Using Markov Chain Monte Carlo to compute the chances that a particular solitaire laid out with 52 cards would come out successfully 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
So Question:
Does anyone have a pretty introductory write up on how Ulam applied MCMC to solitaire?
Thanks.
 A: As already said by Paparazzi, the paper is about Monte Carlo method, not Markov Chain Monte Carlo. MCMC is just a part of a broader family of Monte Carlo methods (i.e., informally, using simulation to solve statistical problems).
This is actually described in the referred paper

[...] I was convalescing from an illness and playing solitaires. The
  question was what are the chances that a Canfield solitaire laid out
  with 52 cards will come out successfully? After spending a lot of time
  trying to estimate them by pure combinatorial calculations, I wondered
  whether a more practical method than "abstract thinking" might not be
  to lay it out say one hundred times and simply observe and count the
  number of successful plays. [...]

So it's pure Monte Carlo: he simulated a number of plays and then counted the number of events of interest among the all simulated events. It was obtained using a direct simulation.
Actually MCMC was discovered later with Metropolis algorithm being the first MCMC algorithm as described in A Short History of Markov Chain Monte Carlo: Subjective Recollections from Incomplete Data paper by Robert and Casella (2011).
A: But there is no evidence he used Markov chain Monte Carlo.  There is no reason to use a probability distribution.  You just shuffle the deck and get a random deck - straight up Monte Carlo.  See Fisher Yates for random shuffle.
