Interesting idea but not sure.

[ADAM TJ]

Probabilities of the attacks in Risk... I saw it in a faq about the board game. I think it can be helpful to you all

Attacker 3 X 2 Defender
Att lose 2: 29.26% (2275/7776)
Def lose 2: 37.17% (2890/7776)
Each lose 1: 33.58% (2611/7776)

Attacker 3 X 1 Defender
Att lose 1: 34.03% (441/1296)
Def lose 1: 65.97% (855/1296)

Attacker 2 X 2 Defender
Att lose 2: 44.83% (581/1296)
(Def lose 2: 22.76% (295/1296)
Each lose 1: 32.41% (420/1296)

Attacker 2 X 1 Defender
Att lose 1: 42.13% (91/216)
Def lose 1: 57.87% (125/216)

Attacker 1 X 2 Defender
Att lose 1: 74.54% (161/216)
Def lose 1: 25.46% (55/216)

Attacker 1 X 1 Defender
Att lose 1: 58.33% (21/36)
Def lose 1: 41.67% (15/36)

took that from another topic but it got me thinking... knowing these ratios provided above, is it better to leave countries as ones or place a 2 men on each of them.

in other words,

what would slow an attacker down more... having 19 one man countries and a big group of 21 or 20 countries of 2? each situation consists of 40 men and 20 countries.

[ADAM TJ]

oh and this is purly mathematicly... i realize that by spreading your armies out you will in effect make it hard to attack next round since you only have 2 man armies.

[areyouincahoots]

i've considered that, and i try to reinforce my countries so i have at least two on each, but I only start to worry about this when enough men are coming to me to make it worth it... like when i cash in some cards, and i know theres no way to make a major move that round. or when i'm facing a much stronger opponent, and i fear they'll be making a big move soon, in hopes the extra army will slow them down.

[ADAM TJ]

i've considered that, and i try to reinforce my countries so i have at least two on each, but I only start to worry about this when enough men are coming to me to make it worth it... like when i cash in some cards, and i know theres no way to make a major move that round. or when i'm facing a much stronger opponent, and i fear they'll be making a big move soon, in hopes the extra army will slow them down.

thats exactly the situation i would be using this. im just curious as to what the advantage is numericaly. seeing as im an art sci my math is shit now. hopping there is a smart person here that would be interested in calculating it

[supermarcol]

Leaving 2 armies is obviously way better, as you have better odds. The problem is that it cost a lot of men. Another problem is that the enemy can still wipe you out in a single blow. The best defence to slow down is haveing 3 on each country. But that costs a LOT. I think the best defense remains offense. Offense has better odds than defense on 3 vs 2. And when you attack a lot, you force your enemy in a defensive mode, and then he will think less about attacking your continent. You can get screwed over pretty rapidly though. Risk is the name of the game!

[SmoKer]

I think they should change the name to "Ah Shit!!" or maybe "Dammit!!"

[Cachorro]

Leaving 2 armies is obviously way better, as you have better odds. The problem is that it cost a lot of men. Another problem is that the enemy can still wipe you out in a single blow. The best defence to slow down is haveing 3 on each country. But that costs a LOT. I think the best defense remains offense. Offense has better odds than defense on 3 vs 2. And when you attack a lot, you force your enemy in a defensive mode, and then he will think less about attacking your continent. You can get screwed over pretty rapidly though. Risk is the name of the game!

You are wrong saying that the best is having 3 in defense. Mathematically said that's the worst thing you do if you just have to defense.

I calculated how many troops the attacker needs in average to wipe out your troops in defense. This assumes that the attackes can always attack with 3 dice.

Def - Att

1 - 0,52
2 - 1,55
3 - 2,31
4 - 3,21
5 - 4,04
6 - 4,90
7 - 5,75
8 - 6,61
9 - 7,46
10 - 8,31
11 - 9,17
12 - 10,02
13 - 10,87
14 - 11,73
15 - 12,58
16 - 13,43
17 - 14,29
18 - 15,14
19 - 15,99
20 - 16,85

From this you can calculate that the best way to use your single unit for defense is to increase the unit amount from one to two as this increases the average loss of the attacker by 1,03 units! Addind the amount from 2 to 3 only increases the average loss by 0,76.

All in all if you just have to defense you'd better put an even number of troops to defense to make it optimal. However, this applies relevant only up to 6 troops as after that the average loss of the attacker is 0,85 if the defense adds one.

Of course, this is just mathematics and the strategy might be sometimes different and you do not want to spread your troops. The only situation this is usable is the one when you have to defense for example Australia and you have 2 extra troops to spread over Siam and Borneo. How is the optimal way - that's some easy thinking for yourselves. Also, in some escalting card games you might want to defense optimally.

One thing you are right - risk is the name of The Game!