Here is the exact solution for the expected value of G/(G+B) with k families. From numerical calculation with k up to 150, it looks like the discrepancy 0.5 - g/(g+b) approaches 0.25/k (from below) as k goes to infinity, which is certainly mysterious.
(The expected value of G-B is always 0, though, so I don’t know what you mean by an excess of 0.3.)
So for a reasonably-sized country of 1 million people, we’re looking at a ratio of B/(B+G) = 0.50000025? I’ll buy that.
And the 0.3 was a screwup on my part (my mistaken reasoning is described in a cousin of this post).
Funny though that the correct answer happens to be really close to my completely erroneous answer. It has the same scaling, the same direction, and similar magnitude (0.25/k instead of 0.3/k).
Here is the exact solution for the expected value of
G/(G+B)withkfamilies. From numerical calculation withkup to 150, it looks like the discrepancy0.5 - g/(g+b)approaches0.25/k(from below) askgoes to infinity, which is certainly mysterious.(The expected value of
G-Bis always 0, though, so I don’t know what you mean by an excess of 0.3.)So for a reasonably-sized country of 1 million people, we’re looking at a ratio of B/(B+G) = 0.50000025? I’ll buy that.
And the 0.3 was a screwup on my part (my mistaken reasoning is described in a cousin of this post).
Funny though that the correct answer happens to be really close to my completely erroneous answer. It has the same scaling, the same direction, and similar magnitude (0.25/k instead of 0.3/k).