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Last Updated: September 25, 2016
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Top Bottom Keno
Introduction
Top Bottom Keno is a keno game in which the player selects either numbers 1 to 40 or 41 to 80. He is paid according to the number of catches in the chosen half.
Rules
- The player shall pick either Top or Bottom. If the player picks Top, then he shall cover numbers 1 to 40. If he picks Bottom, then 41 to 80.
- The game shall draw 20 balls randomly and without replacement from a pool of balls numbered 1 to 80.
- The player shall be paid according to how many balls in the 20-ball draw that fall in the player's chosen half. This is known as the number of catches. An example pay table is below.
The following pay table was seen somewhere on the Las Vegas Strip (I don't remember the exact casino). All pays are on a "for one" basis, meaning the player does not also get back his original bet on a win.
Pay Table
| Catches | Pays |
|---|---|
| 0 or 20 | 12,500 |
| 1 or 19 | 5,000 |
| 2 or 18 | 492 |
| 3 or 17 | 122 |
| 4 or 16 | 28 |
| 5 or 15 | 11 |
| 6 or 14 | 3 |
| 7 or 13 | 2 |
| 12 | 1 |
Analysis
The following table shows the probability and contribution to the return of all possible number of catches from 0 to 20. The lower right cell shows a return of 88.32%.
Analysis
| Catches | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 0 | 12,500 | 137,846,528,820 | 0.00000004 | 0.000487 |
| 1 | 5,000 | 5,251,296,336,000 | 0.00000149 | 0.007427 |
| 2 | 492 | 88,436,604,204,000 | 0.00002502 | 0.012307 |
| 3 | 122 | 876,675,902,544,001 | 0.00024798 | 0.030253 |
| 4 | 28 | 5,744,053,569,793,500 | 0.00162476 | 0.045493 |
| 5 | 11 | 26,468,598,849,608,400 | 0.00748691 | 0.082356 |
| 6 | 3 | 89,077,015,359,259,200 | 0.02519634 | 0.075589 |
| 7 | 2 | 224,342,112,756,653,000 | 0.06345744 | 0.126915 |
| 8 | - | 429,655,207,020,554,000 | 0.12153233 | 0.000000 |
| 9 | - | 632,136,396,535,987,000 | 0.17880619 | 0.000000 |
| 10 | - | 718,528,370,729,238,000 | 0.20324303 | 0.000000 |
| 11 | - | 632,136,396,535,987,000 | 0.17880619 | 0.000000 |
| 12 | 1 | 429,655,207,020,554,000 | 0.12153233 | 0.121532 |
| 13 | 2 | 224,342,112,756,653,000 | 0.06345744 | 0.126915 |
| 14 | 3 | 89,077,015,359,259,200 | 0.02519634 | 0.075589 |
| 15 | 11 | 26,468,598,849,608,400 | 0.00748691 | 0.082356 |
| 16 | 28 | 5,744,053,569,793,500 | 0.00162476 | 0.045493 |
| 17 | 122 | 876,675,902,544,001 | 0.00024798 | 0.030253 |
| 18 | 492 | 88,436,604,204,000 | 0.00002502 | 0.012307 |
| 19 | 5,000 | 5,251,296,336,000 | 0.00000149 | 0.007427 |
| 20 | 12,500 | 137,846,528,820 | 0.00000004 | 0.000487 |
| Total | 3,535,316,142,212,170,000 | 1.00000000 | 0.883189 |
Written by: Michael Shackleford
