subj: Keno 20/80 odds.
ref: <at least> correct, out of <group>.
  e.g.  4/9.  odd 1 : 6.53.
date:  23.02.99  19:28  pm   nzdt.
ng: rec.gambling.lottery

(new zealand) Keno 20/80 draws 20 lucky numbers
from the set 1 to 80.

IF I bet on <group> numbers.. what are the odds
of <at least> correct?

########This satisfying Table tells you.

Example. Keno # 22-2-1999.
Nil correct out of group 23  (1 to 23.)

Lowest numbers that night yesterday were 15, 24.
Included Approx. 10 lucky nos. from 24-43. (group 20.)

Odds 0/23   =  (80-23) C 20 / 80 C 20
= 1 in : 2.9E3.

E-format means the decimal point must be shifted
E(3)**   places to right,
= 1 in : 2921  approx.

IN CASE of group 23, odds of < at least = 0 correct>
which is obviously exactly 1, the Table gives
odds of *exactly 0*.

Odds <At least 1> out of group 23 = 1 to 23.  (lucky no. = 15.)
Odd = 1:1 approx.  Nearly certainty.

Odds <At least 10 correct>  out of group 20 = 24 to 43
odds 1 : 211 etc.

==============
prog lotto.keno.22/88atlest, don mcdonald, 19.11.97,   13.2.99
odds of new zealand keno 20/80. (group 61 certain of. 1 correct.)
or lotto 6+/40, at least etc.

enter no. of balls in barrel 80
enter no. of balls in lucky 6 or lucky 20 etc.?20
-
	# shows example described in text above.

group / AT LEAST correct / **  keno 20/80  odds 1 : ??. cont
     0     1     2     3     4     5     6     7     8     9     10    11c
1   1.3E0  4
2   1.8E0  2.27  16.6
3   2.4E0  1.71  6.55  72.1
4   3.2E0  1.45  3.86  21.6  326-

5   4.4E0  1.29  2.72  10.3  78.5  1551  4.1E9  
6   6.0E0  1.2   2.13  6.19  31.5  310   7753
7   8.2E0  1.14  1.78  4.23  16.2  106   1322  4.1E4  
8   1.1E1  1.1   1.55  3.15  9.77  48    395   6068  2.3E5  -

group / AT LEAST correct / **  keno 20/80  odds 1 : ??. cont
     0     1     2     3     4     5     6     7     8     9     10    11c
9   1.6E1  1.07  1.4   2.51 #6.53  25.7  158   1600  3.0E4  1.4E6
10  2.2E1  1.05  1.29  2.09  4.72  15.5 #75.6  571   7060  1.6E5  8.9E6
11  3.1E1  1.03  1.21  1.8   3.61  10.2  41.2  247   2268  3.4E4  9.3E5  6.1E7  
12  4.3E1  1.02  1.16  1.6   2.89  7.16  24.8  123   892   9901  1.8E5  5.9E6  -

13  6.1E1  1.02  1.12  1.45  2.41  5.31  16.1  67.7  406   3560  4.8E4  1.0E6  
14  8.7E1  1.01  1.09  1.34  2.06  4.12  11.1  40.5  206   1488  1.6E4  2.5E5  
15  1.2E2  1.01  1.06  1.26  1.81  3.32  8     25.9  114   698   6058  7.7E4  
16  1.8E2  1.01  1.05  1.2   1.63  2.76  6.04  17.5  67.8  359   2635  2.7E4  -

group / AT LEAST correct / **  keno 20/80  odds 1 : ??. cont
     0     1     2     3     4     5     6     7     8     9     10    11c
17  2.6E2  1     1.03  1.15  1.49  2.35  4.72  12.4  42.8  199   1261  1.1E4  
18  3.8E2  1     1.03  1.12  1.38  2.05  3.81  9.09  28.4  117   653   4960
19  5.7E2  1     1.02  1.09  1.3   1.82  3.15  6.92  19.6  73    361   2402
20  8.4E2  1     1.01  1.07  1.23  1.65  2.67  5.43  14.1  47.6 # 211   1246-

21  1.3E3  1     1.01  1.05  1.18  1.51  2.31  4.38  10.5  32.3  129   685
22  1.9E3  1     1.01  1.04  1.14  1.4   2.04  3.61  8.02  22.7  82.9  397
23 #2.9E3  1 #   1     1.03  1.11  1.32  1.82  3.04  6.29  16.4  55.1  240
24  4.5E3  1     1     1.02  1.08  1.25  1.66  2.61  5.06  12.3  37.9  151-

group / AT LEAST correct / **  keno 20/80  odds 1 : ??. cont
     0     1     2     3     4     5     6     7     8     9     10    11c 
25  7.0E3  1     1     1.01  1.06  1.2   1.52  2.28  4.16  9.4   26.9  98.6
26  1.1E4  1     1     1.01  1.05  1.16  1.42  2.03  3.48  7.37  19.6  66.4
27  1.7E4  1     1     1.01  1.04  1.12  1.33  1.82  2.97  5.91  14.7  46
28  2.8E4  1     1     1.01  1.03  1.09  1.27  1.66  2.57  4.83  11.2  32.8-

29  4.6E4  1     1     1     1.02  1.07  1.21  1.53  2.26  4.01  8.76  23.9
30  7.5E4  1     1     1     1.01  1.05  1.17  1.43  2.02  3.4   6.98  17.9
31  1.3E5  1     1     1     1.01  1.04  1.13  1.34  1.82  2.92  5.66  13.6
32  2.1E5  1     1     1     1.01  1.03  1.1   1.28  1.67  2.54  4.68  10.6-

group / AT LEAST correct / **  keno 20/80  odds 1 : ??. cont
     0     1     2     3     4     5     6     7     8     9     10    11c 
33  3.6E5  1     1     1     1.01  1.02  1.08  1.22  1.54  2.25  3.92  8.38
34  6.3E5  1     1     1     1     1.02  1.06  1.17  1.43  2.01  3.34  6.75
35  1.1E6  1     1     1     1     1.01  1.05  1.14  1.35  1.82  2.88  5.52
36  2.0E6  1     1     1     1     1.01  1.03  1.11  1.28  1.67  2.52  4.59-

37  3.7E6  1     1     1     1     1.01  1.03  1.08  1.22  1.54  2.24  3.87
38  6.9E6  1     1     1     1     1     1.02  1.06  1.18  1.44  2     3.31
39  1.3E7  1     1     1     1     1     1.01  1.05  1.14  1.35  1.82  2.86
40  2.6E7  1     1     1     1     1     1.01  1.04  1.11  1.28  1.66  2.51-

group / AT LEAST correct / **  keno 20/80  odds 1 : ??. cont
     0     1     2     3     4     5     6     7     8     9     10    11c 
41  5.1E7  1     1     1     1     1     1.01  1.03  1.08  1.22  1.54  2.23
42  1.1E8  1     1     1     1     1     1     1.02  1.06  1.18  1.43  2
43  2.2E8  1     1     1     1     1     1     1.01  1.05  1.14  1.35  1.81
44  4.8E8  1     1     1     1     1     1     1.01  1.04  1.11  1.28  1.66-

45  1.1E9  1     1     1     1     1     1     1.01  1.03  1.08  1.22  1.53
46  2.5E9  1     1     1     1     1     1     1     1.02  1.06  1.17  1.43
47  6.2E9  1     1     1     1     1     1     1     1.01  1.05  1.14  1.34
48  1.6E10 1     1     1     1     1     1     1     1.01  1.03  1.1   1.27-

group / AT LEAST correct / **  keno 20/80  odds 1 : ??. cont
     0     1     2     3     4     5     6     7     8     9     10    11c 
49  4.2E10 1     1     1     1     1     1     1     1.01  1.02  1.08  1.21
50  1.2E11 1     1     1     1     1     1     1     1     1.02  1.06  1.17
51  3.5E11 1     1     1     1     1     1     1     1     1.01  1.04  1.13
52  1.1E12 1     1     1     1     1     1     1     1     1.01  1.03  1.1-

53  4.0E12 1     1     1     1     1     1     1     1     1.01  1.02  1.07
54  1.5E13 1     1     1     1     1     1     1     1     1     1.02  1.05
55  6.7E13 1     1     1     1     1     1     1     1     1     1.01  1.04
56  3.3E14 1     1     1     1     1     1     1     1     1     1.01  1.03-

group / AT LEAST correct / **  keno 20/80  odds 1 : ??. cont
     0     1     2     3     4     5     6     7     8     9     10    11c 
57  2.0E15 1     1     1     1     1     1     1     1     1     1     1.02
58  1.5E16 1     1     1     1     1     1     1     1     1     1     1.01
59  1.7E17 1     1     1     1     1     1     1     1     1     1     1.01
60  3.5E18 1     1     1     1     1     1     1     1     1     1     1
* sp.   e.n.d.======

E.g. tonight 23-2-1999, NZ Keno.  Multiples of 8.
Lucky nos. included 8 16 24 40 56 64.  out of 1 to 80.

At least Six (6) correct out of group=10, multiples of 8.
Odd = 1 : 75.6   ,  not very common but not extremely rare either.
/  don.
