Last Updated: November 1, 2019

# Keno Props

## Introduction

Following are some miscellaneous keno probabilities. You may find them useful to challenge your friends to some keno props the next time you're in a restaurant with a keno board. First, let me define some terms.

• Row: A straight line going side to side, for example the numbers 21 to 30.
• Column: A straight line going up and down, for example that covering the numbers 3, 13, 23, 33, 43, 53, 63, and 73.
• Density: The probability that the total marks will be a specified number exactly.
• Distribution: The probability that the total marks will be a specified number or less.

### Maximum Number of Marks in a Row

Marks Density Distribution
3 0.04527897 0.04527897
4 0.48940972 0.53468869
5 0.36052029 0.89520898
6 0.09077479 0.98598377
7 0.01288264 0.99886641
8 0.00108385 0.99995027
9 0.0000488 0.99999907
10 0.00000093 1

### Maximum Number of Marks in a Column

Marks Density Distribution
2 0.00008424 0.00008424
3 0.24679217 0.24687642
4 0.55201679 0.79889321
5 0.17583628 0.97472949
6 0.02362016 0.99834965
7 0.00160675 0.9999564
8 0.0000436 1

### Total Empty Rows

Marks Density Distribution
0 0.66614523 0.66614523
1 0.30214711 0.96829234
2 0.03096811 0.99926045
3 0.00073693 0.99999739
4 0.00000261 1
5 0 1
6 0 1
7 0 1
8 0 1

### Total Empty Columns

Marks Density Distribution
0 0.34140772 0.34140772
1 0.45924256 0.80065028
2 0.17561107 0.97626135
3 0.02278398 0.99904534
4 0.00094499 0.99999033
5 0.00000966 0.99999999
6 0.00000001 1
7 0 1
8 0 1
9 0 1
10 0 1

### Maximum Marks in Top or Bottom

Marks Density Distribution
10 0.20324741 0.20324741
11 0.35762212 0.56086953
12 0.24306014 0.80392966
13 0.12690566 0.93083532
14 0.05038823 0.98122356
15 0.01497834 0.9962019
16 0.00325002 0.99945191
17 0.00049553 0.99994744
18 0.0000496 0.99999704
19 0.00000287 0.99999992
20 0.00000008 1

The next table is for the maximum number of marks that can be contained in any three rows, columns, or any combination of rows and columns. For example the image below shows the most marks in any three columns is 13. There are various ways this could be done, just one of which is circled.

Image courtesy of the
See why we recommend Bodog.

### Maximum Marks in Three Rows and/or Columns

Marks Density Distribution
0 0 0
1 0 0
2 0 0
3 0 0
4 0 0
5 0 0
6 0 0
7 0 0
8 0 0
9 0.01002066 0.01002066
10 0.12038178 0.13040245
11 0.33280855 0.46321099
12 0.33627509 0.79948608
13 0.1542072 0.95369328
14 0.03941847 0.99311175
15 0.00619848 0.99931023
16 0.00064619 0.99995642
17 0.00004259 0.99999902
18 0.00000098 1
19 0 1
20 0 1

Next are some even money bets to challenge your friends with. The side listed is the good side. The house edge is how much that side can expect to lose.

### Even Money Keno Props

Prop Probability
of a Win
House
Edge
No row will have 5 or more hits 53.47% 6.94%
Greatest number of hits in a column will be exactly 4 55.2% 10.4%
Every row to have at least one mark 66.61% 33.23%
Number of empty columns will not be 1 54.08% 8.15%
Top/bottom to have 9 to 11 marks 56.09% 12.17%
3 lines (rows and/or columns) will contain 12 or more marks 53.68% 7.36%

Methodology: The tables above were created by random simulation of at least 500 million games.

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