Hannibal wins Zama

Nothing, because he's in no room to make Rome do anything by Zama. Even if the Romans don't launch another invasion, Carthage has lost by this point.
 
Carthage gets peace on slightly better terms than before. And by that I mean they might be allowed to actually keep some small army. The Fabians would have the power in the Senate with Scipio's loss, so I'm skeptical another army would be sent. But the war is already lost for Carthage at this point.
 
Rome sends another army and Hannibal loses.

Nothing, because he's in no room to make Rome do anything by Zama. Even if the Romans don't launch another invasion, Carthage has lost by this point.
But whether Rome sends another army or not has implications. Scipio Africanus was criticized for not razing Carthage to the ground OTL. If Carthage is destroyed ~200 BCE in the Second Punic War, that obviously butterflies away the Third Punic War in 149 BCE. Scipio Africanus (if he survives) will have a very different later career as will those who would have been involved in the Third Punic War.

Alternatively, if Rome decides to negotiate a treaty under slightly more favorable conditions, it might change the circumstances under which the Third Punic War happens.
 
I doubt Rome would stomach a siege of Carthage. I imagine the third punic war is a good example of how a siege would look, except the Romans don't have a Scipio Aemilianus to get things in order.

Plus there's trouble brewing in the east. A big butterfly though, is what Hannibal does. He might have enough political capital and fame in Carthage to not be forced out of the city, and he had proven to be a great administrator after the war ended.
 
Carthage gets peace on slightly better terms than before. And by that I mean they might be allowed to actually keep some small army. The Fabians would have the power in the Senate with Scipio's loss, so I'm skeptical another army would be sent. But the war is already lost for Carthage at this point.

Not all potential loses are created equal. There is losing Carthage's European gains and that's that, or something like the end of the Third Punic War, or something like what happened IOTL.
 
This. By the time of the Battle of Zama, the Romans were basically unstoppable.

The Carthaginians would still lose yes, but the Romans, now firmly under the influence of the Fabians, might opt to just cut a peace deal instead of invading a second time. Maybe something that lets both Syphax and Massinissa rule a splintered Numidian Kingdom-Syphax had been captured by Scipio but was still alive and in his camp until his death in Rome after the triumph I believe.

Carthage may also have to supply grain to Rome's armies like in the OTL treaty, but the tribute might be lowered or gotten rid of. Hannibal might still have to flee into exile though.
 
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