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@Chardrian -- great post

"I know that the key words to this problem are "conditional relative frequency" - we aren't talking about what the authors call the "true probability" of flipping a coin...

Before I respond to that, which I'm more than willing to do (I'm enjoying this), is it out of place to suggest you first identify a flaw in the formal argument I laid out, not a link to an intuition...

Eric, I'm working backwards from the table they have in the paper, and the specific thing that I am doing differently than you is I am weighting (multiplying) each of the relative probabilities (e.g....

I see it now, having worked on this at length (3+ hours), did the same exact thing you did Eric 3x, and having read both papers. It's quite subtle.

To be formal, we're sampling length-4 sequences...