| Probabilities of winning a dice roll in Risk (various die combinations) | Attacker | ||||
|---|---|---|---|---|---|
| one die | two dice | three dice | |||
| Defender | one die | Attacker wins | 41.67% | 57.87% | 65.97% |
| Defender wins | 58.33% | 42.13% | 34.03% | ||
| two dice | Attacker wins | 25.46% | 22.76% | 37.17% | |
| Defender wins | 74.54% | 44.83% | 29.26% | ||
| Both win one | n/a | 32.41% | 33.58% | ||
Here's a chart I got from Wikipedia. According to this, the attacker always has the advantage statistically. This chart excludes the use of 8-sided dice as well.

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