Based on some references I got from another question I learned that:
While convalescing from an illness in 1946, Stan Ulam was playing solitaire. It, then, occurred to him to try to compute the chances that a particular solitaire laid out with 52 cards would come out successfully (Eckhard, 1987).
Interest piqued, I googled on an write up on what Ulam would have done but came up empty handed -- I found countless mentions of this episode but nothing that was step by step.
I found the original paper by Eckhard, here, but again it does not address the application to MCMC
Does anyone have a pretty introductory write up on how Ulam applied MCMC to solitaire?