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.
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.
I coded up a similar program and got very similar results
Attack wins 2: 37.16401%
Attack wins 1, defense wins 1: 33.59162%
Defense wins 2: 29.244369999999996%