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.

Rules

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.
At the time of purchase, the player may bet an extra 25¢ to qualify for extra wins for an Exacta.
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 Probabilities
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 Returns
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%.

Internal Links

Keno main page
Keno appendix 1. An analysis of the top/bottom/left/right as as well as edge tickets as played at the Las Vegas Hilton.
Keno appendix 2. An analysis of Caveman Keno as played on IGT's Game King.
Keno appendix 3. Probabilities and returns for basic keno at the Atlantic CityTropicana.
Keno appendix 4. Progressive keno games at the Boyd and Station casinos.
Keno appendix 5. Nevada numbers, a progressive lottery game at some of the NevadaPark Place casinos.
Keno appendix 6. Power Keno.
Keno appendix 7 Super Keno.
Keno appendix 8. Top Bottom Keno.
Keno appendix 9. High/Low/Middle Keno: Keno game seen at the Lisboa in Macau.
Keno appendix 10. Extra Draw Keno.
Keno appendix 11Jumbo Keno Progressive game at the Station Casinos.
Keno appendix 12. Triple Trouble Keno.
Keno appendix 13. Fremont "Super Eight."
Keno appendix 14. Laughlin keno survey.
Keno props Miscellaneous keno bets.
Probabilities in Keno . A lesson in how to calculate keno probabilities.
Cleopatra Keno
Triple Power Keno
Jackpot Party Keno
Keno Calculator
Caveman Keno Plus

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