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# 246 Way Keno

## Introduction

246 Way Keno is a way of playing spot keno with seven different cards at the same time. The player picks three pick-2 cards, all with different picks. The game automatically combines all three ways to combine two of the three cards and plays them as three pick-4 cards, plus one pick-6 game consisting of the numbers picked on the original three cards.

## Rules

- The player picks six numbers from 1 to 80.
- The first two numbers chosen shall form a pick-2 keno card labeled "A."
- The second two numbers chosen shall form a pick-2 keno card labeled "B."
- The final two numbers chosen shall form a pick-2 keno card labeled "C."
- The combined numbers in cards A and B shall form a pick-4 keno card "A+B."
- The combined numbers in cards A and B shall form a pick-4 keno card "A+B."
- The combined numbers in cards B and C shall form a pick-4 keno card "B+C."
- The combined numbers in all three cards shall form a pick-6 keno card "A+B+C."
- The game shall draw 20 numbers from 1 to 80, without replacement.
- The game shall score and pay the player according to the seven cards played and the posted pay table.

## Pay Table 1 Analysis

The following table shows what each number of catches pays for pick 2, 4, and 6 keno under what I call pay table 1.

### Pay Table 1

Catch | Pick 2 | Pick 4 | Pick 6 |
---|---|---|---|

0 | 1 | 1 | 1 |

1 | 0 | 0 | 0 |

2 | 5 | 1 | 0 |

3 | 5 | 2 | |

4 | 40 | 5 | |

5 | 49 | ||

6 | 1,000 |

The following table shows all possible outcomes of 246 keno under pay table 1. The first three columns show the number of catches for cards A, B, and C, respectively. The probability column shows the probability of that combination of catches. The return column is the product of the probability, win, and 1/7. The reason for dividing by 7 is to reflect the return compared to the seven units bet among the seven cards. The lower right cell shows an overall return of 0.858725.

### Pay Table 1 Return

Card A | Card B | Card C | Pays | Probability | Return |
---|---|---|---|---|---|

0 | 0 | 0 | 7 | 0.166602 | 0.166602 |

0 | 0 | 1 | 3 | 0.121165 | 0.051928 |

0 | 0 | 2 | 10 | 0.020555 | 0.029364 |

0 | 1 | 0 | 3 | 0.121165 | 0.051928 |

0 | 1 | 1 | 2 | 0.082219 | 0.023491 |

0 | 1 | 2 | 14 | 0.012982 | 0.025964 |

0 | 2 | 0 | 10 | 0.020555 | 0.029364 |

0 | 2 | 1 | 14 | 0.012982 | 0.025964 |

0 | 2 | 2 | 58 | 0.001903 | 0.015764 |

1 | 0 | 0 | 3 | 0.121165 | 0.051928 |

1 | 0 | 1 | 2 | 0.082219 | 0.023491 |

1 | 0 | 2 | 14 | 0.012982 | 0.025964 |

1 | 1 | 0 | 2 | 0.082219 | 0.023491 |

1 | 1 | 1 | 5 | 0.051928 | 0.037091 |

1 | 1 | 2 | 21 | 0.007610 | 0.022830 |

1 | 2 | 0 | 14 | 0.012982 | 0.025964 |

1 | 2 | 1 | 21 | 0.007610 | 0.022830 |

1 | 2 | 2 | 109 | 0.001032 | 0.016068 |

2 | 0 | 0 | 10 | 0.020555 | 0.029364 |

2 | 0 | 1 | 14 | 0.012982 | 0.025964 |

2 | 0 | 2 | 58 | 0.001903 | 0.015764 |

2 | 1 | 0 | 14 | 0.012982 | 0.025964 |

2 | 1 | 1 | 21 | 0.007610 | 0.022830 |

2 | 1 | 2 | 109 | 0.001032 | 0.016068 |

2 | 2 | 0 | 58 | 0.001903 | 0.015764 |

2 | 2 | 1 | 109 | 0.001032 | 0.016068 |

2 | 2 | 2 | 1135 | 0.000129 | 0.020914 |

Total | 1.000000 | 0.858725 |

The next table summarizes the return table above by combining all the different ways to win the same amount.

### Pay Table 1 Return Summary

Win | Probability | Return |
---|---|---|

1135 | 0.000129 | 0.020914 |

109 | 0.003096 | 0.048204 |

58 | 0.005708 | 0.047291 |

21 | 0.022830 | 0.068491 |

14 | 0.077892 | 0.155783 |

10 | 0.061664 | 0.088092 |

7 | 0.166602 | 0.166602 |

5 | 0.051928 | 0.037091 |

3 | 0.363495 | 0.155783 |

2 | 0.246657 | 0.070473 |

Total | 1.000000 | 0.858725 |

The total variance of all seven cards at one unit bet each is 231.23. The standard deviation over all seven units bet is 15.21. The standard deviation based on the total amount bet as one unit is 2.17.

## Pay Table 2 Analysis

The following table shows what each number of catches pays for pick 2, 4, and 6 keno under what I call pay table 2.

### Pay Table 2

Catch | Pick 2 | Pick 4 | Pick 6 |
---|---|---|---|

0 | 0 | 0 | 0 |

1 | 0 | 0 | 0 |

2 | 14 | 2 | 0 |

3 | 3 | 2 | |

4 | 100 | 4 | |

5 | 92 | ||

6 | 1,500 |

The next table shows the probability and contribution to the return for all possible total wins. The return shows the return relative to a seven-unit bet.

### Pay Table 2 Return Summary

Win | Probability | Return |
---|---|---|

1135 | 0.000129 | 0.020914 |

109 | 0.003096 | 0.048204 |

58 | 0.005708 | 0.047291 |

21 | 0.022830 | 0.068491 |

14 | 0.077892 | 0.155783 |

10 | 0.061664 | 0.088092 |

7 | 0.166602 | 0.166602 |

5 | 0.051928 | 0.037091 |

3 | 0.363495 | 0.155783 |

2 | 0.246657 | 0.070473 |

Total | 1.000000 | 0.858725 |

The total variance of all seven cards at one unit bet each is 739.86. The standard deviation over all seven units bet is 27.20. The standard deviation based on the total amount bet as one unit is 3.89.

## Pay Table 3 Analysis

The following table shows what each number of catches pays for pick 2, 4, and 6 keno under what I call pay table 3.

### Pay Table 3

Catch | Pick 2 | Pick 4 | Pick 6 |
---|---|---|---|

0 | 0 | 0 | 0 |

1 | 0 | 0 | 0 |

2 | 15 | 2 | 0 |

3 | 5 | 3 | |

4 | 77 | 4 | |

5 | 55 | ||

6 | 1,600 |

The next table shows the probability and contribution to the return for all possible total wins. The return shows the return relative to a seven-unit bet.

### Pay Table 3 Return Summary

Win | Probability | Return |
---|---|---|

1876 | 0.000129 | 0.034568 |

172 | 0.003096 | 0.076064 |

115 | 0.005708 | 0.093767 |

31 | 0.022830 | 0.101106 |

25 | 0.077892 | 0.278185 |

19 | 0.061664 | 0.167374 |

9 | 0.051928 | 0.066764 |

2 | 0.246657 | 0.070473 |

0 | 0.530096 | 0.000000 |

Total | 1.000000 | 0.888302 |

The total variance of all seven cards at one unit bet each is 680.42. The standard deviation over all seven units bet is 26.08. The standard deviation based on the total amount bet as one unit is 3.73.

## Pay Table 4 Analysis

The following table shows what each number of catches pays for pick 2, 4, and 6 keno under what I call pay table 4.

### Pay Table 4

Catch | Pick 2 | Pick 4 | Pick 6 |
---|---|---|---|

0 | 0 | 0 | 0 |

1 | 0 | 0 | 0 |

2 | 14 | 2 | 0 |

3 | 5 | 3 | |

4 | 85 | 4 | |

5 | 68 | ||

6 | 1,500 |

The next table shows the probability and contribution to the return for all possible total wins. The return shows the return relative to a seven-unit bet.

### Pay Table 4 Return Summary

Win | Probability | Return |
---|---|---|

1797 | 0.000129 | 0.033112 |

191 | 0.003096 | 0.084467 |

121 | 0.005708 | 0.098660 |

30 | 0.022830 | 0.097844 |

24 | 0.077892 | 0.267057 |

18 | 0.061664 | 0.158565 |

9 | 0.051928 | 0.066764 |

2 | 0.246657 | 0.070473 |

0 | 0.530096 | 0.000000 |

Total | 1.000000 | 0.876943 |

The total variance of all seven cards at one unit bet each is 665.92. The standard deviation over all seven units bet is 25.81. The standard deviation based on the total amount bet as one unit is 3.69.

## Pay Table 5 Analysis

The following table shows what each number of catches pays for pick 2, 4, and 6 keno under what I call pay table 5.

### Pay Table 5

Catch | Pick 2 | Pick 4 | Pick 6 |
---|---|---|---|

0 | 0 | 0 | 0 |

1 | 0 | 0 | 0 |

2 | 15 | 2 | 0 |

3 | 5 | 3 | |

4 | 91 | 4 | |

5 | 70 | ||

6 | 1,600 |

### Pay Table 5 Return Summary

Win | Probability | Return |
---|---|---|

1918 | 0.000129 | 0.035342 |

201 | 0.003096 | 0.088889 |

129 | 0.005708 | 0.105183 |

31 | 0.022830 | 0.101106 |

25 | 0.077892 | 0.278185 |

19 | 0.061664 | 0.167374 |

9 | 0.051928 | 0.066764 |

2 | 0.246657 | 0.070473 |

0 | 0.530096 | 0.000000 |

Total | 1.000000 | 0.913316 |

The total variance of all seven cards at one unit bet each is 751.75. The standard deviation over all seven units bet is 27.42. The standard deviation based on the total amount bet as one unit is 3.92.

## Pay Table 6 Analysis

The following table shows what each number of catches pays for pick 2, 4, and 6 keno under what I call pay table 6.

### Pay Table 6

Catch | Pick 2 | Pick 4 | Pick 6 |
---|---|---|---|

0 | 0 | 0 | 1 |

1 | 0 | 0 | 0 |

2 | 15 | 1 | 0 |

3 | 12 | 1 | |

4 | 64 | 14 | |

5 | 62 | ||

6 | 300 |

### Pay Table 6 Return Summary

Win | Probability | Return |
---|---|---|

537 | 0.000129 | 0.009895 |

180 | 0.003096 | 0.079602 |

110 | 0.005708 | 0.089691 |

54 | 0.022830 | 0.176120 |

29 | 0.077892 | 0.322694 |

17 | 0.061664 | 0.149756 |

4 | 0.051928 | 0.029673 |

1 | 0.413259 | 0.059037 |

0 | 0.363495 | 0.000000 |

Total | 1.000000 | 0.916468 |

The total variance of all seven cards at one unit bet each is 316.55. The standard deviation over all seven units bet is 17.79. The standard deviation based on the total amount bet as one unit is 6.72.

## Pay Table 7 Analysis

The following table shows what each number of catches pays for pick 2, 4, and 6 keno under what I call pay table 7.

### Pay Table 7

Catch | Pick 2 | Pick 4 | Pick 6 |
---|---|---|---|

0 | 0 | 0 | 0 |

1 | 0 | 0 | 0 |

2 | 15 | 2 | 0 |

3 | 5 | 3 | |

4 | 100 | 4 | |

5 | 75 | ||

6 | 1,660 |

### Pay Table 7 Return Summary

Win | Probability | Return |
---|---|---|

2005 | 0.000129 | 0.036945 |

215 | 0.003096 | 0.095080 |

138 | 0.005708 | 0.112521 |

31 | 0.022830 | 0.101106 |

25 | 0.077892 | 0.278185 |

19 | 0.061664 | 0.167374 |

9 | 0.051928 | 0.066764 |

2 | 0.246657 | 0.070473 |

0 | 0.530096 | 0.000000 |

Total | 1.000000 | 0.928449 |

The total variance of all seven cards at one unit bet each is 826.15. The standard deviation over all seven units bet is 28.74. The standard deviation based on the total amount bet as one unit is 4.11.

## Pay Table 8 Analysis

The following table shows what each number of catches pays for pick 2, 4, and 6 keno under what I call pay table 8.

### Pay Table 8

Catch | Pick 2 | Pick 4 | Pick 6 |
---|---|---|---|

0 | 0 | 0 | 0 |

1 | 1 | 0 | 0 |

2 | 10 | 2 | 0 |

3 | 6 | 3 | |

4 | 74 | 4 | |

5 | 58 | ||

6 | 1,700 |

### Pay Table 8 Return Summary

Win | Probability | Return |
---|---|---|

1952 | 0.000129 | 0.035968 |

165 | 0.003096 | 0.072969 |

102 | 0.005708 | 0.083168 |

30 | 0.022830 | 0.097844 |

22 | 0.077892 | 0.244803 |

14 | 0.061664 | 0.123329 |

12 | 0.051928 | 0.089019 |

4 | 0.246657 | 0.140947 |

1 | 0.363495 | 0.051928 |

0 | 0.166602 | 0.000000 |

Total | 1.000000 | 0.939974 |

The total variance of all seven cards at one unit bet each is 717.25. The standard deviation over all seven units bet is 26.78. The standard deviation based on the total amount bet as one unit is 3.83.

## Internal Links

Please also see my page on 369 Way Keno.