Ah! I think they mean that the three have to be compared equally. even/even, odd/odd, odd/even have to be compared equally – that we *don’t* get ‘double the chance” with odd/even simply because odd/even = even/odd ? Maybe something like that? Or maybe it’s the field goal thing…
I suspect it balances out to 50% because you have four combinations:
odd+odd = even
even+even = even
odd+even = odd
even+odd = odd
So, the evens and odds balance each other out.
The mistake I made in thinking that *maybe* odd was more common, is forgetting that I can’t just do “odd+even” without also doing “even+odd”.