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Keno Appendix 3 — Returns from the Atlantic City Tropicana

Last update: September 4, 2001

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

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Keno appendix 1 features an analysis of the top/bottom/left/right as as well as edge tickets as played at the Las Vegas Hilton.

Keno appendix 2 features an analysis of Caveman Keno as played on IGT's Game King.

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