Risk Dice Odds: How Attacker and Defender Rolls Compare

In Risk, the attacker rolls 1, 2 or 3 red dice, the defender rolls 1 or 2 white dice, and the highest dice are compared in pairs. A tie goes to the defender. That tie rule is why rolling three dice against two gives the attacker only a slight edge, and why attacking with equal armies is close to a coin flip. As of October 2026, the rulebook below is the one Hasbro hosts at hasbro.com.

1. How a battle is decided, per the rulebook

Before rolling, the attacker and defender both announce how many dice they will roll, then roll at the same time. The attacker must have at least one more army in the territory than the number of dice rolled, so 3 dice need 4 armies there. The defender may roll 2 dice only with at least 2 armies on the attacked territory. The box holds 5 dice: 2 white and 3 red.

Then the rulebook says to compare the highest die each player rolled. If the attacker's is higher, the defender loses one army. If the defender's is higher, the attacker loses one army. With more than one die each, the two next-highest dice are compared the same way. In case of a tie, the defender always wins, and the attacker can never lose more than 2 armies on a single roll.

2. Odds of each single roll

Every figure below was computed by listing all possible dice outcomes (for example, 3 red against 2 white is 7,776 outcomes). The first number is how many armies the attacker loses and the second is how many the defender loses.

Two things stand out. First, a lone attacker die against a single defender die loses more often than it wins (41.7% to win), purely because of the tie rule. Second, the 3-versus-2 roll is the best the attacker can do against a defender who rolls two dice, and it still leaves the defender with a 29.3% chance of taking out two attacking armies.

3. Expected losses per roll

Averaging those outcomes: a 3 v 2 roll costs the attacker 0.92 armies and the defender 1.08, while a 2 v 2 roll costs the attacker 1.22 and the defender 0.78. The rulebook's own hint: the more dice you roll, the better your odds, but the more armies you may lose or have to move into a captured territory.

4. Odds of actually taking a territory

A territory is captured when the last defending army is removed. Suppose the attacker keeps rolling the maximum dice each time and never stops. Let "attackers" mean armies on the attacking territory minus the one that must stay behind. The table gives the chance of capturing against a given number of defenders.

These are rounded, so 100.0% means above 99.95%, not certainty. When attackers and defenders are equal in number, the attacker still wins slightly more than half the time once the numbers get large (50.6% at 5 against 5, 56.8% at 10 against 10), because the attacker rolls more dice per battle. At smaller sizes the tie rule dominates: 2 against 2 is only 36.3%, and 3 against 3 is 47.0%.

5. Armies you receive each turn

At the start of each turn, count your territories, divide by three and ignore any fraction: 11 territories give 3 armies, 14 give 4, 17 give 5, with a minimum of 3. You also receive armies for each continent you fully control at the start of your turn, using the chart on the board. Card sets trade in for 4, 6, 8, 10, 12 and 15 armies for the first six sets traded by anyone; after that each additional set is worth 5 more armies than the previous one (20, 25 and so on).

6. Key takeaways

• The attacker rolls 1 to 3 red dice, the defender 1 or 2 white dice, and the highest dice are compared in pairs.
• Ties always go to the defender, which is why 1 v 1 favors the defender 58.3% to 41.7%.
• Three dice against two win both armies 37.2% of the time and lose both 29.3% of the time.
• With equal numbers of armies in a long attack, the attacker has only a slight edge (50.6% at 5 against 5).
• Turn supply is territories divided by three (minimum 3), plus continent bonuses and card sets.