The digital electronic computer was one of the most influential scientific instruments of the twentieth century. One of the earliest and still prominent uses is Monte Carlo simulation, a computational method that arose during the Manhattan Project. In this paper, I trace the rise in status of Monte Carlo from its initial use in the forties as an auxiliary heuristic to the seventies, when simulation results were regularly accepted as scientific evidence. I argue that this rise in status depended on the production and communication of “practices of trust” that subsumed Monte Carlo under accepted scientific standards. Ulam, von Neumann, and Metropolis developed Monte Carlo for use in cases where analytic methods proved intractable and real experiments too dangerous or expensive. Monte Carlo was intended as merely a heuristic, a way for scientists to gain insight into intractable analytic equations so that they could be simplified for hand-calculation. But the calculations quickly came to be accepted as scientific evidence in their own right. For example, aspects of the simulation that were initially proposed as estimates or idealizations, for example the stochastic behavior of simulated neutrons, were reinterpreted as being representative of reality, leading to new hypotheses about the nature of actual neutrons. When the focus of the Manhattan Project shifted from the atomic to the hydrogen bomb—that is, from a fission to a fusion bomb—reliance on Monte Carlo evidence became even more essential, for there simply were no experimentally available instances of fusion. The question is how this initially contested method became an acceptable source of scientific evidence. I attempt to get at the answer through an analysis of the early published papers that introduced Monte Carlo to various scientific communities, which implicitly or explicitly include arguments for the acceptance of Monte Carlo results. As the method developed and spread, scientists renegotiated standards of evidence in order to include evidence from the new practice, and at the same time they modified the practice itself to be ever more compatible with existing standards. Of particular importance for the acceptance of Monte Carlo was the development and communication of the practices of trust that gave scientists confidence in the validity and appropriate use of simulation results. I detail several such practices and argue that they were co-produced with the simulation during its design.