# Book of Keno

## Introduction

Book of Keno is a keno variant by Evoplay Entertainment, a software company that makes games for Internet casinos. It works like regular keno, except there are 36 balls instead of 80.

## Rules

The following table shows the pay table for 1 to 10 picks in Book of Keno.

### Pay Table

Catch Pick 1 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 0
1 3.46 1.5 1 0.5 0 0 0 0 0 0
2   4.78 2.3 1.8 1.1 0.5 0.2 0 0 0
3     7.6 4.1 3.8 2.9 2.3 1.4 1 1
4       21 14 7.3 4.2 3 2.1 1.5
5         35 18 10 10 6.2 3.2
6           55 31 28 17 10
7             60 40 25 25
8               70 55 40
9                 85 75
10                   100

## Analysis

The following table shows the number of winning combinations for all possible number of catches for 1 to 10 picks in Book of Keno.

### Combinations Table

Catch Pick 1 Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 26 325 2,600 14,950 65,780 230,230 657,800 1,562,275 3,124,550 5,311,735
1 10 260 3,250 26,000 149,500 657,800 2,302,300 6,578,000 15,622,750 31,245,500
2   45 1,170 14,625 117,000 672,750 2,960,100 10,360,350 29,601,000 70,302,375
3     120 3,120 39,000 312,000 1,794,000 7,893,600 27,627,600 78,936,000
4       210 5,460 68,250 546,000 3,139,500 13,813,800 48,348,300
5         252 6,552 81,900 655,200 3,767,400 16,576,560
6           210 5,460 68,250 546,000 3,139,500
7             120 3,120 39,000 312,000
8               45 1,170 14,625
9                 10 260
10                   1
Total 36 630 7,140 58,905 376,992 1,947,792 8,347,680 30,260,340 94,143,280 254,186,856

The following table shows the probability for all possible number of catches for 1 to 10 picks in Book of Keno.

### Probability Table

Catch Pick 1 Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0.722222 0.515873 0.364146 0.253798 0.174486 0.118201 0.078800 0.051628 0.033189 0.020897
1 0.277778 0.412698 0.455182 0.441389 0.396560 0.337716 0.275801 0.217380 0.165947 0.122923
2   0.071429 0.163866 0.248281 0.310351 0.345391 0.354602 0.342374 0.314425 0.276578
3     0.016807 0.052967 0.103450 0.160181 0.214910 0.260856 0.293463 0.310543
4       0.003565 0.014483 0.035040 0.065407 0.103750 0.146732 0.190208
5         0.000668 0.003364 0.009811 0.021652 0.040018 0.065214
6           0.000108 0.000654 0.002255 0.005800 0.012351
7             0.000014 0.000103 0.000414 0.001227
8               0.000001 0.000012 0.000058
9                 0.000000 0.000001
10                   0.000000
Total 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000

The following table shows the return table for 1 to 10 picks in Book of Keno. The bottom row shows the total return for all possible number of picks.

### Return Table

Catch Pick 1 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 0.000000
1 0.961111 0.619048 0.455182 0.220694 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
2   0.341429 0.376891 0.446906 0.341387 0.172696 0.070920 0.000000 0.000000 0.000000
3     0.127731 0.217163 0.393112 0.464526 0.494293 0.365199 0.293463 0.310543
4       0.074866 0.202763 0.255790 0.274711 0.311249 0.308136 0.285312
5         0.023396 0.060549 0.098111 0.216521 0.248110 0.208685
6           0.005930 0.020276 0.063152 0.098594 0.123512
7             0.000863 0.004124 0.010357 0.030686
8               0.000104 0.000684 0.002301
9                 0.000009 0.000077
10                   0.000000
Total 0.961111 0.960476 0.959804 0.959630 0.960657 0.959490 0.959174 0.960349 0.959353 0.961116

The following table summarizes the expected return for all number of picks. The greatest return is 96.11% for both the pick 1 and pick 10.

Pick Return
1 96.11%
2 96.05%
3 95.98%
4 95.96%
5 96.07%
6 95.95%
7 95.92%
8 96.03%
9 95.94%
10 96.11%

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