I think the most common understanding nowadays is that, rather than live or die, it had another meaning. Basically if defeated, the loser was expected to be killed, and the thumbs up or down sign merely indicated whether the soul went to hades or up to heaven
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Hades was a Greek god ..
When you die ("you" being a good Roman of the Religio persuasion), you are escorted to the River Styx by spirits. There, you and the other recently life-challenged are met by Charon, the ferryman. A coin, an obolus, will have been placed in your former body's mouth to pay Charon (although an aurus gets you a better seat in the boat, some believed). This payment is not representative of money so much as of the relationship between god and man, acknowledging your debt to the gods and their protection and guidance to you.
On the other side of Styx, you will pass Cerberus, the three-headed watchdog belonging to Father Dis, god of the Underworld. Cerberus will be friendly