Here’s the actual odds for each how often each number of loci is needed. This is how many times a specific red-black deck configuration occurs out of the total possible red-black deck configurations, with decimal remainders rounded up.
Note: these odds should apply to any 2-card system that uses a two-block approach, not just Shadow.
1 loci: 1 in 18,367,353,072,152
2 loci: 1 in 56,514,932,530
3 loci: 1 in 565,149,326
4 loci: 1 in 12,285,855
5 loci: 1 in 485,607
6 loci: 1 in 31,533
7 loci: 1 in 3,154
8 loci: 1 in 465
9 loci: 1 in 98
10 loci: 1 in 29
11 loci: 1 in 12
12 loci: 1 in 7
13 loci: 1 in 5
14 loci: 1 in 5
15 loci: 1 in 7
16 loci: 1 in 12
17 loci: 1 in 29
18 loci: 1 in 98
19 loci: 1 in 465
20 loci: 1 in 3,154
21 loci: 1 in 31,533
22 loci: 1 in 485,607
23 loci: 1 in 12,285,855
24 loci: 1 in 565,149,326
25 loci: 1 in 56,514,932,530
26 loci: 1 in 18,367,353,072,152