in the previous two we looked at different ways of using randomness in computations many of the examples we presented fall into the class of computation known as monte carlo simulation stanislaw ulam and nicholas metropolis coined the term monte carlo simulation in in homage to the games of chance played in the casino in the principality of monaco ulamwho is best known for designing the hydrogen bomb with edward tellerdescribed the invention of the model as followsthe first thoughts and attempts made to practice [the monte carlo methodwere suggested by question which occurred to me in as was convalescing from an illness and playing solitaires the question was what are the chances that canfield solitaire laid out with cards will come out successfullyafter spending lot of time trying to estimate them by pure combinatorial calculationsi wondered whether more practical method than "abstract thinkingmight not be to lay it out say one hundred times and simply observe and count the number of successful plays this was already possible to envisage with the beginning of the new era of fast computers, and immediately thought of problems of neutron diffusion and other questions of mathematical physicsand more generally how to change processes described by certain differential equations into an equivalent form interpretable as succession of random operations later [in idescribed the idea to john von neumannand we began to plan actual calculations the technique was effectively used during the manhattan project to predict what would happen during nuclear fission reactionbut did not really take off until the when computers became both more common and more powerful ulam was not the first mathematician to think about using the tools of probability to understand game of chance the history of probability is intimately connected to the history of gambling it is the existence of uncertainty that makes gambling possible and the existence of gambling provoked the development of much of the mathematics needed to reason about uncertainty contributions to the foundations of probability theory by cardanopascalfermatbernoullide moivreand laplace were all motivated by desire to better understand (and perhaps profit fromgames of chance "fastis relative term ulam was probably referring to the eniacwhich could perform about additions second (and weighed more than tonstoday' computers perform about additions second (and weigh maybe - tons eckhardtroger ( "stan ulamjohn von neumannand the monte carlo method,los alamos sciencespecial issue ( ) -