Could Carthage have won the Punic Wars?

The first one, definitely. The second one it is possible; Rome had a big resource and manpower advantage, but Hannibal's campaign into Italy demonstrated its vulnerability, unfortunately he didn't have the men to capaitalize on it and Rome ultimately just raised more men to replace it's literally massacred armies, ultimately forcing Hannibal to withdraw. Carthage needs to be able to successfully muster the resources for Hannibal to be able to launch a decapitating strike on Rome itself, when he has the oppertunity (in OTL, he never had the men or resources to invade Rome directly which meant even when he was in Italy, decimating Roman armies, he wasn't a existential threat for Rome on a strategic level).

The third Punic War, no. Carthage was essentially just another Roman vassal at that time that wash crushed when it rebelled.
 
First Punic War:

Yes. The FPW was mostly a naval war and Carthage was the main naval power of the Western Mediterranean at that time, Rome had no navy before the war, so Carthage could win this one by cutting off the Roman armies in Sicily from reinforcements from mainland Italy. Ironically enough Rome ended up winning the war in the sea while Carthage managed to to force the land war into a stalemate. With some luck in some of the naval battles Carthage could win the naval war and then defeat the Romans by simple attrition.

Second Punic War:

Hard to say. The problem was that, as it could be seen during their previous wars, the Romans were more than willing to keep fighting long after others would had made peace, any other power of the day would had begged for peace after a Cannae-like disaster. Maybe if the Carthaginian Senate sends a fleet to block the port of Ostia and sends the needed men to Italy so that Hannibal can besiege Rome they can win, but doing that would allow the Roman armies in Iberia to make progresses there against Carthage and that would hit economically the Punic City, and then there's the problem that the Romans could gather men on the countryside and then attack the besieging army from the rear.

Possible but hard to guess how it would happen.

Third Punic War:

Nope. Carthage was screwed when this one started.
 
What other nations were in a good position to take advantage and attack Rome on other fronts?
The underdog can always use allies whether formal or just "The enemy of my enemy ".
 
What other nations were in a good position to take advantage and attack Rome on other fronts?
The underdog can always use allies whether formal or just "The enemy of my enemy ".

Hannibal sought an alliance with Phillip V of Macedon IIRC.

A Macedonian army landing in Italy and Hasdrubal successfully linking up with his brother would be an interesting butterfly.
 
The second one it is possible; Rome had a big resource and manpower advantage, but Hannibal's campaign into Italy demonstrated its vulnerability, unfortunately he didn't have the men to capaitalize on it and Rome ultimately just raised more men to replace it's literally massacred armies, ultimately forcing Hannibal to withdraw. Carthage needs to be able to successfully muster the resources for Hannibal to be able to launch a decapitating strike on Rome itself, when he has the oppertunity (in OTL, he never had the men or resources to invade Rome directly which meant even when he was in Italy, decimating Roman armies, he wasn't a existential threat for Rome on a strategic level).

Maybe if Philip of Macedon actually sends an army to Italy, it could link up with Hannibal, providing the Carthaginian general with the manpower he needs to attack Rome directly.
 
Hannibal's main problem was that he never had enough men to both secure his base of operations/protect his Italian allies and besiege Rome (and that the armies in Spain kept losing despite often outnumbering the Romans); as soon as he marched out from Campagna or Apulia, the Romans could march right in. If Hasdrubal had his army there in Southern Italy, he could protect Hannibal's while he reduced Naples or vice versa, while keeping interior lines for reinforcement. From Naples, Hannibal would be able to reach Rome in ~11 days march; if he captured Ostia, he would have a very close base of operations against Rome itself.
 
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