Joseph
Your assumptions are incorrect. Statistically for a 50/50 event there is a huge difference in likelihood of it being 50/50 vs 80/20. The more times you “flip” the greater difference in likelihood. Given a large enough sample size the likelihood of even 52/48 can be infinitesimal kal v’chomer 80/20.
As a more visual example take 6 children. Since there are 2 possibilites per child (m/f), there are 2^6 = 64 possible combinations for all these children. (ie. MMMMMM, MMMMMF, FMMMMM, MMFFMF, etc..) So, because there is only 1 possible way for all to be male, the odds of 100% male is 1/64. Same with all female. The would make odds of 100% either way is only (1+1)/64 = 1/32.
However, to have 5 male and 1 female there are 6 different combination of that. MMMMMF, MMMMFM, MMMFMM, MMFMMM, MFMMMM, FMMMMM. That means there is a 6/64 chance that there will be 5 male and same for female. So, odds of there being 5 of either (which would be 83%) is 12/64 or 3/16 (approx 19%). This is more much more likely than 100% but not so likely.
4 males has 15 combinations MMMMFF, MMMFMF, MMFMMF, MFMMMF, FMMMMF, MMMFFM, MMFMFM, MFMMFM, FMMMFM, MMFFMM, MFMFMM, FMMFMM, MFFMMM, FMFMMM, FFMMMM. 4 females the same. That would be 30/64. So, 50/50 has 64-30-12-2 = 20/64 chance of happening.
To summarize likelihoods:
6M = 1/64
5M1F = 6/64
4M2F = 15/64
3M3F = 20/64
2M4F = 15/64
1M5F = 6/64
6F = 1/64
In other words, the closer you get to the 50% mark the more likelihood of it.