Risk: how the dice combat really works

Risk is a game of world conquest decided by armies and dice. You reinforce, you attack neighbouring territories, and you try to hold continents for bonus armies. Every attack is resolved by rolling dice — and because the rules quietly favour the defender on ties, knowing the odds matters more than most players realise.

The dice and how combat works

Combat uses six-sided dice, coloured for attacker and defender:

• The attacker rolls up to three dice — one for each attacking army beyond the one that must stay behind. You need at least four armies in a territory to roll the full three.
• The defender rolls up to two dice — two if they have at least two armies defending, otherwise one.
• Each side sorts its dice highest-first. The highest attacker die is compared to the highest defender die, then the second-highest of each. The defender wins ties. Whoever’s number is lower loses one army per comparison.

Because you compare two pairs when both sides roll two or three dice, a single exchange can cost each side up to two armies at once.

The attacker-vs-defender odds

The tie-goes-to-the-defender rule sounds like it should favour defence, and in a single die-versus-die roll it does. But the attacker’s extra dice more than make up for it. In the most common big battle — three attacker dice against two defender dice — the outcomes of one exchange are:

On average the attacker loses about 0.92 armies and the defender about 1.08 per exchange — a real edge to the attacker as long as they can roll three dice. The picture flips when the attacker is down to one die: a lone attacker die against a single defender die wins only about 42% of the time (15 of 36 outcomes), because the defender takes the ties. You can feel this asymmetry by rolling three dice against two and comparing the top pairs.

Winning strategy

• Attack from strength. Keep enough armies stacked to roll three dice every exchange. A big army grinding a small one wins comfortably; small skirmishes are a coin-flip you should avoid.
• Know when to stop. The odds favour you only while you outnumber the defender. Once an attack has thinned your stack so you can no longer roll three dice, break off — do not throw your last armies into a fair fight.
• Hold defensible continents. Continent bonuses are the engine of the game. Australia (one entry point) and South America are the classic early targets because they are cheap to defend.
• Time your cards. Turning in sets of cards for escalating army bonuses can dwarf continent income late-game. Attack at least once per turn to earn a card, and cash in when the bonus is worth the exposure.

Common mistakes

• Attacking with too few armies. Rolling one or two dice throws away the attacker’s advantage. If you cannot bring three dice, you are usually better off waiting or reinforcing first.
• Over-extending. Conquering a long chain of territories leaves each one thinly held and easy to retake. Depth of stack beats breadth of map.
• Ignoring the tie rule. “Ties go to the defender” is why fair fights are bad for the attacker. Always aim to fight with more dice than your opponent.
• Forgetting to earn a card. Ending a turn without a single successful attack means no card — and cards are where the game-winning army bonuses come from.

Want another game where dice odds decide the board? See where to build in our Catan guide.