Was the Death Penalty Really a Thing?

It's hard to say how coreographed individual combats were. Part of that is because outside rome, in particular, a people who were contracting with a gladiatorial troop would be using fighters who were very experienced and knew each other. That said, the roman audience didn't want to see something that looked rehearsed. They wanted to see a good, dynamic, dramatic, challenging show. So i think this is one that we've all seen in particularly in the films. But was the thumbs up thumbs down thing as for the death sentence? Was that actually a thing or is that just kind of made up for popular audiences in the films?