A method for operating a computer-based solitaire game which collects a player's fee at the start of the game and pays a player award as a function of a per-card payout award and one or more of the number and/or identities of cards that have been transferred from the card deck on foundation stacks. The per-card payout award is determined as a function of an expected number of transferred cards, which number has been determined as a function of a discrete probability density function calculated from outcomes produced in a multi-game simulation. The number of games in the multi-game simulation is selected to provide a statistically stable result, and may be on the order of more than one million games. The simulated games are played by applying a set of ordinally-ranked solitaire game play rules.