Risk Dice Odds

I’ve been playing a lot of the Risk Boardgame with my two boys recently. The game involves rolling dice to determine the outcome of a battle.

While it was always clear to me that the attacker has an advantage when attacking with three dice, I was curious about how great the advantage is so I wrote some JavaScript code to calculate the odds.

Risk Odds When Rolling 3 Dice against 2

When rolling 3 attacking dice against 2 defending dice.

attacker wins 2: 37.17%
attacker wins 1, defender wins 1: 33.58%
defender wins 2: 29.26%

The code I used to calculate these odds is available at github.com/salcode/risk-board-game-dice-odds.

Risk Dice Rules of Battle

The following explanation comes from gamerules.org.

How to Attack:

Begin by announcing where you plan to attack and what territory you are attacking from. Roll the dice against you opponent.

• Before you roll, both you and your opponent must announce the number of dice you plan to roll, and both you and your opponent must roll at the same time.
• Attacker, rolls 1, 2, or 3 red dice. The attacker must have at least one more army than the amount of dice they roll.
• Defender, rolls 1 or 2 white dice. In order to roll 2 dice, the defender must have two or more armies in their territory.

Deciding a Battle:

Compare the highest die rolled. If the attacker’s is higher, the defender loses one army. Conversely, if the defender’s is higher, the attacker loses one amy from the territory attacked from. If both rolled more than one die, compare the next highest pair and apply the same rules. In the event of a tie, the defender always wins. Also, the attacker can never lose more than two armies per roll.

Sal Ferrarello (@salcode)

Sal is a PHP developer with a focus on the WordPress platform. He is a conference speaker with a background including Piano Player, Radio DJ, Magician/Juggler, Beach Photographer, and High School Math Teacher. Sal can be found professionally at WebDevStudios, where he works as a senior backend engineer.