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Hannibal was perfectly conscious, since the beginning, of what type of sacrifices his plan would have implied in terms of human lives and animal losses. But he also knew that the overall strategy would have created a major astonishment among the Roman generals. And, indeed, the overall plan was successful, it didn't create astonishment, it created chaos.
When Hannibal arrived near the Po River with the surviving army, he was able to defeat the Romans twice: in a cavalry fight near the river Ticinus (east of Turin) and after at the river Trebia (west of actual Piacenza).
He then continued further south in direction of Rome, while the chaos in Roman army became panic………….. and in March 217 b.c. (nearly one year after his march through the Alps) after having traversed the mountains called Apennines he defeated two entire Roman legions in a major battle near the lake of Trasimene.
At that point, Hannibal was really on the edge of defeating the Romans and very historian or military leader would agree that his series of victories were due to his audacious strategy and his leveraging of LOGISTICS as a KEY WINNING TACTIC. The surprise effect of invading Italy from the Alps was so strong that the Romans couldn't oppose any valid resistance to Hannibal progress towards the "Urbe".
Did he eventually win the war? No, he did not. The second punic war ended with the victory of the Romans.
Hannibal, the logistics military genius, made two major mistakes. First of all, he thought that the Roman league would fall apart once he had invaded Italy. It wasn't the case at all; nearly all Roman allies remained loyal and continue to fight against the invaders.
The second mistake was even worse. After having arrived at few miles from Rome, he didn't take the city but prefer to go further South to wait to get better re-organized. However, while wasting his time in negotiating with his government to get additional fresh troops, he under-evaluated the Roman organization capability and capacity. Infact, who benefit from the pause were indeed the Romans who, after 16 long years of fight with the enemy, ended up beating them in Zama.
But this is another story's chapter…………
