Gaming · Board game odds
Risk battle odds calculator.
Enter the armies in your attacking territory and the armies defending, and the calculator plays out every possible dice roll to the end. It uses the Hasbro rulebook: the attacker rolls up to three dice and must leave one army behind, the defender rolls up to two, and the defender wins ties. Example: 10 armies attacking 8 defenders wins 64.6% of the time; the attacker is expected to lose 6.0 armies and the defender 6.8.
Your numbers
Result
Working out the result.
How the Risk battle odds are calculated
The Hasbro rulebook (B7404) sets the dice rules: the attacker rolls one red die per attacking army, never more than three and always leaving one army behind; the defender rolls one or two blue dice whatever the army count; the highest dice are paired, extra dice are ignored, and “in case of a tie, the defender always wins.” This page enumerates all 6n dice combinations for each roll type, which gives exact per-roll odds, then steps through every (attackers, defenders) state until one side runs out. Nothing is simulated, so the same inputs always give the same answer.
The attacker count on this page is the number of armies standing in the attacking territory, because that is what players actually know at the table. With 10 there, only 9 can roll in total, and the fight ends when the attacker has taken every defending army or is down to the stopping number you set.
Worked examples with real numbers
- One roll, 3 dice against 2. Of the 7,776 equally likely outcomes, the defender loses both armies in 2,890 (37.2%), each side loses one in 2,611 (33.6%) and the attacker loses both in 2,275 (29.3%).
- 5 against 5. Four attacking armies can roll, because one must stay. The attacker wins only 35.9% of the time, even though the armies are equal, because every tie goes to the defender.
- 10 against 8. The attacker wins 64.6%. Reaching 90% against 8 defenders takes 15 attacking armies; 50% takes 9.
- 10 against 10. The attacker wins 48.0%, close to even but still just short of it.
- 20 against 15. The attacker wins 82.2% and is expected to lose 12.2 armies on average.
Chance the attacker wins, fighting to the end
| Attacking armies | v 5 defenders | v 10 defenders | v 15 defenders |
|---|---|---|---|
| 5 armies | 35.9% | 5.7% | 0.7% |
| 10 armies | 87.3% | 48.0% | 17.3% |
| 15 armies | 98.5% | 83.5% | 53.8% |
| 20 armies | 99.9% | 96.5% | 82.2% |
What one roll does
Each row is a single roll for the dice counts shown (attacker v defender). The 2 v 2 and 3 v 2 rows reproduce the table in MIT OpenCourseWare's “Strategy of Risk” paper to the decimal place printed there.
| Dice | Defender loses 2 (or 1) | Each loses 1 | Attacker loses 2 (or 1) |
|---|---|---|---|
| 3 v 2 | 37.2% | 33.6% | 29.3% |
| 2 v 2 | 22.8% | 32.4% | 44.8% |
| 1 v 2 | 25.5% (defender loses 1) | — | 74.5% (attacker loses 1) |
| 3 v 1 | 66.0% (defender loses 1) | — | 34.0% (attacker loses 1) |
| 2 v 1 | 57.9% (defender loses 1) | — | 42.1% (attacker loses 1) |
| 1 v 1 | 41.7% (defender loses 1) | — | 58.3% (attacker loses 1) |
What this calculator leaves out
It models the standard rules only. It ignores territory cards, continent bonuses, mission cards, fortifying after the battle and any house rule. It assumes the attacker always rolls the maximum three dice and, unless you pick one die, the defender always rolls two, which the rulebook notes gives the better chance of winning each roll. Some published variants differ: Wikipedia notes the Italian RisiKo! lets the defender roll up to three dice, which this page does not cover. Fan-made tool, not affiliated with Hasbro.
Common mix-ups
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Often assumedA fight with equal dice on each side is an even contest.
What the source saysThe rulebook says that in case of a tie the defender always wins. In the published single-roll table, two attacking dice against two defending dice cost the attacker both armies 44.8% of the time and the defender both armies only 22.8%. [1] [2]
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Often assumedThe defender can roll as many dice as they have armies, so a big stack defends with three.
What the source saysThe rulebook says that no matter how many armies the defender has in the territory, they can defend with only one or two. [1]
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Often assumedAn attacker with 10 armies in a territory can attack with all 10, or with the last army if it has to.
What the source saysThe rulebook says that no matter how many armies you have in a territory you can attack with only one, two or three, and that you must always leave at least one army behind so the territory is never empty. [1]
- Hasbro: RISK game rules (B7404, en-us)
- MIT OpenCourseWare ES.268: Strategy of Risk (per-roll probability table)
Checked against these sources on .
Frequently asked questions
How do you calculate Risk battle odds?
List every dice outcome for each roll, then follow every path until one side has no armies. This calculator does that exactly. For 10 armies against 8 defenders it gives the attacker a 64.6% chance of taking the territory.
Do ties go to the attacker or the defender in Risk?
The defender. The Hasbro rulebook says that in case of a tie the defender always wins. That is why 5 attacking armies against 5 defenders wins only 35.9% of the time.
How many armies do I need to take a territory in Risk?
Against 8 defenders, 9 armies is the first count that wins at least half the time and 15 reaches 90%. Against 10 defenders, 14 armies reach 75%. The calculator shows the counts for 50, 75 and 90% for whatever defenders you enter.
Is it better to roll three dice or fewer in Risk?
The rulebook notes that the more dice you roll, the greater your odds of winning the battle, but also the more armies you may lose. Wikipedia adds that attacking with fewer dice can be useful to avoid leaving a dead-end territory.
Why does the attacker count include the army that stays behind?
You cannot leave a territory empty, so one army always stays and can never roll. This page counts every army in the territory because that is the number you see on the board, and it reduces the dice for you.
Does this work for other versions of Risk?
It follows the standard Hasbro rules. Variants differ: the Italian RisiKo! lets a defender roll three dice, according to Wikipedia, and many house rules change tie handling or dice limits, so check yours before relying on the percentages.
Sources
Retrieved
- Hasbro RISK rules, B7404 (en-us) — dice counts, one army must stay, highest dice paired, defender wins ties, attacker never loses more than two per roll (read 2026-10-26)
- MIT OpenCourseWare ES.268: The Strategy of Risk — table of per-roll outcome probabilities used to check this code (read 2026-10-26)
- Wikipedia: Risk (game) — RisiKo! variant where the defender may roll three dice (read 2026-10-26)
Fan-made tool for the standard Risk dice rules
Not affiliated with Hasbro. Risk is a trademark of its owner. The percentages are exact for the rules stated above as read on 26 October 2026. Nothing you type is sent or stored.