Last Updated: August 16, 2019

## Introduction

Crossroads Keno is a game found on multi-game machines made by U1 Gaming. I have seen such machines at the Las Vegas Club, Rampart and Dotty's casinos in Las Vegas. The thrust of Crossroads Keno is the game randomly chooses a "Crossroads" spot unchosen by the player. The player can win extra balls if the crossroads number is drawn. The player can also win according to how many numbers are drawn on the row and column the Crossroads ball is on.

## Rules

1. The player chooses 2 to 10 numbers from a range of 1 to 80.
2. The game will randomly choose a "Crossroads" spot from the remaining, unchosen numbers.
3. The game will choose 20 numbers from the same 1 to 80 range.
4. If the Crossroads spot is hit on the first or 20th ball drawn, then the player will win ten extra balls.
5. If the Crossroads spot is hit on the second to 19th ball drawn, then the player will win three extra balls.
6. The player is paid according to the number of his picks that are caught and the pay table. Below is one example, taken from making a \$2 bet at the Rampart casino.

### Crossroads Keno — Pay Table

Catch Pick
2 3 4 5 6 7 8 9 10
10 15000
9 10000 2150
8 4000 1055 240
7 1270 368 142 40
6 534 82 40 15 7
5 222 45 8 6 3 2
4 61.5 15 5 3 2 1 1
3 28.475 3 2 1 1 0 0 0
2 9.25 1 1 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0

7. The player will also be paid according to the number of balls drawn on the same row as the Crossroads spot, known as the "Victory Row," and the following pay table.

8. ### Victory Row

Catch Pays
10 3,000
9 300
8 30
7 10
6 3
5 1
4 -
3 -
2 -
1 -
0 -

9. The player will also be paid according to the number of balls drawn on the same column as the Crossroads spot, known as the "Rally Column," and the following pay table.

10. ### Rally Column

Catch Pays
8 1,000
7 50
6 7
5 2
4 -
3 -
2 -
1 -
0 -

Finally, there is a mystery bonus game, which adds 0.5% to the return of the game. This page does not address this mystery bonus, since I consider it to be outside the scope of the game.

## Analysis

The following table shows the probability of each number of picks and catches after considering the possibility of extra balls.

Catch Pick
2 3 4 5 6 7 8 9 10
10 0.000001
9 0.000002 0.000018
8 0.000010 0.000073 0.000283
7 0.000047 0.000290 0.001013 0.002622
6 0.000208 0.001127 0.003491 0.008109 0.015685
5 0.000911 0.004217 0.011380 0.023365 0.040408 0.061994
4 0.003909 0.014993 0.034435 0.061380 0.093554 0.127988 0.161652
3 0.016349 0.049759 0.094413 0.142912 0.188716 0.227103 0.255329 0.272383
2 0.066415 0.150199 0.225759 0.281853 0.315595 0.328603 0.324586 0.307899 0.282730
1 0.390587 0.435682 0.430404 0.397078 0.350256 0.299097 0.249087 0.203248 0.163002
0 0.542997 0.397770 0.290169 0.210753 0.152377 0.109649 0.078513 0.055930 0.039630
Total 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000

The following table shows the return from each number of picks and catches, after considering the possibility of extra balls.

Catch Pick
2 3 4 5 6 7 8 9 10
10 0.008171
9 0.023724 0.039294
8 0.041969 0.077098 0.067956
7 0.059379 0.106758 0.143867 0.104885
6 0.110913 0.092384 0.139646 0.121641 0.109794
5 0.202147 0.189775 0.091043 0.140192 0.121224 0.123988
4 0.240408 0.224889 0.172173 0.184140 0.187107 0.127988 0.161652
3 0.465532 0.149277 0.188825 0.142912 0.188716 0.000000 0.000000 0.000000
2 0.614340 0.150199 0.225759 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
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
Total 0.614340 0.615731 0.615444 0.615861 0.615773 0.615662 0.615672 0.615542 0.615740

The following table shows the probability and return for each possible outcome of the Victory Row, after considering the possibility of extra balls.

### Victory Row

Catch Pays Probability Return
10 3,000 0.000002 0.005281
9 300 0.000047 0.013982
8 30 0.000557 0.016707
7 10 0.004001 0.040010
6 3 0.019286 0.057858
5 1 0.065311 0.065311
4 - 0.156539 0.000000
3 - 0.258875 0.000000
2 - 0.277839 0.000000
1 - 0.171754 0.000000
0 - 0.045791 0.000000
Total 1.000000 0.199148

The following table shows the probability and return for each possible outcome of the Rally Column, after considering the possibility of extra balls.

### Rally Column

Catch Pays Probability Return
8 1,000 0.000027 0.026698
7 50 0.000555 0.027750
6 7 0.005109 0.035760
5 2 0.027492 0.054983
4 - 0.095227 0.000000
3 - 0.216736 0.000000
2 - 0.312051 0.000000
1 - 0.254539 0.000000
0 - 0.088266 0.000000
Total 1.000000 0.145192

Pick Keno Victory
Row
Rally
Column
Total
2 0.614340 0.199148 0.145192 0.958680
3 0.615731 0.199148 0.145192 0.960072
4 0.615444 0.199148 0.145192 0.959785
5 0.615861 0.199148 0.145192 0.960202
6 0.615773 0.199148 0.145192 0.960113
7 0.615662 0.199148 0.145192 0.960003
8 0.615672 0.199148 0.145192 0.960013
9 0.615542 0.199148 0.145192 0.959883
10 0.615740 0.199148 0.145192 0.960081

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