How Risk dice work
- The attacker rolls up to 3 dice (one fewer than the armies on the attacking territory). The defender rolls up to 2.
- Compare the highest attacker die with the highest defender die, then the second highest of each if both rolled two or more.
- The higher die wins each pair, and the defender wins ties. Each lost pair costs that side one army.
Press Roll for one roll, or set both armies and press Battle to the end: the roller keeps attacking with the most dice allowed until the defender is gone or the attacker has 1 army left.
Odds for one roll
Counted over every way the dice can land. With one pair compared, the loser loses 1 army; with two pairs, each pair costs 1 army.
| Dice (attacker vs defender) | Attacker wins every pair | Each side loses 1 | Defender wins every pair |
|---|---|---|---|
| 3 vs 2 | 37.2% | 33.6% | 29.3% |
| 3 vs 1 | 66.0% | not possible | 34.0% |
| 2 vs 2 | 22.8% | 32.4% | 44.8% |
| 2 vs 1 | 57.9% | not possible | 42.1% |
| 1 vs 2 | 25.5% | not possible | 74.5% |
| 1 vs 1 | 41.7% | not possible | 58.3% |
Odds of winning a battle
The chance the attacker wipes out the defender, attacking with the most dice every time. Attacking armies include the one that must stay behind:
| Attacking armies | 1 defender | 2 defenders | 3 defenders | 4 defenders | 5 defenders |
|---|---|---|---|---|---|
| 3 | 75.4% | 36.3% | 20.6% | 9.1% | 4.9% |
| 5 | 97.2% | 78.5% | 64.2% | 47.7% | 35.9% |
| 6 | 99.0% | 89.0% | 76.9% | 63.8% | 50.6% |
| 8 | 99.9% | 96.7% | 91.0% | 83.4% | 73.6% |
| 10 | 100% | 99.0% | 96.7% | 93.0% | 87.3% |
As a rule of thumb, attack with at least one more army than the defender has, and the more armies on both sides, the more the attacker's extra die pays off.
Wheel Mango is not affiliated with Hasbro. Yahtzee and Risk are trademarks of Hasbro.
Questions
Who wins a tie in Risk?
The defender. When the attacker's die equals the defender's die, the attacker loses that army.
How many dice can each side roll?
The attacker rolls up to 3 dice but must leave one army behind, so 3 dice need 4 armies. The defender rolls up to 2.
What are the best odds for the attacker?
3 dice against 1: the attacker wins that roll 66% of the time. Against 2 defending dice, 3 attacking dice win both pairs 37.2% of the time.
Is the roller fair?
Yes. Every die uses your browser's secure random numbers, so each face is equally likely.