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Last Updated: Dec. 5, 2016

Triple Power Keno


Introduction



Triple Power Keno is a keno variation I noticed on a multi-game machine at the Red Rock casino on January 26, 2012. It plays like conventional keno, except if the last ball is one of the player's picks, then the player gets three extra balls and any win is tripled.

Return Tables



Following are various pay tables and their associated returns for various sets of pay tables I have seen.

Pay Table 1 has a maximum return of 88.75% for a pick 2.

Pay Table 1Expand

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 1 0 0 0 0 0 0 0 0
2 6 2 1 1 0 0 0 0 0
3 27 6 2 2 1 1 0 0
4 48 10 6 4 2 2 1
5 85 31 11 6 5 4
6 125 54 12 10 6
7 200 90 32 16
8 500 150 50
9 1000 400
10 1000
Return 86.49% 88.75% 88.62% 88.34% 88.50% 88.62% 88.55% 88.62% 88.40%


Pay Table 2 has a maximum return of 90.77% for a pick 2.

Pay Table 2Expand

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 1 0 0 0 0 0 0 0 0
2 6 2 1 1 0 0 0 0 0
3 28 6 2 2 1 1 0 0
4 51 10 6 4 2 2 1
5 100 33 12 5 3 3
6 150 55 20 13 7
7 200 100 80 25
8 500 200 120
9 1000 500
10 1000
Return 86.49% 90.77% 90.24% 90.44% 90.68% 90.56% 90.31% 90.41% 90.59%


Pay Table 3 has a maximum return of 91.33% for a pick 7.

Pay Table 3Expand

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 1 0 0 0 0 0 0 0 0
2 6 2 1 1 0 0 0 0 0
3 28 7 2 2 1 1 0 0
4 40 12 8 4 2 2 1
5 75 19 12 6 5 4
6 150 59 16 10 7
7 200 95 42 14
8 500 200 72
9 1000 350
10 1000
Return 86.49% 90.77% 90.50% 91.07% 91.08% 91.33% 91.22% 91.27% 91.18%


Pay Table 4 has a maximum return of 92.50% for a pick 5.

Pay Table 4Expand

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 1 0 0 0 0 0 0 0 0
2 6 2 1 1 0 0 0 0 0
3 28 6 2 2 1 1 0 0
4 55 11 7 4 2 2 1
5 100 28 12 5 5 4
6 150 65 24 10 7
7 200 95 50 15
8 500 175 90
9 1000 250
10 1000
Return 86.49% 90.77% 92.38% 92.50% 92.18% 92.49% 92.44% 92.45% 92.35%


Pay Table 5 has a maximum return of 94.56% for a pick 5.

Pay Table 5Expand

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 1 0 0 0 0 0 0 0 0
2 6 3 1 1 0 0 0 0 0
3 21 6 2 2 1 1 0 0
4 58 12 8 5 2 2 1
5 100 24 8 5 5 3
6 150 65 27 12 9
7 250 92 45 27
8 500 180 80
9 1000 400
10 1000
Return 86.49% 93.68% 94.00% 94.56% 94.32% 94.35% 94.08% 94.35% 94.32%


Analysis



Following is an example pay table seen at the Red Rock.

Example Pay Table

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 1 0 0 0 0 0 0 0 0
2 6 2 1 1 0 0 0 0 0
3 27 6 2 2 1 1 0 0
4 48 10 6 4 2 2 1
5 85 31 11 6 5 4
6 125 54 12 10 6
7 200 90 32 16
8 500 150 50
9 1000 400
10 1000

The next table shows the probabilities for catching any given number of balls, assuming that the player did NOT catch the last ball.

20-Ball Probabilities if the 20th Ball Was Not CaughtExpand

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 0.360759 0.409323 0.411095 0.385402 0.345320 0.299433 0.253141 0.209632 0.170593
2 0.054114 0.124878 0.191372 0.243412 0.277489 0.293989 0.295331 0.284784 0.265731
3 0.011794 0.036761 0.071345 0.110347 0.148744 0.182568 0.209193 0.227292
4 0.002451 0.009674 0.022830 0.041753 0.065203 0.091284 0.117855
5 0.000484 0.002322 0.006479 0.013727 0.024451 0.038571
6 0.000090 0.000512 0.001657 0.004004 0.008036
7 0.000016 0.000104 0.000385 0.001047
8 0.000003 0.000020 0.000081
9 0.000000 0.000003
10 0.000000
Total 0.975000 0.962500 0.950000 0.937500 0.925000 0.912500 0.900000 0.887500 0.875000


The next table shows the probability of each combination of picks and catches assuming the player DID catch the 20th ball.

20-Ball Probabilities if the 20th Ball Was CaughtExpand

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 0.018038 0.019426 0.018500 0.016431 0.013934 0.011423 0.009121 0.007126 0.005464
2 0.006962 0.015263 0.022201 0.026777 0.028919 0.028997 0.027541 0.025082 0.022079
3 0.002812 0.008325 0.015336 0.022493 0.028724 0.033367 0.036147 0.037093
4 0.000974 0.003651 0.008179 0.014185 0.020985 0.027806 0.033941
5 0.000304 0.001388 0.003675 0.007384 0.012460 0.018602
6 0.000088 0.000473 0.001450 0.003323 0.006318
7 0.000023 0.000147 0.000514 0.001326
8 0.000006 0.000042 0.000165
9 0.000001 0.000011
10 0.000000
Total 0.025000 0.037500 0.050000 0.062500 0.075000 0.087500 0.100000 0.112500 0.125000


The next table shows the contribution to the return for all combinations of picks and catches, assuming the 20th ball was not caught.

Return if the 20th Ball Was Not CaughtExpand

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 0.360759 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
2 0.324684 0.374635 0.191372 0.243412 0.000000 0.000000 0.000000 0.000000 0.000000
3 0.247675 0.220564 0.142690 0.220693 0.148744 0.182568 0.000000 0.000000
4 0.142141 0.116086 0.182643 0.208764 0.130406 0.182568 0.117855
5 0.048369 0.055721 0.051831 0.068635 0.122256 0.115712
6 0.013543 0.033309 0.044731 0.048044 0.072320
7 0.003965 0.009595 0.017307 0.028276
8 0.001304 0.003520 0.006500
9 0.000398 0.001347
10 0.000056
Total 0.685443 0.622310 0.554078 0.550557 0.472601 0.446614 0.437239 0.374093 0.342066


The next table shows the contribution to the return for all combinations of picks and catches, assuming the 20th ball was caught.

Return Table if 20th Ball Was CaughtExpand

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 0.054114 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
2 0.125316 0.137366 0.066602 0.080331 0.000000 0.000000 0.000000 0.000000 0.000000
3 0.177130 0.149854 0.092016 0.134956 0.086171 0.100100 0.000000 0.000000
4 0.169426 0.131451 0.196300 0.212769 0.125912 0.166834 0.101824
5 0.091285 0.099903 0.088202 0.110756 0.186901 0.167421
6 0.039435 0.092140 0.117442 0.119617 0.170580
7 0.017616 0.040494 0.069323 0.107402
8 0.008825 0.022636 0.039675
9 0.004137 0.013284
10 0.000906
Total 0.179430 0.314496 0.385881 0.395083 0.470594 0.496898 0.503530 0.569449 0.601094


The final analysis table shows the combined return for all picks and catches, whether or not the 20th ball was caught.

Combined ReturnExpand

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 0.414873 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
2 0.450000 0.512001 0.257974 0.323743 0.000000 0.000000 0.000000 0.000000 0.000000
3 0.424805 0.370418 0.234705 0.355649 0.234916 0.282669 0.000000 0.000000
4 0.311567 0.247537 0.378943 0.421533 0.256318 0.349402 0.219679
5 0.139655 0.155624 0.140033 0.179391 0.309157 0.283134
6 0.052979 0.125449 0.162173 0.167661 0.242901
7 0.021581 0.050089 0.086630 0.135678
8 0.010129 0.026156 0.046175
9 0.004535 0.014631
10 0.000962
Total 0.864873 0.936806 0.939959 0.945640 0.943195 0.943512 0.940769 0.943542 0.943160