"Yup. Though embarrassingly I don't recall the exact constant. Back when I was memorizing those numbers in order to impress the younger kids I was teaching, by pretending to calculate it all on the spot, they were too young to ask that question so I didn't memorize the answer."
"But as you say, Willa, you did indeed try to do something naughty, by calculating the likelihoods for 'latent' frequencies that exactly matched the observed frequencies. Maybe if you'd run a pilot experiment and found 40% YESes for all-10s and 60% YESes for all-14s, you would have written down the numbers 40% and 60% in advance, in the 'preregistered' version of your 'published-experimental-report' that you'd put out and gotten... signed and time-stamped... by larger Civilization, before you'd collected any data. Then nobody would call you naughty if you ran the likelihoods for the 40%-and-60% hypothesis, and compared that exact hypothesis to the fair-coinspin hypothesis."
"So hopefully it's starting to become clear that all of the pieces of Science! hang together, even if I didn't explain them all that well?"
"Anyways, let's say you didn't run a 'pilot-experiment' that produced 40%-and-60% as a hypothesis distinguished in advance, or 49% and 51.2%. Then what might you say in your 'preregistered' 'published-experimental-report' that doesn't have the results filled in yet, about how you plan to analyze the data? People besides Willa are allowed to answer too."