Triple Power Keno
Introduction
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 |
Written by:
Michael Shackleford