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Last Updated: Sep. 26, 2016

Power Keno


Introduction



The rules in Power Keno are the same as regular keno, except if the player catches the 20th ball drawn, then any winnings are quadrupled. There is also a similar game called Fire Power, which is the same except in that game wins are quadrupled if the first ball is a catch, not the last one.

Rules



  1. The player chooses 2 to 10 numbers from 1 to 80.
  2. The game will randomly choose 20 numbers from the same range of 1 to 80.
  3. The player is paid to number of his picks that match the numbers drawn by the game.
  4. If the first number drawn is a match then any win will be quadrupled.

Pay Tables



Following are some common pay tables for Power Keno. The returns are shown in the bottom row.

Pay Table 1

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 - - - - - - - - -
1 - - - - - - - - -
2 12 3 1 1 - - - - -
3 20 6 2 2 1 1 - -
4 59 12 8 5 2 2 1
5 100 30 10 7 6 4
6 150 75 25 14 10
7 200 80 50 25
8 500 200 120
9 1,000 500
10 1,000
Return 93.80% 94.35% 94.19% 94.00% 94.10% 93.68% 94.00% 93.63% 93.96%

Pay Table 2

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 - - - - - - - - -
1 1 - - - - - - - -
2 6 2 1 1 - - - - -
3 27 7 2 2 1 1 - -
4 40 12 8 4 2 2 1
5 75 24 12 6 5 4
6 160 90 24 15 8
7 200 100 60 25
8 533 200 150
9 1,000 500
10 1,000
Return 90.57% 90.40% 91.14% 91.18% 91.10% 90.44% 91.03% 90.22% 90.49%

Pay Table 3

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 - - - - - - - - -
1 - - - - - - - - -
2 11 2 1 - - - - - -
3 26 5 2 1 1 - - -
4 61 20 5 2 2 1 1
5 230 65 14 7 4 2
6 500 140 41 20 7
7 1,250 600 150 45
8 2,500 1,000 500
9 3,750 1,750
10 5,000
Return 85.98% 88.39% 88.90% 88.99% 89.12% 88.97% 89.06% 88.81% 89.25%

Pay Table 4

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 - - - - - - - - -
1 - - - - - - - - -
2 11 2 1 1 - - - - -
3 26 5 2 2 1 1 - -
4 60 11 7 4 2 2 1
5 75 30 12 6 5 4
6 125 75 17 14 8
7 200 120 55 24
8 500 200 100
9 1,000 500
10 1,000
Return 85.98% 88.39% 88.41% 89.25% 88.93% 88.35% 88.51% 88.53% 88.67%

Analysis

The next table shows the probability of each number of picks and catches for Pay Table 3 above.

Power Keno — ProbabilitiesExpand

Catch Pick
2 3 4 5 6 7 8 9 10
0 0.56012658 0.41650438 0.30832143 0.22718421 0.16660175 0.12157425 0.08826624 0.06374784 0.0457907
1 0.37974684 0.4308666 0.43273183 0.40568609 0.36349473 0.31519251 0.26646411 0.22066559 0.17957138
2 0.06012658 0.13875365 0.21263547 0.27045739 0.30832143 0.32665405 0.32814562 0.31642614 0.29525678
3 0 0.01387537 0.04324789 0.08393505 0.12981955 0.17499324 0.21478623 0.24610922 0.26740237
4 0 0 0.00306339 0.01209234 0.02853792 0.05219097 0.0815037 0.11410518 0.1473189
5 0 0 0 0.00064492 0.00309564 0.0086385 0.01830259 0.03260148 0.05142769
6 0 0 0 0 0.00012898 0.00073208 0.00236671 0.00571956 0.01147939
7 0 0 0 0 0 0.0000244 0.00016046 0.00059168 0.00161114
8 0 0 0 0 0 0 0.00000435 0.00003259 0.00013542
9 0 0 0 0 0 0 0 0.00000072 0.00000612
10 0 0 0 0 0 0 0 0 0.00000011
Total 1 1 1 1 1 1 1 1 1

The next table shows the return of each number of picks and catches. The bottom row is the total return of the game. The body of the table is the payoff*probability*(1+3*(catches/20)). The bottom row shows the total return. For example, the lower right cell shows a return of 89.25% for the pick-10 game.

Power Keno — ReturnsExpand

Catch Pick
2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
2 0.85981013 0.36075949 0.27642611 0 0 0 0 0 0
3 0 0.52310127 0.31354721 0.24341165 0.18823834 0.2537402 0 0 0
4 0 0 0.29898709 0.38695482 0.22830334 0.16701109 0.26081184 0.18256829 0.23571024
5 0 0 0 0.25958219 0.35212888 0.21164337 0.22420667 0.22821036 0.17999691
6 0 0 0 0 0.12253569 0.1947324 0.18436699 0.2173432 0.15267595
7 0 0 0 0 0 0.06253155 0.19735985 0.18194111 0.14862795
8 0 0 0 0 0 0 0.02390113 0.0717034 0.14896129
9 0 0 0 0 0 0 0 0.00638269 0.02517117
10 0 0 0 0 0 0 0 0 0.00140265
Total 0.85981013 0.88386076 0.88896041 0.88994866 0.89120626 0.88965861 0.8906465 0.88814906 0.89254615

The bottom row shows the overall return is about 89%, with the best return on the pick-10 at 89.25%.

Calculator



Calculate the odds for any pay table with my Power Keno calculator.

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