- 23 Sep '04 14:45 / 1 editMe and a couple of friends have been wondering about the attacking odds in the board game Risk. I haven't given it a huge amount of thought but essentially the problem boils down to "given the size of my opponents army, what size attacking force do I need to be odds on to win the territory?"

For those that don't know, the attacking works (something) like this.

The attacker decides how many troops to attack with.

He gets to role one die per troop to a maximum of 3.

The defender roles a maximum of 2 die (and only 1 if he has a single defending unit).

Each players best roles are then compared. If the attacker's best roll is higher than the defender's best roll then the defender loses a troop. Otherwise the attacker loses a troop.

If both players roled more than one die then their second best roles are compared in a similar fashion.

At this point the attack is over, but the attacker may decide to attack again immediately (and generally does).

If the defender loses all his troops then the territory is lost.

I'm not even sure who has the best odds in a single attack of 3 against 2, but I'm sure someone can work it out (or tell me why it isn't possible!)

- Mike - 24 Sep '04 02:11

I don't know the mathematics behind it, but being a veteran Risk player I can tell you it's about even. The attacker's extra die will balance out the defender winning all ties. Losses should be about equal over the long haul. But then any experienced Risk player can give you a litany of woe about how his losses exceeded probability more often than he would care to remember.*Originally posted by mikenay***Me and a couple of friends have been wondering about the attacking odds in the board game Risk. I haven't given it a huge amount of thought but essentially the problem boils down to "given the size of my opponents army, what size attacking force do I need to be odds on to win the territory?"**

For those that don't know, the attacking works (something) ...[text shortened]... against 2, but I'm sure someone can work it out (or tell me why it isn't possible!)

- Mike - 24 Sep '04 12:43

Cheers rwingett! I would ask for more strategy tips but my regular opponents are on this site as well so they'd just get the same information! I haven't played much myself and assumed the defender had the advantage, as a result I tended to prefer being defending when there were two big armies close to a border. I may change my style a little given what you've said. (Although given that I've never won a game it's suprising I didn't realise something was wrong!)*Originally posted by rwingett***I don't know the mathematics behind it, but being a veteran Risk player I can tell you it's about even. The attacker's extra die will balance out the defender winning all ties. Losses should be about equal over the long haul. But then any experienced Risk player can give you a litany of woe about how his losses exceeded probability more often than he would care to remember.** - 25 Sep '04 00:59
y posted by mikenay[/i]

The losses from any individual battle should be about equal. But the attacker has the edge in that he gets to decide where the battles will be fought. It's always good to attack aggressively without spreading your forces too thin, which will only invite counter-attack.**Cheers rwingett! I would ask for more strategy tips but my regular opponents are on this site as well so they'd just get the same information! I haven't played much myself and assumed the defender had the advantage, as a result I tended to prefer being defending when there were two big armies close to a border. I may change my style a little given what yo ...[text shortened]... though given that I've never won a game it's suprising I didn't realise something was wrong!)** - 01 Oct '04 11:56

Indeed we are Mikenay, indeed we are. For the record Mikenay is an awful lot more dangerous opponent over a chess board than a RISK board. His ability to sit in a corner and fail to occupy continents until someone gets around to killing him is almost legendry. However, I have never come close to beating him at chess.*Originally posted by mikenay***Cheers rwingett! I would ask for more strategy tips but my regular opponents are on this site as well so they'd just get the same information! I haven't played much myself and assumed the defender had the advantage, as a result I tended to prefer being defending when there were two big armies close to a border. I may change my style a little given what ...[text shortened]... though given that I've never won a game it's suprising I didn't realise something was wrong!)**

Mike if you give me some chess tutoring when you move in I promise not to kill you in our next game of RISK, we'll just gang up and kill Olliefrench.... - 02 Oct '04 23:11

In 3 dice against 2 dice the defender will lose about 1.17 men for every man lost by the attacker. This is to some extent compensated by the fact that the attacker has to stop throwing his max dice when he gets down to 2 men, but the defender can throw his max dice until he is down to 1 man.*Originally posted by mikenay***Me and a couple of friends have been wondering about the attacking odds in the board game Risk. I haven't given it a huge amount of thought but essentially the problem boils down to "given the size of my opponents army, what size attacking force do I need to be odds on to win the territory?"**

For those that don't know, the attacking works (something) ...[text shortened]... against 2, but I'm sure someone can work it out (or tell me why it isn't possible!)

- Mike

I calculated that myself, but http://www.sciencenews.org/articles/20030712/mathtrek.asp completes the stats: The attacker needs to have 1 more man than the defender to have a >50% chance of winning UP TO 5 attack / 5 defence (and more) where the odds are with the attacker.