In fact, the probability of winning at Monopoly can be described by interesting constructions known as Markov chains. In the early 1900s the Russian mathematician Andrey Andreyevich Markov invented a general theory of probability. I will ignore much of his work. And I won't review all of Monopoly's rules, but I will convince you that the game is fair. First, we must recall how to play it.
Players take turns throwing a pair of dice.
The number of dots on the dice determines how many squares around the board a player may move. Some rolls, such as 7, naturally happen more often than others. Thus, the first player has an excellent chance of securing one of these properties. If he does buy one, it lessens the opportunity for the other players to make a purchase on their first throw. This fact is no doubt one reason why the game's designers put cheap properties near the start.