When the Romans besieged Syracuse, they were thwarted not by a larger army, but by the futuristic war machines of Archimedes. His catapults, giant claws, and missile launchers created a technological moat that neutralized overwhelming conventional force, showing that superior innovation can be a decisive strategic advantage.

Despite commanding armies of tens of thousands, Inca generals were so disoriented by the unheard-of capture of their divine emperor that they offered no resistance. This complete bewilderment allowed a handful of Spaniards to dictate terms to a vastly superior force.

Focused on winning his civil war, Atahualpa fatally misjudged the Spanish. He saw the small group as a potential asset—a source of mercenaries, horses, and superior swords to be captured and repurposed. He never considered them an existential threat to his empire, which sealed his fate.

The Spanish didn't defeat the Inca Empire at its height. They arrived after a smallpox epidemic killed the emperor and a subsequent brutal civil war between his sons shattered the empire. This left the civilization politically fractured and militarily exhausted, making it ripe for conquest by a small force.

Despite their aggressive plan, the psychological toll on the 168 Spaniards facing an army of thousands was immense. A firsthand account reveals their sheer terror, noting that many "urinate without noticing it out of pure terror" while waiting in hiding for the ambush to begin.

Joan's success relied on an "infectious bravery" that inspired demoralized troops and overrode the caution of veteran commanders. She consistently pushed for aggressive attacks when professionals advised delay. This highlights how a leader's conviction and confidence can become a tangible strategic advantage, transforming a unit's psychology and capacity for risk.

Military technology often evolves incrementally. However, a breakthrough like the Maxim machine gun can suddenly render centuries of established doctrine—such as the drilled infantry charge—completely obsolete. This creates a strategic crisis that forces an equally radical technological and tactical response, like the tank.

To project absolute strength, Atahualpa engaged in psychological warfare against his own men. After he remained stoic as a Spanish horse breathed on him, he ordered the execution of soldiers (and their families) who had flinched, brutally enforcing a public code of fearlessness.

Francisco Pizarro's invasion of Peru was heavily influenced by the recent success of his cousin, Hernán Cortés, in Mexico. The fall of the Aztecs provided a tangible model for conquest, proving that small bands of conquistadors could topple vast empires. This precedent made it easier for Pizarro to secure funding and royal support.