Closest CallAttacker against defender dice odds
Up to three attacking dice against up to two defending dice, highest compared with highest, ties to the defender.
The rule this covers
In many territory-conquest board games the attacker rolls one, two or three dice and the defender rolls one or two. The highest die on each side is compared, then the second highest if both sides rolled at least two. The lower die in each pair loses a piece, and the defender wins ties.
| Dice (attacker against defender) | Defender loses | One each | Attacker loses |
|---|---|---|---|
| 3 against 2 | 37.2% (loses 2) | 33.6% | 29.3% (loses 2) |
| 3 against 1 | 66.0% | n/a | 34.0% |
| 2 against 2 | 22.8% (loses 2) | 32.4% | 44.8% (loses 2) |
| 2 against 1 | 57.9% | n/a | 42.1% |
| 1 against 2 | 25.5% | n/a | 74.5% |
| 1 against 1 | 41.7% | n/a | 58.3% |
What the chart tells you
- Three against two slightly favours the attacker. Over many battles the attacker loses about 0.92 pieces per roll and the defender about 1.08.
- Three against one is the attacker's best case: the defender loses 66.0% of the time.
- One against one favours the defender, who wins 58.3% of the time, because ties go their way.
- The tie rule is worth a lot. Without it, one die against one would be an even contest apart from ties being re-rolled.
- Rolling more dice always helps the attacker, which is why attacking with large numbers works and attacking with small numbers does not.
More dice odds
- Dice odds library: every chart in one place
- Two dice (2d6) odds chart
- Three dice (3d6) odds chart
- 4d6 drop the lowest: ability score odds
- d20 with advantage and disadvantage
- Five of a kind and other five-dice odds
- Two twenty-sided dice (2d20) odds chart
- At least one six in 1 to 10 rolls
- Dice calculator: the exact odds for any total with any number of dice, plus a dice roller.
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Every figure on this page was computed by counting all possible outcomes. Game names mentioned here are trademarks of their owners; this site is not affiliated with or endorsed by them.