Keno Odds
Introduction
Following are 15 tables, according to the number of numbers chosen, and the probability of matching any given number, the payoff table at the Atlantic City
Tropicana, the contribution toward the expected return, and the total expected return for all possible matches. Following the tables is an explanation of how the probabilities were calculated.
Pick 1
Catch |
Pays |
Combinations |
Probability |
Return |
0 |
0 |
20 |
0.250000 |
0.000000 |
1 |
3 |
60 |
0.750000 |
2.250000 |
Total |
0 |
80 |
1.000000 |
2.250000 |
Pick 2
Catch |
Pays |
Combinations |
Probability |
Return |
0 |
0 |
1770 |
0.560127 |
0.000000 |
1 |
0 |
1200 |
0.379747 |
0.000000 |
2 |
12 |
190 |
0.060127 |
0.721519 |
Total |
0 |
3160 |
1.000000 |
0.721519 |
Pick 3
Catch |
Pays |
Combinations |
Probability |
Return |
0 |
0 |
34220 |
0.416504 |
0.000000 |
1 |
0 |
35400 |
0.430867 |
0.000000 |
2 |
1 |
11400 |
0.138754 |
0.138754 |
3 |
43 |
1140 |
0.013875 |
0.596641 |
Total |
0 |
82160 |
1.000000 |
0.735394 |
Pick 4
Catch |
Pays |
Combinations |
Probability |
Return |
0 |
0 |
487635 |
0.308321 |
0.000000 |
1 |
0 |
684400 |
0.432732 |
0.000000 |
2 |
1 |
336300 |
0.212635 |
0.212635 |
3 |
3 |
68400 |
0.043248 |
0.129744 |
4 |
130 |
4845 |
0.003063 |
0.398241 |
Total |
0 |
1581580 |
1.000000 |
0.740620 |
Pick 5
Catch |
Pays |
Combinations |
Probability |
Return |
0 |
0 |
5461512 |
0.227184 |
0.000000 |
1 |
0 |
9752700 |
0.405686 |
0.000000 |
2 |
0 |
6501800 |
0.270457 |
0.000000 |
3 |
1 |
2017800 |
0.083935 |
0.083935 |
4 |
10 |
290700 |
0.012092 |
0.120923 |
5 |
800 |
15504 |
0.000645 |
0.515940 |
Total |
0 |
24040016 |
1.000000 |
0.720798 |
Pick 6
Catch |
Pays |
Combinations |
Probability |
Return |
0 |
0 |
50063860 |
0.166602 |
0.000000 |
1 |
0 |
109230240 |
0.363495 |
0.000000 |
2 |
0 |
92650650 |
0.308321 |
0.000000 |
3 |
1 |
39010800 |
0.129820 |
0.129820 |
4 |
4 |
8575650 |
0.028538 |
0.114152 |
5 |
95 |
930240 |
0.003096 |
0.294086 |
6 |
1500 |
38760 |
0.000129 |
0.193477 |
Total |
0 |
300500200 |
1.000000 |
0.731534 |
Pick 7
Catch |
Pays |
Combinations |
Probability |
Return |
0 |
0 |
386206920 |
0.121574 |
0.000000 |
1 |
0 |
1001277200 |
0.315193 |
0.000000 |
2 |
0 |
1037687280 |
0.326654 |
0.000000 |
3 |
0 |
555903900 |
0.174993 |
0.000000 |
4 |
1 |
165795900 |
0.052191 |
0.052191 |
5 |
25 |
27442080 |
0.008639 |
0.215963 |
6 |
350 |
2325600 |
0.000732 |
0.256227 |
7 |
8000 |
77520 |
0.000024 |
0.195220 |
Total |
0 |
3176716400 |
1.000000 |
0.719601 |
Pick 8
Catch |
Pays |
Combinations |
Probability |
Return |
0 |
0 |
2558620845 |
0.088266 |
0.000000 |
1 |
0 |
7724138400 |
0.266464 |
0.000000 |
2 |
0 |
9512133400 |
0.328146 |
0.000000 |
3 |
0 |
6226123680 |
0.214786 |
0.000000 |
4 |
0 |
2362591575 |
0.081504 |
0.000000 |
5 |
9 |
530546880 |
0.018303 |
0.164723 |
6 |
90 |
68605200 |
0.002367 |
0.213004 |
7 |
1500 |
4651200 |
0.000160 |
0.240683 |
8 |
25000 |
125970 |
0.000004 |
0.108642 |
Total |
0 |
28987537150 |
1.000000 |
0.727052 |
Pick 9
Catch |
Pays |
Combinations |
Probability |
Return |
0 |
0 |
14,783,142,660 |
0.063748 |
0.000000 |
1 |
0 |
51,172,416,900 |
0.220666 |
0.000000 |
2 |
0 |
73,379,314,800 |
0.316426 |
0.000000 |
3 |
0 |
57,072,800,400 |
0.246109 |
0.000000 |
4 |
0 |
26,461,025,640 |
0.114105 |
0.000000 |
5 |
4 |
7,560,293,040 |
0.032601 |
0.130406 |
6 |
50 |
1,326,367,200 |
0.005720 |
0.285978 |
7 |
280 |
137,210,400 |
0.000592 |
0.165670 |
8 |
4000 |
7,558,200 |
0.000033 |
0.130370 |
9 |
50000 |
167,960 |
0.000001 |
0.036214 |
Total |
0 |
231,900,297,200 |
1.000000 |
0.748637 |
Pick 10
Catch |
Pays |
Combinations |
Probability |
Return |
0 |
0 |
75,394,027,566 |
0.045791 |
0.000000 |
1 |
0 |
295,662,853,200 |
0.179571 |
0.000000 |
2 |
0 |
486,137,960,550 |
0.295257 |
0.000000 |
3 |
0 |
440,275,888,800 |
0.267402 |
0.000000 |
4 |
0 |
242,559,401,700 |
0.147319 |
0.000000 |
5 |
1 |
84,675,282,048 |
0.051428 |
0.051428 |
6 |
22 |
18,900,732,600 |
0.011479 |
0.252547 |
7 |
150 |
2,652,734,400 |
0.001611 |
0.241671 |
8 |
1000 |
222,966,900 |
0.000135 |
0.135419 |
9 |
5000 |
10,077,600 |
0.000006 |
0.030603 |
10 |
100000 |
184,756 |
0.000000 |
0.011221 |
Total |
0 |
1,646,492,110,120 |
1.000000 |
0.722890 |
Pick 11
Catch |
Pays |
Combinations |
Probability |
Return |
0 |
0 |
342,700,125,300 |
0.032708 |
0.000000 |
1 |
0 |
1,507,880,551,320 |
0.143914 |
0.000000 |
2 |
0 |
2,808,797,105,400 |
0.268074 |
0.000000 |
3 |
0 |
2,916,827,763,300 |
0.278385 |
0.000000 |
4 |
0 |
1,871,172,527,400 |
0.178587 |
0.000000 |
5 |
0 |
776,190,085,440 |
0.074080 |
0.000000 |
6 |
8 |
211,688,205,120 |
0.020204 |
0.161630 |
7 |
80 |
37,801,465,200 |
0.003608 |
0.288625 |
8 |
400 |
4,310,693,400 |
0.000411 |
0.164567 |
9 |
2500 |
297,289,200 |
0.000028 |
0.070934 |
10 |
25000 |
11,085,360 |
0.000001 |
0.026450 |
11 |
100000 |
167,960 |
0.000000 |
0.001603 |
Total |
0 |
10,477,677,064,400 |
1.000000 |
0.713808 |
Pick 12
Catch |
Pays |
Combinations |
Probability |
Return |
0 |
0 |
1,399,358,844,975 |
0.023227 |
0.000000 |
1 |
0 |
6,854,002,506,000 |
0.113766 |
0.000000 |
2 |
0 |
14,324,865,237,540 |
0.237770 |
0.000000 |
3 |
0 |
16,852,782,632,400 |
0.279730 |
0.000000 |
4 |
0 |
12,396,517,994,025 |
0.205763 |
0.000000 |
5 |
0 |
5,987,752,087,680 |
0.099387 |
0.000000 |
6 |
5 |
1,940,475,213,600 |
0.032209 |
0.161044 |
7 |
32 |
423,376,410,240 |
0.007027 |
0.224876 |
8 |
200 |
61,427,380,950 |
0.001020 |
0.203920 |
9 |
1000 |
5,747,591,200 |
0.000095 |
0.095401 |
10 |
5000 |
327,018,120 |
0.000005 |
0.027140 |
11 |
25000 |
10,077,600 |
0.000000 |
0.004182 |
12 |
100000 |
125,970 |
0.000000 |
0.000209 |
Total |
0 |
60,246,643,120,300 |
1.000000 |
0.716772 |
Pick 13
Catch |
Pays |
Combinations |
Probability |
Return |
0 |
1 |
5,166,863,427,600 |
0.016396 |
0.016396 |
1 |
0 |
27,987,176,899,500 |
0.088810 |
0.000000 |
2 |
0 |
65,113,023,807,000 |
0.206619 |
0.000000 |
3 |
0 |
85,949,191,425,240 |
0.272737 |
0.000000 |
4 |
0 |
71,624,326,187,700 |
0.227280 |
0.000000 |
5 |
0 |
39,668,857,580,880 |
0.125878 |
0.000000 |
6 |
1 |
14,969,380,219,200 |
0.047501 |
0.047501 |
7 |
20 |
3,880,950,427,200 |
0.012315 |
0.246303 |
8 |
80 |
687,986,666,640 |
0.002183 |
0.174651 |
9 |
600 |
81,903,174,600 |
0.000260 |
0.155939 |
10 |
3500 |
6,322,350,320 |
0.000020 |
0.070218 |
11 |
10000 |
297,289,200 |
0.000001 |
0.009434 |
12 |
50000 |
7,558,200 |
0.000000 |
0.001199 |
13 |
100000 |
77,520 |
0.000000 |
0.000025 |
Total |
0 |
315,136,287,090,800 |
1.000000 |
0.721665 |
Pick 14
Catch |
Pays |
Combinations |
Probability |
Return |
0 |
1 |
17,345,898,649,800 |
0.011501 |
0.011501 |
1 |
0 |
103,337,268,552,000 |
0.068519 |
0.000000 |
2 |
0 |
265,878,180,545,250 |
0.176294 |
0.000000 |
3 |
0 |
390,678,142,842,000 |
0.259044 |
0.000000 |
4 |
0 |
365,284,063,557,270 |
0.242206 |
0.000000 |
5 |
0 |
229,197,843,800,640 |
0.151973 |
0.000000 |
6 |
1 |
99,172,143,952,200 |
0.065757 |
0.065757 |
7 |
9 |
29,938,760,438,400 |
0.019851 |
0.178662 |
8 |
42 |
6,306,544,444,200 |
0.004182 |
0.175629 |
9 |
310 |
917,315,555,520 |
0.000608 |
0.188554 |
10 |
1100 |
90,093,492,060 |
0.000060 |
0.065711 |
11 |
8000 |
5,747,591,200 |
0.000004 |
0.030488 |
12 |
25000 |
222,966,900 |
0.000000 |
0.003696 |
13 |
50000 |
4,651,200 |
0.000000 |
0.000154 |
14 |
100000 |
38,760 |
0.000000 |
0.000035 |
Total |
0 |
1,508,152,231,077,400 |
1.000000 |
0.720188 |
Pick 15
Catch |
Pays |
Combinations |
Probability |
Return |
0 |
1 |
53,194,089,192,720 |
0.008016 |
0.008016 |
1 |
0 |
346,917,972,996,000 |
0.052279 |
0.000000 |
2 |
0 |
981,704,051,244,000 |
0.147939 |
0.000000 |
3 |
0 |
1,595,269,083,271,500 |
0.240401 |
0.000000 |
4 |
0 |
1,660,382,107,078,500 |
0.250213 |
0.000000 |
5 |
0 |
1,168,909,003,383,260 |
0.176150 |
0.000000 |
6 |
0 |
572,994,609,501,600 |
0.086348 |
0.000000 |
7 |
10 |
198,344,287,904,400 |
0.029890 |
0.298897 |
8 |
25 |
48,650,485,712,400 |
0.007331 |
0.183286 |
9 |
100 |
8,408,725,925,600 |
0.001267 |
0.126716 |
10 |
300 |
1,009,047,111,072 |
0.000152 |
0.045618 |
11 |
2800 |
81,903,174,600 |
0.000012 |
0.034559 |
12 |
25000 |
4,310,693,400 |
0.000001 |
0.016240 |
13 |
50000 |
137,210,400 |
0.000000 |
0.001034 |
14 |
100000 |
2,325,600 |
0.000000 |
0.000035 |
15 |
100000 |
15,504 |
0.000000 |
0.000000 |
Total |
0 |
6,635,869,816,740,560 |
1.000000 |
0.714402 |
Go back to keno main page.
See Also: Learn to calculate the odds in Keno
Written by:
Michael Shackleford