Implementations of the present disclosure are directed to a method, a system, and an article for managing the use of global position information in a multi-player online game. An example computer-implemented method can include: identifying a number of random events for which each random event has a plurality of possible outcomes and each possible outcome has a respective probability of occurrence for each random event; selecting a first possible outcome from the plurality of possible outcomes; determining a probability distribution for the first possible outcome that defines a relationship between (i) a number of occurrences of the first possible outcome in the number of random events and (ii) a range of probabilities; selecting a first probability from the range of probabilities; and determining the number of occurrences of the first possible outcome based on the probability distribution and the selected first probability.