# Keno Exacta

## Introduction

Keno Exacta is a keno game I noticed at the Orleans on April 20, 2012. It pays if two consecutive keno games have the same number of catches, and are withing a specified range of catches. For example, if the player purchased two consecutive eight-spot games, and caught five numbers on both of them, then the 25¢ Exacta bet would be \$490.

Eleven years later, in 2023, I found the game at the Swinomish casino in Washington. There the Exacta was an optional side bet with different pay tables from those at the Orleans. I address the Swinomish pay tables later in this page.

## Rules

1. To bet the Exacta the player must first bet two games for \$1 each. These two games will pay according to the standard Orleans pay table.
2. At the time of purchase, the player may bet an extra 25¢ to qualify for extra wins for an Exacta.
3. If both games have the same number of catches, above a certain number, then the Exacta bet will win.

The following is the base game pay table.

### Base Pay Table

Catch Pick 1 Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0 0 0 0 0 0 0 0 0 0
1 3 0 0 0 0 0 0 0 0 0
2   12 1 1 0 0 0 0 0 0
3     45 2 1 1 0 0 0 0
4       160 15 4 1 0 0 0
5         750 80 15 5 6 1
6           2000 400 75 30 25
7             10000 1500 300 125
8               50000 5000 1000
9                 50000 10000
10                   100000

The following is the Exacta pay table.

### Exacta Pay Table

Catch Pick 1 Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0 0 0 0 0 0 0 0 0 0
1 4 0 0 0 0 0 0 0 0 0
2   66 3 1 0 0 0 0 0 0
3     910 56 8 3 2 0 0 0
4       9680 1170 117 18 5 3 2
5         48500 9840 1470 490 113 25
6           246000 49200 7350 1940 500
7             480000 97000 49400 25000
8               900000 490000 250000
9                 900000 1000000
10                   1000000

## Base Game Odds

The following are the probabilities of winning for the base game.

### Base Pay ProbabilitiesExpand

match Pick 1 Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0.750000000 0.560126582 0.416504382 0.308321425 0.227184208 0.166601753 0.121574252 0.088266238 0.063747838 0.045790701
1 0.250000000 0.379746835 0.430866602 0.432731825 0.405686086 0.363494733 0.315192505 0.266464114 0.220665594 0.179571376
2 0.000000000 0.060126582 0.138753651 0.212635466 0.270457391 0.308321425 0.326654051 0.328145622 0.316426135 0.295256781
3 0.000000000 0.000000000 0.013875365 0.043247891 0.083935052 0.129819548 0.174993241 0.214786225 0.246109216 0.267402368
4 0.000000000 0.000000000 0.000000000 0.003063392 0.012092338 0.028537918 0.052190967 0.081503701 0.114105182 0.147318897
5 0.000000000 0.000000000 0.000000000 0.000000000 0.000644925 0.003095639 0.008638505 0.018302586 0.032601481 0.051427688
6 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000128985 0.000732077 0.002366714 0.005719558 0.011479395
7 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000024403 0.000160455 0.000591678 0.001611143
8 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000004346 0.000032592 0.000135419
9 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000724 0.000006121
10 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000112
Total 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000

The next table shows the return for each win. The bottom row shows the total return by number of picks.

### Base Pay ReturnsExpand

match Pick 1 Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 0.750000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
2 0.000000 0.721519 0.138754 0.212635 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
3 0.000000 0.000000 0.624391 0.086496 0.083935 0.129820 0.000000 0.000000 0.000000 0.000000
4 0.000000 0.000000 0.000000 0.490143 0.181385 0.114152 0.052191 0.000000 0.000000 0.000000
5 0.000000 0.000000 0.000000 0.000000 0.483694 0.247651 0.129578 0.091513 0.195609 0.051428
6 0.000000 0.000000 0.000000 0.000000 0.000000 0.257970 0.292831 0.177504 0.171587 0.286985
7 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.244026 0.240683 0.177504 0.201393
8 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.217283 0.162962 0.135419
9 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.036214 0.061206
10 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.011221
Return 0.750000 0.721519 0.763145 0.789274 0.749014 0.749592 0.718625 0.726982 0.743875 0.747652

## Exacta Odds

The following two tables are the probabilities for the Exacta game, which are simply the square of the odds in the base game.

### Exacta Probabilities — Pick 1 to 6

Catch Pick 1 Pick 2 Pick 3 Pick 4 Pick 5 Pick 6
0 0.562500 0.313742 0.173476 0.09506210 0.051612664 0.0277561440
1 0.062500 0.144208 0.185646 0.18725683 0.164581200 0.1321284210
2 0.000000 0.003615 0.019253 0.04521384 0.073147200 0.0950621014
3 0.000000 0.000000 0.000193 0.00187038 0.007045093 0.0168531149
4 0.000000 0.000000 0.000000 0.00000938 0.000146225 0.0008144128
5 0.000000 0.000000 0.000000 0.00000000 0.000000416 0.0000095830
6 0.000000 0.000000 0.000000 0.00000000 0.000000000 0.0000000166
Total 0.625000 0.461565 0.378567 0.32941254 0.296532799 0.2726237937

### Exacta Probabilities — Pick 7 to 10

Catch Pick 7 Pick 8 Pick 9 Pick 10
0 0.014780298738 0.0077909287212 0.004063786894725 0.0020967882787503
1 0.099346315250 0.0710031239815 0.048693304507802 0.0322458789504079
2 0.106702868842 0.1076795490491 0.100125499051997 0.0871765667889125
3 0.030622634553 0.0461331225017 0.060569746340097 0.0715040263017637
4 0.002723897010 0.0066428533577 0.013019992581041 0.0217028574343981
5 0.000074623766 0.0003349846396 0.001062856537228 0.0026448070626831
6 0.000000535936 0.0000056013335 0.000032713343713 0.0001317764998547
7 0.000000000595 0.0000000257459 0.000000350083345 0.0000025957820839
8 0.000000000000 0.0000000000189 0.000000001062268 0.0000000183384018
9 0.000000000000 0.0000000000000 0.000000000000525 0.0000000000374623
10 0.000000000000 0.0000000000000 0.000000000000000 0.0000000000000126
Total 0.254251174690 0.2395901893490 0.227568250402741 0.2175053154747310

The following two tables are the returns for the Exacta game.

### Exacta Returns — Pick 1 to 6

match Pick 1 Pick 2 Pick 3 Pick 4 Pick 5 Pick 6
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 0.250000 0.000000 0.000000 0.000000 0.000000 0.000000
2 0.000000 0.238604 0.057758 0.045214 0.000000 0.000000
3 0.000000 0.000000 0.175198 0.104741 0.056361 0.050559
4 0.000000 0.000000 0.000000 0.090841 0.171083 0.095286
5 0.000000 0.000000 0.000000 0.000000 0.020173 0.094297
6 0.000000 0.000000 0.000000 0.000000 0.000000 0.004093
Return 1.000000 0.954414 0.931825 0.963183 0.990464 0.976939

### Exacta Returns — Pick 7 to 10

Catch Pick 7 Pick 8 Pick 9 Pick 10
0 0.0000000000 0.0000000000 0.0000000000 0.0000000000
1 0.0000000000 0.0000000000 0.0000000000 0.0000000000
2 0.0000000000 0.0000000000 0.0000000000 0.0000000000
3 0.0612452691 0.0000000000 0.0000000000 0.0000000000
4 0.0490301462 0.0332142668 0.0390599777 0.0434057149
5 0.1096969359 0.1641424734 0.1201027887 0.0661201766
6 0.0263680644 0.0411698014 0.0634638868 0.0658882499
7 0.0002858327 0.0024973484 0.0172941173 0.0648945521
8 0.0000000000 0.0000169963 0.0005205114 0.0045846004
9 0.0000000000 0.0000000000 0.0000004721 0.0000374623
10 0.0000000000 0.0000000000 0.0000000000 0.0000000126
Return 0.9865049927 0.9641635450 0.9617670160 0.9797230754

The probability of hitting the \$1,000,000 jackpot on the pick 9 Exacta are 1 in 1,906,298,378,741. Nevada Gaming Control Board regulation 2.070 bears quoting at this moment. "2.070 Jackpot Odds. If the odds of hitting any advertised jackpot that is offered by a gaming device exceeds 100 million to one, the odds of the advertised jackpot must be prominently displayed on the award glass or video display."

However, I don't think this regulation applies, because this is not based on an electronic game.

## Combined Odds

The following table shows the expected return of the base game and Exacta according to the number of picks. The weighted return is a weighted average of 8 parts base game and 1 part Exacta.

### Exacta Summary

Number Base Game
Return
Exacta
Return
Weighted
Return
1 75.00% 100.00% 77.78%
2 72.15% 95.44% 74.74%
3 76.31% 93.18% 78.19%
4 78.93% 96.32% 80.86%
5 74.90% 99.05% 77.58%
6 74.96% 97.69% 77.49%
7 71.86% 98.65% 74.84%
8 72.70% 96.42% 75.33%
9 74.39% 96.18% 76.81%
10 74.77% 97.97% 77.34%

## Strategy

If the player is going to play a pick 1 to 10 game at the \$1 rate at the Orleans anyway, he should also bet the Exacta, which returns between 93% and 100% of the Exacta wager, which is good for live keno. Considering both bets combined, the best bet is on the pick 4, with a weighted return of 80.86%.

## Swinomish Rules

In July 2023 I noticed this game at the Swinomish casino near Anacortes, Washington. As at the Orleans, the bet on base game is \$1 and on the Exacta side bet is \$0.25. They used the following base pay table.

### Swinomish Base Pay Table

Catch Pick 1 Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8
0 0 0 0 0 0 0 0 0
1 3 0 0 0 0 0 0 0
2   12.5 1 1 0 0 0 0
3     45 4 1 1 0 0
4       124 12 5 1 0
5         824 95 22 10
6           1500 420 100
7             8300 1550
8               20000

The following is the pay table for the Exacta side bet. The side bet is always \$0.25 and the pays are listed in dollars.

### Swinomish Exacta Pay Table

Catch Pick 1 Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8
0 0 0 0 0 0 0 0 0
1 4 0 0 0 0 0 0 0
2   70 3 1 0 0 0 0
3     1016 84 12 3 2 0
4       5012 1122 152 28 5
5         10000 8216 1450 512
6           12000 11100 7500
7             14000 14500
8               10000

The following table shows the return for both the base game, Exacta side bet, and the combined return. The combined return is a weighted average of \$2 bet on the base game (two games of \$1) and one \$0.25 bet on the Exacta. Yes, this does show the Exacta bet often has a player advantage. Unfortunately, making the base game is mandated.

### Swinomish Return Table

Pick Base Game Exacta Combined
1 0.750000 1.000000 0.777778
2 0.751582 1.012258 0.780546
3 0.763145 1.013456 0.790957
4 0.765488 0.997441 0.791260
5 0.760461 1.011058 0.788305
6 0.760072 1.013134 0.788190
7 0.752251 1.006704 0.780524
8 0.755316 0.988440 0.781219