As a child, I was playing Monopoly in a local tournament against "Chuck" (the hero of some of my other game questions). Early on, he got a Monopoly of his namesake maroons: St. Charles Place, State Street, and Virginia Ave. After he acquired "stops" on all the other Monopolies, the game should have ended there except for one thing.
Toward the end of the game, a bystander, a girl named Martha, urged Chuck to give me a "fighting chance." He agreed to give me his defense to the Purple monopoly (Baltic and Mediterranean), in exchange for my defense to the orange Monopoly (St. James, Tennessee, New York). The other matters of note were that Chuck had hotels on the maroons, I had three railroads and one utility, and we each had about $1000 of cash.
Through what quantitative analysis (Monte Carlo simulation, perhaps), can I determine how much of a "fighting chance" I had at this point? I would guess that I would win less than one game in a hundred, perhaps less than one in a thousand, but in a million trials, I should have one or more wins.