Win at Monopoly using Monte Carlo simulations

Now that we are experts at Risk, let's turn to Monopoly, the classic board game. In Monopoly, players determine whether to buy properties and build houses, so as to maximise rental yield. To some extent, one should gun for the most visited spaces, so that your opponents pay rent more often.

Which spaces are the most popular? Once again, drawing out the theoretical probabilities would be rather tedious, so we turn to Monopoly game simulations.

Win at Risk using Monte Carlo simulations

The objective in Risk is simple: world domination. In this board game, players attack each other's territories using dice. The attacker gets to roll three dice, and the defender two dice. The highest numbers are compared, and if the attacker has a larger number the defender loses one soldier (and vice versa). The same is done for the second highest numbers. For example, if the attacker rolls 6, 4, 2 and the defender rolls 5, 5, players loses one soldier each.

However, even though the attacker rolls an extra dice, the defender has an edge as well. In the event of a tie, the attacker will lose one soldier. Is this enough to offset the attacker's 3-dice advantage? What does this mean for rolling strategies?