I was looking at the distribution of the number of distinct numbers that come out in 8 consecutive drawings of 5/39 (CA Fantasy Five). This is what I got for 1 million simulations.
number of distinct numbers in 8 consecutive draws of 5/39
1 million simulations
17 distinct numbers: 0.0002%
18 distinct numbers: 0.0022%
19 distinct numbers: 0.0237%
20 distinct numbers: 0.1564%
21 distinct numbers: 0.7009%
22 distinct numbers: 2.3915%
23 distinct numbers: 6.1395%
24 distinct numbers: 12.1178%
25 distinct numbers: 18.1189%
26 distinct numbers: 20.9162%
27 distinct numbers: 18.2370%
28 distinct numbers: 12.1156%
29 distinct numbers: 6.0332%
30 distinct numbers: 2.2738%
31 distinct numbers: 0.6316%
32 distinct numbers: 0.1232%
33 distinct numbers: 0.0167%
34 distinct numbers: 0.0016%
The random simulations never resulted in a set of 8 consecutive drawings with fewer than 17 nor more than 34 distinct numbers. The distribution has a bell curve shape, but the underlying true distribution isn't Gaussian. More than half the time you should see 25-27 distinct numbers over 8 consecutive drawings. I checked it against the actual draw data and it hews pretty close. Not sure how you can apply it to picking winning numbers, but maybe someone will find it of use.
I also ran some sims for other k/N games:
number of distinct numbers in 7 consecutive draws of 5/35
1 million simulations
15 distinct numbers: 0.0013%
16 distinct numbers: 0.0083%
17 distinct numbers: 0.0678%
18 distinct numbers: 0.4022%
19 distinct numbers: 1.6290%
20 distinct numbers: 4.9901%
21 distinct numbers: 11.1579%
22 distinct numbers: 18.3341%
23 distinct numbers: 22.1149%
24 distinct numbers: 19.6929%
25 distinct numbers: 12.8480%
26 distinct numbers: 6.1063%
27 distinct numbers: 2.0623%
28 distinct numbers: 0.4931%
29 distinct numbers: 0.0822%
30 distinct numbers: 0.0089%
31 distinct numbers: 0.0007%
number of distinct numbers in 7 consecutive draws of 5/36
1 million simulations
14 distinct numbers: 0.0001%
15 distinct numbers: 0.0001%
16 distinct numbers: 0.0059%
17 distinct numbers: 0.0463%
18 distinct numbers: 0.2715%
19 distinct numbers: 1.2275%
20 distinct numbers: 3.9813%
21 distinct numbers: 9.3899%
22 distinct numbers: 16.4923%
23 distinct numbers: 21.5070%
24 distinct numbers: 20.7106%
25 distinct numbers: 14.8097%
26 distinct numbers: 7.7064%
27 distinct numbers: 2.9005%
28 distinct numbers: 0.7789%
29 distinct numbers: 0.1519%
30 distinct numbers: 0.0193%
31 distinct numbers: 0.0006%
32 distinct numbers: 0.0002%
number of distinct numbers in 8 consecutive draws of 5/36
1 million simulations
16 distinct numbers: 0.0002%
17 distinct numbers: 0.0017%
18 distinct numbers: 0.0140%
19 distinct numbers: 0.0917%
20 distinct numbers: 0.4958%
21 distinct numbers: 1.8420%
22 distinct numbers: 5.2649%
23 distinct numbers: 11.1472%
24 distinct numbers: 17.8356%
25 distinct numbers: 21.4305%
26 distinct numbers: 19.3556%
27 distinct numbers: 12.9918%
28 distinct numbers: 6.4208%
29 distinct numbers: 2.3664%
30 distinct numbers: 0.6154%
31 distinct numbers: 0.1118%
32 distinct numbers: 0.0129%
33 distinct numbers: 0.0017%
number of distinct numbers in 10 consecutive draws of 5/47 (CA SLP white balls)
1 million simulations
22 distinct numbers: 0.0006%
23 distinct numbers: 0.0049%
24 distinct numbers: 0.0220%
25 distinct numbers: 0.1239%
26 distinct numbers: 0.4837%
27 distinct numbers: 1.5579%
28 distinct numbers: 3.9742%
29 distinct numbers: 8.1618%
30 distinct numbers: 13.3472%
31 distinct numbers: 17.6032%
32 distinct numbers: 18.7832%
33 distinct numbers: 15.9078%
34 distinct numbers: 10.7101%
35 distinct numbers: 5.7900%
36 distinct numbers: 2.4449%
37 distinct numbers: 0.8233%
38 distinct numbers: 0.2142%
39 distinct numbers: 0.0397%
40 distinct numbers: 0.0065%
41 distinct numbers: 0.0008%
42 distinct numbers: 0.0001%
I can do other games by request.