Two gladiators enter the arena, one leaves, the emperor jerks a thumb down, the loser is killed where he lies. Every sword-and-sandal film runs on it, and the thumbs-down gesture is shorthand for doom. Roman blood sport, fought to the last man, every single time.
Death in the arena happened, but most matches were not fights to the death, for the same reason a footy club does not deliberately injure its star players. Gladiators were a serious investment. They were fed, housed, trained for years by a 'lanista', and a dead one was a write-off, so the owner had to be compensated if his fighter was killed. Estimates from inscriptions suggest a gladiator had a good chance of surviving any given bout, and many fought a few times a year and retired. Matches were refereed, fighters could yield, and a defeated man might be spared by the crowd and the editor running the games. Even the thumbs gesture is uncertain; historians are not sure which direction meant death. Brutal, yes. A guaranteed funeral, no.