# Super Pays Keno

## Introduction

Super Pays Keno is a simple variant of Four Card Keno. Bets must be evenly divisible by five coins. 80% of the total bet is divided equally between the four cards. The other 20% is a fee, which pays for boosting the top pays above what conventional keno usually pays.

I am aware of two pay tables, which I label Pay Tables 1 and 2 below.

### Pay Table 1

Catch 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
1 0 0 0 0 0 0 0 0
2 2 2 0 0 0 0 0 0
3 61 5 3 3 1 0 0 0
4   160 11 4 2 2 1 0
5     1150 77 20 12 6 5
6       3000 460 98 45 23
7         14000 2650 420 175
8           20000 9400 2000
9             20000 9000
10               20000
Return 89.91% 90.53% 90.12% 90.31% 90.44% 90.14% 90.92% 90.50%
Std Dev 7.17 8.92 29.23 34.35 70.29 53.76 57.32 33.74

The following table shows Pay Table 2

### Pay Table 2

Catch 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
1 0 0 0 0 0 0 0 0
2 2 2 0 0 0 0 0 0
3 65 5 3 3 1 0 0 0
4   180 13 5 2 2 1 0
5     1210 75 22 13 6 5
6       3320 520 105 46 25
7         14000 2850 500 200
8           20000 9400 2000
9             20000 9000
10               20000
Return 94.35% 95.43% 95.15% 95.40% 95.34% 95.49% 95.16% 95.56%
Std. Dev. 7.63 10.01 30.76 37.95 70.60 55.41 57.71 33.98

## Analysis

The following table shows the probability of all possible combinations of picks and catches to six decimal places for keno as well as Super Pays Keno.

### Keno Probabilities

Catch Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0.416504 0.308321 0.227184 0.166602 0.121574 0.088266 0.063748 0.045791
1 0.430867 0.432732 0.405686 0.363495 0.315193 0.266464 0.220666 0.179571
2 0.138754 0.212635 0.270457 0.308321 0.326654 0.328146 0.316426 0.295257
3 0.013875 0.043248 0.083935 0.129820 0.174993 0.214786 0.246109 0.267402
4   0.003063 0.012092 0.028538 0.052191 0.081504 0.114105 0.147319
5     0.000645 0.003096 0.008639 0.018303 0.032601 0.051428
6       0.000129 0.000732 0.002367 0.005720 0.011479
7         0.000024 0.000160 0.000592 0.001611
8           0.000004 0.000033 0.000135
9             0.000001 0.000006
10               0.000000

The following table shows the contribution to the return for pay table 1. Each cell is the product of the probability, win, and 4/5. The reason for multiplying by 4/5 is 1/5 of the total bet is a fee for the enhanced pay table.

### Pay Table 1 Analysis

Catch 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
1 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
2 0.222006 0.340217 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
3 0.677118 0.172992 0.201444 0.311567 0.139995 0.000000 0.000000 0.000000
4   0.392114 0.106413 0.091321 0.083506 0.130406 0.091284 0.000000
5     0.593331 0.190691 0.138216 0.175705 0.156487 0.205711
6       0.309564 0.269404 0.185550 0.205904 0.211221
7         0.273309 0.340165 0.198804 0.225560
8           0.069531 0.245095 0.216671
9             0.011588 0.044069
10               0.001795
Total 0.899124 0.905323 0.901187 0.903143 0.904429 0.901357 0.909163 0.905027

The following table shows the contribution to the return for pay table 2. Each cell is the product of the probability, win, and 4/5. The reason for multiplying by 4/5 is 1/5 of the total bet is a fee for the enhanced pay table.

### Pay Table 2 Analysis

Catch 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
1 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
2 0.222006 0.340217 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
3 0.721519 0.172992 0.201444 0.311567 0.139995 0.000000 0.000000 0.000000
4   0.441128 0.125760 0.114152 0.083506 0.130406 0.091284 0.000000
5     0.624287 0.185738 0.152038 0.190347 0.156487 0.205711
6       0.342584 0.304544 0.198804 0.210480 0.229588
7         0.273309 0.365838 0.236671 0.257783
8           0.069531 0.245095 0.216671
9             0.011588 0.044069
10               0.001795
Total 0.943525 0.954337 0.951492 0.954041 0.953390 0.954925 0.951606 0.955617