[vivekd]

I was just reading a book about this, "The undoing project". The point of the book was that statically even distribution only works in large numbers, in small numbers its normal to get uneven distributions like this. That's why sample size is so important in scientific research.

So, for example, when have a group of 10 men and 10 women, and you randomly pair them up in a tournament, it is normal and possible for a woman to be playing against 5 women in a row. It's not an aberration because small numbers won't necessarily even out. However, when you get a group of 1000 men and 1000 women, and start paring them up for tournament matches, it would still be possible for a woman to end up playing against 5 woman in a row, but on the whole when taking all 500 matches she plays, it should approach 50, the aberration would be if she had played against 500 women in a row. That would be an indication of something suspicious.

This is an example of the gambler's fallacy.

https://onlinecourses.science.psu.edu/stat100/node/46