 0.119048 0.138889 0.151515 0.159091 0.16317 0.164835 0.164835
1 0.238095 0.267857 0.277778 0.277778 0.272727 0.265152 0.25641 0.247253 0.238095
0 0.714286 0.625 0.555556 0.5 0.454545 0.416667 0.384615 0.357143 0.333333
Total 1 1 1 1 1 1 1 1 1

 

The following pay table shows the expected return with five Pooper Balls, according to the number of picks the player makes, from 2 to 10, and number of catches. The bottom row shows the overall return according to number of picks. The greatest return is for the pick 7 at 92.17%.

 

 

Probabilities of Winning for Five Pooper BallsExpand

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
10 0 0 0 0 0 0 0 0 0.279054
9 0 0 0 0 0 0 0 0.174825 0.1665
8 0 0 0 0 0 0 0.40404 0.17982 0.1998
7 0 0 0 0 0 0.40404 0.2331 0.187313 0.11655
6 0 0 0 0 0.47619 0.189394 0.09324 0.20979 0.11655
5 0 0 0 0.523810 0.194805 0.151515 0.081585 0.104895 0.041958
4 0 0 0.515873 0.218254 0.097403 0.088384 0.10878 0.062937 0
3 0 0.642857 0.15873 0.178571 0.151515 0.088384 0 0 0
2 0.904762 0.267857 0.238095 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
Total 0.904762 0.910714 0.912698 0.920635 0.919913 0.921717 0.920746 0.919580 0.920413

 

Six Pooper Balls

The following pay table shows the win with six Pooper Balls, according to the number of picks the player makes, from 2 to 10, and the number of matching balls drawn.

 

 

Pay Table for Six Pooper Balls

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
10                 1850
9               1000 160
8             1320 100 80
7           800 100 48 20
6         478 55 20 20 10
5       290 20 10 3 5 2
4     100 12 4 2 2 1 0
3   47 5 3 3 1 0 0 0
2 26 5 3 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0

 

The following pay table shows the probability of winning with six Pooper Balls, according to the number of picks the player makes, from 2 to 10, and number of catches.

 

 

Probabilities of Winning for Six Pooper BallsExpand

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
10                 0.000125
9               0.000200 0.000749
8             0.000333 0.001199 0.002622
7           0.000583 0.001998 0.004196 0.006993
6         0.001082 0.003497 0.006993 0.011189 0.015734
5       0.002165 0.006494 0.012238 0.018648 0.025175 0.031469
4     0.004762 0.012987 0.022727 0.032634 0.041958 0.05035 0.057692
3   0.011905 0.028571 0.045455 0.060606 0.073427 0.083916 0.092308 0.098901
2 0.035714 0.071429 0.1 0.121212 0.136364 0.146853 0.153846 0.158242 0.160714
1 0.214286 0.250000 0.266667 0.272727 0.272727 0.269231 0.263736 0.257143 0.250000
0 0.750000 0.666667 0.600000 0.545455 0.500000 0.461538 0.428571 0.400000 0.375000
Total 1 1 1 1 1 1 1 1 1

 

The following pay table shows the expected return with six Pooper Balls, according to the number of picks the player makes, from 2 to 10, and number of catches. The bottom row shows the overall return according to number of picks. The greatest return is for the pick 2 at 92.86%.

 

 

Probabilities of Winning for Six Pooper BallsExpand

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
10 0 0 0 0 0 0 0 0 0.231019
9 0 0 0 0 0 0 0 0.1998 0.11988
8 0 0 0 0 0 0 0.43956 0.11988 0.20979
7 0 0 0 0 0 0.466200 0.199800 0.201399 0.139860
6 0 0 0 0 0.517316 0.192308 0.13986 0.223776 0.157343
5 0 0 0 0.627706 0.129870 0.122378 0.055944 0.125874 0.0629370
4 0 0 0.47619 0.155844 0.090909 0.065268 0.083916 0.050350 0
3 0 0.559524 0.142857 0.136364 0.181818 0.073427 0 0 0
2 0.928571 0.357143 0.3 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
Total 0.928571 0.916667 0.919048 0.919913 0.919913 0.91958 0.919081 0.921079 0.920829

 

Seven Pooper Balls

The following pay table shows the win with seven Pooper Balls, according to the number of picks the player makes, from 2 to 10, and the number of matching balls drawn.

 

 

Pay Table for Seven Pooper Balls

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
10                 3650
9               2300 300
8             2125 300 150
7           1750 250 75 30
6         928 100 40 30 15
5       554 25 12 6 5 5
4     136 13 5 2 2 1 0
3   54 8 3 4 1 0 0 0
2 33 8 4 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0

 

The following pay table shows the probability of winning with seven Pooper Balls, according to the number of picks the player makes, from 2 to 10, and number of catches.

 

 

Probabilities of Winning for Seven Pooper BallsExpand

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
10                 0.000051
9               0.000087 0.00036
8             0.000155 0.000612 0.00144
7           0.000291 0.001088 0.002448 0.004319
6         0.000583 0.00204 0.004351 0.007343 0.010798
5       0.001263 0.004079 0.008159 0.013054 0.018357 0.023756
4     0.00303 0.008838 0.016317 0.024476 0.032634 0.040385 0.047511
3   0.008333 0.021212 0.035354 0.048951 0.061189 0.071795 0.080769 0.088235
2 0.027778 0.058333 0.084848 0.106061 0.122378 0.134615 0.143590 0.15 0.154412
1 0.194444 0.233333 0.254545 0.265152 0.269231 0.269231 0.266667 0.2625 0.257353
0 0.777778 0.7 0.636364 0.583333 0.538462 0.5 0.466667 0.437500 0.411765
Total 1 1 1 1 1 1 1 1 1

 

The following pay table shows the expected return with seven Pooper Balls, according to the number of picks the player makes, from 2 to 10, and number of catches. The bottom row shows the overall return according to number of picks. The greatest return is for the pick 10 at 92.19%.

 

 

Probabilities of Winning for Seven Pooper BallsExpand

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
10 0 0 0 0 0 0 0 0 0.18768
9 0 0 0 0 0 0 0 0.201049 0.10798
8 0 0 0 0 0 0 0.330225 0.183566 0.215961
7 0 0 0 0 0 0.509907 0.27195 0.183566 0.129576
6 0 0 0 0 0.540793 0.203963 0.174048 0.22028 0.16197
5 0 0 0 0.699495 0.101981 0.097902 0.078322 0.091783 0.118778
4 0 0 0.412121 0.114899 0.081585 0.048951 0.065268 0.040385 0
3 0 0.45 0.169697 0.106061 0.195804 0.061189 0 0 0
2 0.916667 0.466667 0.339394 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
Total 0.916667 0.916667 0.921212 0.920455 0.920163 0.921911 0.919814 0.920629 0.921946

 

Strategy

Based on the Red Rock pay table, the highest return is 92.86% on the pick 2 game with 6 Pooper Balls. Other pay tables are likely available, in which case, the optimal number of picks and Pooper Balls would likely be different.

Written by: Michael Shackleford