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Mad Yeti Keno

Introduction

The rules in Mad Yeti Keno are the same as regular keno, except if the player catches the 20th ball drawn, then any winnings are multiplied by 8. In other words, it is the same as Power Keno, except wins are multiplied by 8 instead of 4, if the last ball drawn is a catch.

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 multiplied by 8.
 

Pay Table

 

Following is the pay table followed by DraftKings.

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 0 0 0 0 0 0 0 0 0
2 9 1 1 0 0 0 0 0 0
3   24 3 2 1 1 0 0 0
4     40 16 6 2 2 1 1
5       63 22 6 6 3 2
6         140 60 18 14 4
7           380 150 40 14
8             700 360 100
9               1000 440
10                 1600
Return 91.99% 91.85% 92.15% 92.02% 92.03% 91.99% 91.99% 92.03% 92.00%

The maximum return is for a pick 4 at 92.15%.

Example

Mad Yeti Keno

In the image above, I bet $1 and picked 10 numbers (1 to 5 and 11 to 15). In the first 19 balls I caught 2, ,5, 12, and 15. Then the 20th ball was an 11, for a total of five catches. Normally, five catches pays 2 for 1. However, the last ball was a catch, so my win was 2×8 = 16 for 1, or $16 times my $1 bet.

Analysis

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

Mad Yeti Keno — ProbabilitiesExpand

Catch Pick
2 3 4 5 6 7 8 9 10
0 0.560127 0.416504 0.308321 0.227184 0.166602 0.121574 0.0882662 0.06374784 0.04579070
1 0.379747 0.430867 0.432732 0.405686 0.363495 0.315193 0.2664641 0.22066559 0.17957138
2 0.060127 0.138754 0.212635 0.270457 0.308321 0.326654 0.3281456 0.31642614 0.29525678
3   0.013875 0.043248 0.083935 0.129820 0.174993 0.2147862 0.24610922 0.26740237
4     0.003063 0.012092 0.028538 0.052191 0.0815037 0.11410518 0.14731890
5       0.000645 0.003096 0.008639 0.0183026 0.03260148 0.05142769
6         0.000129 0.000732 0.0023667 0.00571956 0.01147939
7           0.000024 0.0001605 0.00059168 0.00161114
8             0.0000043 0.00003259 0.00013542
9               0.00000072 0.00000612
10                 0.00000011
Total 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.0000000 1.00000000 1.00000000

The probability the last ball is a catch is c/20, where c is the number of catches.

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+7*(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 — ReturnExpand

Catch Pick
2 3 4 5 6 7 8 9 10
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
2 0.919937 0.235881 0.361480 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
3   0.682668 0.265975 0.344134 0.266130 0.358736 0.000000 0.000000 0.000000
4     0.294086 0.464346 0.410946 0.250517 0.391218 0.273852 0.353565
5       0.111733 0.187286 0.142535 0.301993 0.268962 0.282852
6         0.055979 0.136166 0.132063 0.248229 0.142344
7           0.031992 0.083036 0.081652 0.077818
8             0.011559 0.044586 0.051459
9               0.003006 0.011176
10                 0.000808
Total 0.919937 0.918549 0.921540 0.920213 0.920342 0.919946 0.919868 0.920287 0.920024

The bottom row shows the average return is 92.01%, with the best return on the pick-4 at 92.15%.

Written by: Michael Shackleford