The convention about a common point will go back to what it was originally -- it is considered a borderline.
This makes bigger countries succeed for all odd numbers, fail for all even numbers. That's a success rate for 50% of all infinite cases. All that's needed is take the other 50% of all infinite cases that fail, and make it work.
But one of the previous posts have proven beyond a doubt that for countries of equal size (or maybe even a little bigger but not bigger by two times or more), the theorem works 100% of all cases.
Both proofs appear indisputably irrefutable. They both eagerly await constructive criticism.