Alexander of Macedon vs. Hannibal of Carthage

I originally posted this in ASB, but by request, I am reposting this theoretical battle here.

The scenario is Alexander is campeigning in the west, he has set up a siege against Carthage itself, but to meet him is Hannibal and his troops...

I will post a short story based on the outcome of the debate. Please give me a reasonable order of battle as wel.l
 
This belongs back in ASB. There is a 75 year seperation between the death of Alexander and the birth of Hannibal.
 
Alexander wins. Hannibal was (probably) the better general - he did amazing things coming back from a numerical and qualitative advantage in Italy - but in a head-on battle Alexander is more than good enough to hand Hannibal his own ass.
 
Hannibal's biggest victories, such as Lake Trasimene and Cannae, were built around finding suitable terrain and getting the enemy to attack him on his terms. Alexander was just as good at this, and also excelled at shifting his army to fight in various terrains. Alexander wins.
 
The Macedonian army is a well-balanced force of light infantry, medium phalanx pikemen and a small cadre of elite heavy infantry and superb heavy cavalry. the Carthaganians fought with whatever mercenaries were available. There were no Carthaganian sacred band after the first punic war.

So, the Carthaganian army will vary depending on where the war is fought. If the Carthaganians still hold (parts of) Sicily and try to prevent Alexander from taking Magna Graecia, they will probably have a lot of old-style Greek phalanxes, Italian cavalry and Samnite infantry. Perhaps a sprinkling of Balearic slingers and Carthagianian Cavalry can be added. If the Carthaganians have good sea communications (if their navy has not been destroyed in a first pubic war) you might see Iberian tribal sword infantry (excellent infantry) and Mauretanian and Numidian javelineers and cavalry.

However, the Carthaganians lack a force to meet both the Macedonian phalanx and the heavy cavalry (both Companions and Thessalians) of Alexander's army.

If Hannibal can draw the phalanx into rough and hilly terrain he might be able to get it to break up and send light infantry to attack through the gaps, but he won't be able to flank it, the Macedonain cavalry will prevent it. He might, if he is smart, be able to lure some Macedonian cavalry from the field himself (Alexander was very prone to go after the enemy leader), but the best he can do I think is a bloody draw - the Macedonian hammer-and-anvil army is just too high-quality and well-rounded to defeat when commanded by a competent commander and wehn all parts did what they were supposed to (the Macedonian defeat against Rome was when an incompetent King fled almost immediately and the cavalry being inactive or fleeing with the King).
 
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