In battles, opponents exhibit positive illusions in both believing they can win. With great costs of failure and uncertain success, this represents extreme risk-taking behaviour. Conflict may be expected if one side is cornered, a sacrificial pawn in an overall war strategy, or demanded into action by politicians. However, in many cases even patently weaker forces fight despite nonviolent options. This is "military incompetence", a failure in the assessment of winning probability. Previous explanations (stupidity, psychological deviance and cognitive constraints) have been rejected. Recently, Wrangham [Evol. Hum. Behav. 20 (1999) 3.] proposed that such risk-taking could be adaptive through one of two effects: (1) Performance Enhancement through exaggerated resolve or (2) Opponent Deception by bluffing. Although adaptive if they confer a tendency to win, both processes promote risk-taking behaviour and are therefore potentially responsible for military incompetence. These hypotheses can be distinguished because the Performance Enhancement hypothesis predicts positive illusions in any type of conflict. In contrast, the Opponent Deception hypothesis predicts them in battles but not in surprise attacks, where lack of communication disables any bluff. We conducted a test of these hypotheses using data collected by the US Historical Evaluation Research Organisation, mainly from the Arab-Israeli and Second World Wars. The Opponent Deception hypothesis is supported over the Performance Enhancement hypothesis, but other explanations are not ruled out.