In Risk (the board game), who has the stronger position: offense or defense?

The Game Room
1

I’m looking for a statistical answer here, I suppose- who’s got the greater statistical chance of winning a long, protracted battle? Assuming no house rules or variants, of course; offense has three dice, defense has two and wins ties. Who should win?

2

Moving to The Game Room from GQ.

Colibri
General Questions Moderator

3

3-dice-on-2, it appears the attacker wins both about 40% of the time, they split just over 30% of the time, and the defender wins both just under 30% of the time. So it seems like even the attacker’s having a slight disadvantage in army size could be made up over the long run (i.e. I wouldn’t try it with 8 v. 10, but maybe 80 v. 100.

4

Thanks! That’s just what I was looking for.

5

To clarify though, this does not imply that in a 3-army attack against a 2-army defense that the attacker is favored. In fact, the opposite is the case. This site lets you calculate various odds using Risk dice rules. If you input 3 attackers against 2 defenders you see that the attack wins only 36% of the time. I can’t guarantee that site is accurate but it matches my understanding that the you generally want at least 2 additional armies before you are favored as an attacker.

What I’m finding odd about the numbers generated is that as one army is added to each side the odds begin to favor the attacker. I suppose this is because he will have more time with a one-dice advantage (and once it becomes 2 on 2 the defender is at a heavy advantage). Once you get to 6 attackers vs. 5 defenders the odds swing to the attacker, and by the time you get to 25 v. 25 it is something like 60% to the attacker. So I guess the upshot is that in small-scale battles the defender has the upper hand, but large-scale it is the attacker.

6

Right. I was surprised in a game this last weekend that an attacker with ~20 armies beat my territory with over 25 armies. I had intuited that the attacker needed more armies than the defender, but I guess my intuition was wrong.

I would have been better off initiating the battle in question during my previous turn, I guess, instead of waiting for him to attack me.