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OrphanWilde comments on [Link] A rational response to the Paris attacks and ISIS - Less Wrong Discussion
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Their fundamental mistake wasn't pursuing; that was merely a symptom. Their fundamental mistake is that they either had no plan of their own, or abandoned that plan. Because had they not pursued, the Mongols would have harried them with regular raiding skirmishes, a tactic they excelled at.
Pursuing-or-not-pursuing is playing the game according to the rules your opponent has set. Your first act should always be to change the rules.
If the Mongols are running away in panic you should pursue since pursuers normally have a big advantage, if they are running away as part of planned strategy you should not.
What you should or should not do is better determined by whether or not it helps win the war than whether it helps win a battle. If pursuing causes your unit to leave the territory you should have been defending, the mere accident of another of their units stumbling across the undefended territory could lose you the war, without any planned strategy on their part.
It is insufficient to know their plans. You have to know your own.