I've been playing a board game called risk lately, and I'm very interested in the probability behind it. Sorry if this question is it the wrong category, but I assumed that it was largely statistical. Consider the following:
Suppose two people are playing a dice game involving troop exchanges called Risk. Each player (either attacker or defender) begins with a certain number of "troops" and rolls three dice. Depending on how many of one player's dice beats those of another (based on a special scoring system), each player can lose a fraction of their troops. A defending player has a 62% chance for a net win, while an attacking player has only a 37% chance. Specifically, a defending player has a 37.5% chance to take three of the attacking player's troops, while an attacking player has a 15.6% chance to do the opposite. There is a 25.5% chance that the attacking player will lose 2 troops while the defending one loses 1, and there is a 21.4% chance that the attacking player loses 1 troop while the defending player loses 2.
I've gotten this far, through a very long program, but I can't figure this out: How many troops should the attacking player have in comparison to the defending player to make it fair, or so that there should be 0 players left on both sides in theory?
Thanks!
