Looking at the “better model” graph https://jasmcole.files.wordpress.com/2022/09/image-16.png — a “coin” with a thickness of nearly the diameter ratio ~0.85. Note h is half the thickness (r is more obviously half the diameter).

In the comments, someone asked a similar question:

> So what should the value of h be?

To which the author replied:

> It's about the journey, not the destination

Also, the fit they did for lambda was based on simulations, not actual "coin" tosses. So the exact answer for h/r probably wouldn't be very helpful.