The Mathematics of Risk

First, a brief summary of Risk. The objective in the game is to conquer the globe, which is accomplished by placing down troops and battling other players. The battle is what we’ll focus on. A battle is started when an attacker chooses to invade the territory of another player, in which the attacker uses his troops to stage a battle with the defender’s troops. Based on each individual fight, the attacker either kills some of the defender’s troops, or some of his/her troops die. If either side runs out of troops, the opposing side wins. The battle is simulated with dice rolls. The attacker gets up to 3 dice to roll, while the defender gets up to 2; each player chooses how many to use based on available troops and strategy. In a battle, the highest rolled dice are matched up while the rest are discarded. The defender wins if his/her dice are greater than or equal to the attacker’s dice.  <a href="https://medium.com/@divijgarg04/the-mathematics-of-risk-64fe4525d327">Learn More</a>