You can use combinatorics to calculate the likelihood. If your PRNG is in a cycle of length N in its state space (assuming N>200), and half the state space corresponds to heads (vs tails), then the likelihood would be (N/2 choose 100)^2/(N choose 200) versus your baseline likelihood (for a truly random coin) of (200 choose 100)/2^200.

Graphing here https://www.wolframalpha.com/input?i=graph+%28%28N%2F2+choos... and it does look like it's only a slight improvement in likelihood, so I did overstate the claim. A more interesting case would be to look at some self-correcting physical process.