Last Updated: June 2, 2013

Power Keno

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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.

Following is an example pay table I observed somewhere. This is what the player wins if he doesn't catch the 20th ball.

Power Keno — Pay Table

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 11 2 1 0 0 0 0 0 0
3 0 26 5 2 1 1 0 0 0
4 0 0 61 20 5 2 2 1 1
5 0 0 0 230 65 14 7 4 2
6 0 0 0 0 500 140 41 20 7
7 0 0 0 0 0 1250 600 150 45
8 0 0 0 0 0 0 2500 1000 500
9 0 0 0 0 0 0 0 3750 1750
10 0 0 0 0 0 0 0 0 5000

Odds

The next table shows the probability of each number of picks and catches.

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%.

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