Keno Exacta

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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.

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%.

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