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Triple Power Keno

Introduction



Triple Power Keno is a unique variation of keno that I discovered on a multi-game machine at the Red Rock casino on January 26, 2012. It operates similarly to traditional keno; however, if the last ball drawn happens to match one of the player's selections, they receive three additional balls and all winnings are multiplied by three.

Return Tables

Below are several pay tables along with their potential returns for different groups of pay tables I have encountered.

Pay Table 1 offers a maximum payout of 88.75% for selecting 2 numbers.

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 provides a maximum payout of 90.77% for a selection of 2 numbers.

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 potential of 91.33% when selecting 7 numbers.

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 yields a maximum return of 92.50% for a selection of 5 numbers.

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 boasts a maximum return of 94.56% for picking 5 numbers.

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

Here’s a sample pay table that I observed at the Red Rock casino.

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 subsequent table outlines the probabilities of hitting a certain number of balls, under the assumption that the player DID NOT catch the last ball.

Probabilities for catching 20 balls when the 20th ball was not hit.Expand

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 following table illustrates the probability of each possible combination of picks and catches, given that the player DID catch the 20th ball.

Probabilities for catching 20 balls when the 20th ball was successfully hit.Expand

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 showcases how each combination of picks and catches contributes to the return, presuming 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 subsequent table demonstrates the contribution to return for all possible combinations of picks and catches, assuming the 20th ball was indeed 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 provides an overview of the overall return for all picks and catches, regardless of whether 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