Let's say the Roman general of the day, Varro, critically analyzes the battle plan and realize the Roman's strategy is a race against time. Can the inferior Roman cavalry on each wing hold out against the superior Carthage cavalry long enough for the Roman infantry to break through in the middle? Not liking his odds, Varro dispatches reserve Roman infantry to each wing directly behind and in support of the cavalry. So when the Roman cavalry is inevitably defeated, the Carthaginian cavalry has to face an extra line of defense before it can attack the vulnerable Roman rear.
The strategy works to perfection in that the Roman infantry break through the Carthaginian center, and it is the Carthaginian's who in turn are attacked on each wing and double enveloped in the process. Hannibal loses his life in the battle and goes down as a footnote in history; Varro, in turn, is hailed as a military genius.
The Carthaginian army is for all practical purposes wiped out and the Second Punic War comes to a conclusive end in the favor of Rome.