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Last Updated: June 14, 2023

# Mega Keno

## Introduction

Mega Keno is a progressive keno game found at the Plaza in downtown Las Vegas.

## Rules

1. Tickets cost \$1.50.
2. The player picks 5 to 10 numbers from a range of 1 to 80.
3. The game shall pick 20 numbers from the same range.
4. If enough of the player's picks match the 20 numbers chosen by the casino, the player will win.
5. Matching all the player's picks awards a progressive jackpot.
6. The pay table is shown below.
7. The pick-10 jackpot is paid as an 11-payment annuity, with one annual payment, with the first payment immediately and the final one in 10 years.

### Mega Keno Pay Table

Catch Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0 0 0 0 0 0
1 0 0 0 0 0 0
2 0 0 0 0 0 0
3 1 1 0 0 0 0
4 11.5 4 1.25 0 0 0
5 Jackpot 100 22 10 4 1.5
6   Jackpot 430 100 55 10
7     Jackpot 2000 425 100
8       Jackpot 7000 1000
9         Jackpot 7500
10           Jackpot

## Analysis

The next table shows the number of combinations for all possible combinations of picks and catches.

### Keno Combinations

Catch Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 5,461,512 50,063,860 386,206,920 2,558,620,845 14,783,142,660 75,394,027,566
1 9,752,700 109,230,240 1,001,277,200 7,724,138,400 51,172,416,900 295,662,853,200
2 6,501,800 92,650,650 1,037,687,280 9,512,133,400 73,379,314,800 486,137,960,550
3 2,017,800 39,010,800 555,903,900 6,226,123,680 57,072,800,400 440,275,888,800
4 290,700 8,575,650 165,795,900 2,362,591,575 26,461,025,640 242,559,401,700
5 15,504 930,240 27,442,080 530,546,880 7,560,293,040 84,675,282,048
6   38,760 2,325,600 68,605,200 1,326,367,200 18,900,732,600
7     77,520 4,651,200 137,210,400 2,652,734,400
8       125,970 7,558,200 222,966,900
9         167,960 10,077,600
10           184,756

The next table shows the probability for all possible combinations of picks and catches.

### Keno Probabilities

Catch Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0.2271842 0.1666018 0.1215743 0.0882662 0.0637478 0.0457907
1 0.4056861 0.3634947 0.3151925 0.2664641 0.2206656 0.1795714
2 0.2704574 0.3083214 0.3266541 0.3281456 0.3164261 0.2952568
3 0.0839351 0.1298195 0.1749932 0.2147862 0.2461092 0.2674024
4 0.0120923 0.0285379 0.0521910 0.0815037 0.1141052 0.1473189
5 0.0006449 0.0030956 0.0086385 0.0183026 0.0326015 0.0514277
6   0.0001290 0.0007321 0.0023667 0.0057196 0.0114794
7     0.0000244 0.0001605 0.0005917 0.0016111
8       0.0000043 0.0000326 0.0001354
9         0.0000007 0.0000061
10           0.0000001
Total 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000

The next table shows the contribution towards the return for all possible combinations of picks and catches, relative to a \$1.50 bet. In other words, the return is the product of the win and probability and then divided by the bet amount.

### Mega Keno Return

Catch Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
2 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
3 0.0559567 0.0865464 0.0000000 0.0000000 0.0000000 0.0000000
4 0.0927079 0.0761011 0.0434925 0.0000000 0.0000000 0.0000000
5 0.0000000 0.2063759 0.1266981 0.1220172 0.0869373 0.0514277
6   0.0000000 0.2098620 0.1577809 0.2097171 0.0765293
7     0.0000000 0.2139402 0.1676422 0.1074095
8       0.0000000 0.1520981 0.0902796
9         0.0000000 0.0306032
10           0.0000000
Total 0.1486646 0.3690234 0.3800525 0.4937384 0.6163947 0.3562493

The final table below shows the fixed return, jackpot probability, return per \$1,000 in the jackpot and breakeven jackpot for all picks from 5 to 10. The 10-year breakeven jackpot does not consider the time value of money lost in the annuity.

### Mega Keno Summary

Pick Fixed
Return
Jackpot
Probability
Jackpot
Return
Breakeven
Jackpot
5 0.1486646 0.0006449 0.4299498 \$1,980.08
6 0.3690234 0.0001290 0.0859900 \$8,768.28
7 0.3800525 0.0000244 0.0162684 \$38,107.53
8 0.4937384 0.0000043 0.0028971 \$231,555.50
9 0.6163947 0.0000007 0.0004829 \$1,219,982.86
10 0.3562493 0.0000001 0.0000748 \$10,192,775.55

Here are the jackpot amounts when last I checked on June 13, 2023.

• Pick 5: \$1,344.17
• Pick 6: \$4,256.84
• Pick 7: \$15,446.78
• Pick 8: \$61,231.37
• Pick 9: \$152,675.30
• Pick 10: \$3,958,460.20

Here is an example return calculation on the pick 5. The value of the fixed wins is 0.148665. The value of the jackpot is (\$1,344.17/\$1,000) × 0.4299498 = 0.577926. This makes the total return 0.148665 + 0.577926 = 0.726590.