Every 7 kittens born, 6 are normal size and 1 special size!

[jwenting Resident]

your conclusions are not correct. While the 1 in 7 may well be true, as well as the percentages of special sizes, there's no way of telling how this is implemented on the server.
In fact rather than the server deciding every 7th kitten that's birthed to be a special size, it's far more likely there's a relatively simple random number generator involved that pulls a random number of 1-100 and from that takes the first 80 to be normal, then 81-81 Bigger de Big, 83-84 Mega, etc. etc.

The result would be an identical chance for everyone to get one of the special sizes over the course of a time period, the mechanism you describe would effectively cause the special sizes to be almost completely monopolised by the very large breeders who produce dozens of kittens every day.