If the sampled marble is green, then Gabriela wins and if it is blue then Billy wins. If is the number of blue marbles and is the number of green marbles in the bag, then the probability of Billy winning against Gabriela is

In this example, the marble game satisfies linear stochastic transitivity, where the comparison function is given by and the merit function is given by , where is the number of marbles of the player. This game happens to be an example of a Bradley-Terry model.