Risk Roll Calculator: Exact Dice Odds for Every Attack and Defence Combination
A single roll in Risk pits up to three attacking dice against up to two defending dice, with the highest dice compared in pairs and ties going to the defender. With three attackers against two defenders the attacker clears two armies about 37.2% of the time, loses two about 29.3% of the time, and trades one for one about 33.6% of the time.
How a Risk roll is resolved
- The attacker rolls one, two or three dice; the defender rolls one or two.
- Both sets are sorted highest first and compared pair by pair.
- The lower die loses an army, and the defender wins every tie.
- Only as many pairs are compared as the smaller side rolled — 3v1 compares just one pair.
The exact probabilities
- 3 vs 2 — defender loses 2: 37.17%; attacker loses 2: 29.26%; one each: 33.58%.
- 3 vs 1 — defender loses 1: 65.97%; attacker loses 1: 34.03%.
- 2 vs 2 — defender loses 2: 22.76%; attacker loses 2: 44.83%; one each: 32.41%.
- 2 vs 1 — defender loses 1: 57.87%; attacker loses 1: 42.13%.
- 1 vs 1 — defender loses 1: 41.67%; attacker loses 1: 58.33%.
Why the defender has the edge
Ties going to the defender is a small rule with a large effect. On a one-die-each roll the attacker wins only 15 of the 36 equally likely combinations. Rolling three dice against two swings the average trade back in the attacker's favour — the attacker loses about 0.92 armies per roll while the defender loses about 1.08 — which is why you should attack with the maximum dice whenever your army count allows it.
From one roll to a whole battle
A single roll tells you the immediate trade, not who takes the territory. Chaining roll probabilities across every remaining army state gives the campaign odds: roughly a 1.5x numbers advantage is needed for a comfortable conquest. Use this page for the per-roll decision — whether to press or stop — and the Risk global domination battle calculator for the full attack.
Key takeaways — Risk Roll Calculator
- Ties go to the defender, so 1v1 favours defence 58.3% to 41.7%.
- 3v2 is the attacker's best roll: 37.2% to clear two armies, 29.3% to lose two.
- Always attack with three dice when you have the armies; one roll never decides a territory.