Dice Rolling in Risk the Board Game - Probability of Winning a Roll
From StatWiki
In the board game Risk, which is produced by Parker Brothers, battles consist of two players rolling dice. The attacker can have up to 3 dice and the defender can have up to 2 dice, depending on how many armies each player is using in the battle.
The outcome of the battle is determined by comparing the results of the dice. Attacking and defending diced are paired off, beginning with the highest die from each player, and ending in the next highest die from each player. The player that controls the lower die in each pair loses an army; ties favor the defender.
The table below summarizes the probability of winning a battle in Risk.
| Probabilities of winning a dice roll in Risk | Attacker | ||||
|---|---|---|---|---|---|
| one die | two dice | three dice | |||
| Defender | one die | Attacker wins | 15/36 = 41.67% | 125/216 = 57.87% | 855/1296 = 65.97% |
| Defender wins | 21/36 = 58.33% | 91/216 = 42.13% | 441/1296 = 34.03% | ||
| two dice | Attacker wins | 55/216 = 25.46% | 295/1296 = 22.76% | 2890/7776 = 37.17% | |
| Defender wins | 161/216 = 74.54% | 581/1296 = 44.83% | 2275/7776 = 29.26% | ||
| Both win one | n/a | 420/1296 = 32.41% | 2611/7776 = 33.58% | ||
[edit] Source
"The Probability Distribution of Risk Battles" by Daniel C. Taflin, November 25, 2001. HTML version can be found here (last accessed on June 2, 2008).
The Wikipedia article "Risk (game)" was also used to build the table above.
