An interesting article bobbed up from the ocean on Twitter today: Stan Ulam, John Von Neumann, and the Monte Carlo method, by Roger Eckhardt. This was in the Los Alamos Science Special Issue of 1987, which was dedicated to Stan Ulam. The whole issue looks quite interesting, as does indeed much of the whole publication, which was the flagship publication of the Los Alamos National Laboratory from 1980 to 2005. I suspect the articles on history would be a good place to start.
The article starts out with the now well-known story that Ulam invented the Monte Carlo method while trying to work out the win probability of a particular solitaire game, and indeed that probability has been worked out by simulation!. (Wikipedia cites the Eckhardt article, which is probably the original published source as Eckhardt only cites unpublished notes left by Ulam.) The original scientific problem to be solved was one about neutron diffusion, which gives the Los Alamos connection. There are also some nice inclusions of letters between Ulam and von Neumann.