How likely are chance resemblances between languages?

That site has a lot of good stuff. It's often mentioned by conlangers due to the Language Construction Kit.

Regarding those pseudo-scientific proto-world "reconstructions", there are four patterns that are damn easy to spot, that appear in almost all of them:

1. Usage of modern languages to force resemblances, even when older relatives are well attested. (e.g. using French instead of Latin)
2. Complete disregard for the morphology.
3. No effort whatsoever to lay out regular sound changes.
4. Once applied to real cognates with obfuscating sound changes, they fail hard.

And... really, even the idea that there's some sort of "ancestral language" is debatable; Rosenfelder himself mentions the possibility in another text. And if Chomsky is right about Language being primarily to structure thought, instead of communication, it's fairly reasonable that there's no ancestral language to reconstruct a proto-world of.