Overconfidence has long been considered a cause of war. Like other decision-making biases, overconfidence seems detrimental because it increases the frequency and costs of fighting. However, evolutionary biologists have proposed that overconfidence may also confer adaptive advantages: increasing ambition, resolve, persistence, bluffing opponents, and winning net payoffs from risky opportunities despite occasional failures. We report the results of an agent-based model of inter-state conflict, which allows us to evaluate the performance of different strategies in competition with each other. Counter-intuitively, we find that overconfident states predominate in the population at the expense of unbiased or underconfident states. Overconfident states win because: (1) they are more likely to accumulate resources from frequent attempts at conquest; (2) they are more likely to gang up on weak states, forcing victims to split their defences; and (3) when the decision threshold for attacking requires an overwhelming asymmetry of power, unbiased and underconfident states shirk many conflicts they are actually likely to win. These “adaptive advantages” of overconfidence may, via selection effects, learning, or evolved psychology, have spread and become entrenched among modern states, organizations and decision-makers. This would help to explain the frequent association of overconfidence and war, even if it no longer brings benefits today.