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Repel is how Dominions represents the effectiveness of long weapons, such as halberds, pikes, and the like. If a unit attacks an enemy who has a longer weapon than the attacker, the defender may actually repel the attack and prevent it from happening. This occurs as follows:
This simulates the defender successfully placing his longer weapon between himself and the attacker. All of this occurs before the attacker’s strike is resolved. Note that units with low morale are more likely to be repelled, and thus using long weapons against low-morale troops is very effective. Also, units with claws and bites (weapon length zero) are easier to repel.
The result of the repel attack roll is carried over to the morale check. This means that units with low defense will often get repelled even if their morale is high. In theory it's even possible for thugs with extremely high attack values to repel mindless units (who has morale 50 and are normally immune to repel) but that is unlikely to happen in a normal game.
Bear in mind that the defender gets one repel roll per weapon regardless of the number of attacks of that weapon. So a Dancing Trident is just as good at repelling as a Stone Bird