The Battle of Zama took place near Carthage on October 18, 202 B.C. It was a battle between Carthage and Rome. The Romans were commanded by Scipio and Hannibal commanded Carthage's troops.
Army sizes:
Carthage: Infantry 36, 000
Cavalry 4,000
Elephants 80
Rome Infantry 30,000
{Cavalry] 7,000

The order of Battle X == Infantry, C == Cavalry, D == Elite Units, And E == Elephants

               X  X  X  X  Triarii
 Massinissa    X  X  X  X  Principes
      C        X  X  X  X  Hastati     C Laelius
               D D D D D D Velites

                 E E E E  
    C          X  X  X  X  Mercenaries  C 
  Numid.       X  X  X  X  Punic        Punic
               X  X  X  X  Vetrans

The elephants were ordered to charge first. The elite roman units stepped aside revealing a checkbox patern, which is effective in decimating elephant cavalry. Hannibal, who could not see the progress of the battle because of the dust raised by his elephants, ordered his mercenaries forward. At the same time the roman Cavalry charged forward eliminating the Hannibal's cavalry. The mercanaries were easily defeated by the fresh roman troops, and when they broke, they tried to cut their way through the Punic Infantry, wasting Carthage's troops. Sicipo split his troops, creating a broad line, a bold move because it increases the likely hood that the line will be broken. Hannibal attacked with his Vetrans. The romans resisted, and the battle was ended when the Roman cavalry returned encircling Hannibal's army. Hannibal was able to break through and escape with a few of his troops but Carthage's army was broken.

Carthage lost this battle, the Romans had adjusted their battle tactics to compensate for the elephants which were used so effectively in The Battle of Canae.

From an Email that I received:
The checkbox pattern of Scipio Africanus' infantry was to allow Hannibal's elephants room to run without overrunning Scipio's infantry. Remember the typical infantry formation of that era was a massed formation, with cavalry to the flanks. Also I believe Scipio had trumpeters with his army who allowed the elephants to get close then they sounded their horns. This caused the elephants to panic and charge back through Hannibals lines, stampeding his massed infantry lines.

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