The Mongol Calvary under the command of Genghis Khan unexpectedly runs away. The enemy can't figure out why but doesn't worry about the Mongol's motivation and starts pursuing . An hour later, at a spot carefully prepared last night, the Mongol cavalry turns around and catches the enemy on ground that maximizes the Mongol advantage over its enemy.
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.
Here's my op-ed that uses long-term orientation, probabilistic thinking, numeracy, consider the alternative, reaching our actual goals, avoiding intuitive emotional reactions and attention bias, and other rationality techniques to suggest more rational responses to the Paris attacks and the ISIS threat. It's published in the Sunday edition of The Plain Dealer, a major newspaper (16th in the US). This is part of my broader project, Intentional Insights, of conveying rational thinking, including about politics, to a broad audience to raise the sanity waterline.