Quote from: NotATether on Today at 05:31:18 PM

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In my testing, sequences of greater than 11 zeros or ones only occurred maximum once in an entire sample of 1000 256-bit random numbers.

I previously did tests of the probability of repeating bits 1111x and 0000x on a range of 256 bits. To do this I generated 100 million urandom(32) keys and looked for bits 0 and 1. Below is a table of the probabilities of repeating bits 1 or 0 on a 256-bit key.
For example, the probability of a key having 16 ones or 16 zeros is 0.367964%
I can look up the code if I need to

Code:

1 100,000000%
2 100,000000%
3 100,000000%
4 100,000000%
5 99,991147%
6 98,673109%
7 87,345356%
8 63,436401%
9 39,012922%
10 21,689362%
11 11,414800%
12 5,843793%
13 2,949750%
14 1,479510%
15 0,737481%
16 0,367964%
17 0,183264%
18 0,091321%
19 0,045563%
20 0,022649%
21 0,011249%
22 0,005631%
23 0,002762%
24 0,001374%
25 0,000654%
26 0,000339%
27 0,000176%
28 0,000086%
29 0,000042%
30 0,000025%
31 0,000016%
32 0,000005%