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Spot Keno

Introduction

This is the page for standard keno, known in the industry as "spot keno." Variations with special rules are indexed in my main page on keno.

Rules

Following are the rules of standard spot keno.

  1. The game is played with 80 keno balls, numbered 1 to 80.
  2. In most cases, the player picks 1 to 10 numbers from the same range of 1 to 80.
  3. The game draws 20 balls, without replacement, from 1 to 80.
  4. If the number of a ball drawn matches that chosen by a player, that counts as a "catch."
  5. The player is paid according to the number of picks he chose and the number of catches. Several pay tables are shown below.

Analysis

The following table shows the number of combinations for picking and catching up to 10 numbers.

Combinations in Keno — Pick 1 to 6

Catch Pick 1 Pick 2 Pick 3 Pick 4 Pick 5 Pick 6
0 60 1,770 34,220 487,635 5,461,512 50,063,860  
1 20 1,200 35,400 684,400 9,752,700 109,230,240  
2   190 11,400 336,300 6,501,800 92,650,650  
3     1,140 68,400 2,017,800 39,010,800  
4       4,845 290,700 8,575,650  
5         15,504 930,240  
6           38,760  
Total   3,160 82,160 1,581,580 24,040,016 300,500,200  

Combinations in Keno — Pick 7 to 10

Catch Pick 7 Pick 8 Pick 9 Pick 10
0 386,206,920 2,558,620,845 14,783,142,660 75,394,027,566
1 1,001,277,200 7,724,138,400 51,172,416,900 295,662,853,200
2 1,037,687,280 9,512,133,400 73,379,314,800 486,137,960,550
3 555,903,900 6,226,123,680 57,072,800,400 440,275,888,800
4 165,795,900 2,362,591,575 26,461,025,640 242,559,401,700
5 27,442,080 530,546,880 7,560,293,040 84,675,282,048
6 2,325,600 68,605,200 1,326,367,200 18,900,732,600
7 77,520 4,651,200 137,210,400 2,652,734,400
8   125,970 7,558,200 222,966,900
9     167,960 10,077,600
10       184,756
Total 3,176,716,400 28,987,537,150 231,900,297,200 1,646,492,110,120

The formula for catching c numbers out of p picks is combin(p,c) = p!/((c! × (p-c)!), where n! = 1 ×2 ×3 × ... × n

The next table shows the probability of all combinations of picks and catches up for 1 to 10 picks.

Probabilities in Keno — Pick 1 to 10

Catch Pick 1 Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0.750000 0.560127 0.416504 0.308321 0.227184 0.166602 0.121574 0.088266 0.063748 0.045791
1 0.250000 0.379747 0.430867 0.432732 0.405686 0.363495 0.315193 0.266464 0.220666 0.179571
2   0.060127 0.138754 0.212635 0.270457 0.308321 0.326654 0.328146 0.316426 0.295257
3     0.013875 0.043248 0.083935 0.129820 0.174993 0.214786 0.246109 0.267402
4       0.003063 0.012092 0.028538 0.052191 0.081504 0.114105 0.147319
5         0.000645 0.003096 0.008639 0.018303 0.032601 0.051428
6           0.000129 0.000732 0.002367 0.005720 0.011479
7             0.000024 0.000160 0.000592 0.001611
8               0.000004 0.000033 0.000135
9                 0.000001 0.000006
10                   0.000000
Total 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000

The following table shows what I call Pay Table 1. The bottom row shows the expected return for each number of picks.

Pay Table 1

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 1 1 1 1 1 1 1 1 1
1 0 0 0 0 0 0 0 0 -
2 5 2 1 0 0 0 0 0 -
3   11 5 3 2 1 1 0 -
4     40 10 5 2 2 1 -
5       400 49 22 10 5 5
6         1,000 275 40 40 25
7           2,500 500 400 120
8             5,000 1,000 500
9               5,000 2,000
10                 10,000
Return 86.08% 84.66% 85.97% 85.79% 84.96% 85.33% 84.57% 84.25% 86.43%

The following table shows what I call Pay Table 2. The bottom row shows the expected return for each number of picks.

Pay Table 2v

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 1 0 0 1 0 1 1 0 -
1 0 0 0 0 0 0 0 0 -
2 5 2 2 0 0 0 0 0 -
3   40 3 3 2 1 1 0 -
4     100 10 4 2 2 1 -
5       400 92 22 10 3 3
6         1,500 275 40 47 28
7           2,500 500 352 140
8             5,000 4,700 1,000
9               9,000 4,800
10                 10,000
Return 86.08% 83.25% 86.14% 85.79% 85.21% 85.33% 84.57% 84.87% 86.72%

The following table shows what I call Pay Table 3. The bottom row shows the expected return for each number of picks.

Pay Table 3

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 -
1 3 0 0 0 0 0 0 0 0 -
2   15 2 2 0 0 0 0 0 -
3     43 5 3 3 1 0 0 -
4       77 12 4 2 2 1 -
5         750 55 21 12 6 5
6           1,600 335 98 40 21
7             7,000 1,450 300 142
8               10,000 4,700 1,000
9                 9,000 4,000
10                   10,000
Return 75.00% 90.19% 87.41% 87.74% 88.06% 88.02% 87.68% 89.07% 87.57% 88.80%

The following table shows what I call Pay Table 4. The bottom row shows the expected return for each number of picks.

Pay Table 4

Catch 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 -
1 0 0 0 0 0 0 0 0 -
2 14 2 2 0 0 0 0 0 -
3   45 5 3 3 1 0 0 -
4     85 11 4 2 2 1 -
5       804 68 20 12 6 5
6         1,500 390 98 44 23
7           7,000 1,550 300 132
8             10,000 4,700 1,000
9               10,000 4,500
10                 10,000
Return 84.18% 90.19% 90.19% 90.33% 90.76% 90.85% 90.67% 89.93% 89.79%

The following table shows what I call Pay Table 5. The bottom row shows the expected return for each number of picks.

Pay Table 5

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 -
1 3 0 0 0 0 0 0 0 0 -
2   15 2 2 0 0 0 0 0 -
3     46 5 3 3 1 0 0 -
4       91 12 4 2 2 1 -
5         810 70 21 12 6 5
6           1,600 400 98 44 24
7             7,000 1,652 335 142
8               10,000 4,700 1,000
9                 10,000 4,500
10                   10,000
Return 75.00% 90.19% 91.58% 92.03% 91.93% 92.67% 92.44% 92.31% 92.00% 92.55%

The following table shows what I call Pay Table 6. The bottom row shows the expected return for each number of picks.

Pay Table 6

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0 0 0 1 1 1 1 1 1
1 0 0 0 0 0 0 0 0 -
2 0 3 1 0 0 0 0 0 -
3   37 12 3 1 1 0 0 -
4     64 28 14 4 1 1 1
5       170 62 33 30 8 2
6         300 175 70 65 36
7           325 250 178 115
8             350 325 225
9               375 300
10                 400
Return 0.00% 92.96% 92.77% 92.72% 92.66% 92.64% 92.62% 92.66% 92.69%

The following table shows what I call Pay Table 7. The bottom row shows the expected return for each number of picks.

Pay Table 7

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 -
1 3 0 0 0 0 0 0 0 0 -
2   15 2 2 0 0 0 0 0 -
3     48 5 3 3 1 0 0 -
4       100 13 4 2 2 1 -
5         838 75 22 13 6 5
6           1,660 422 100 44 24
7             7,000 1,670 362 146
8               10,000 4,700 1,000
9                 10,000 4,500
10                   10,000
Return 75.00% 90.19% 94.35% 94.78% 94.95% 94.99% 94.92% 94.90% 93.60% 93.20%

Internal Links

Go to my main page on keno.

Written by: Michael Shackleford