Imprisoned by a madman a teen must argue her survive twelve times in a game where the loser of each round is murdered

Great suggestion. Thanks.

Good premise for a low budget contained thriller, but the details of the plot seem unclear.

I strongly suggest re wording the logline to describe the plot with more clarity. Perhaps re think your descriptions from a different dramatic point of view specific to the MC?
My try:
After waking up in a cage a teen must win 12 rounds of a deadly game or be killed by the mad man who imprisoned her and the other 11 participants.

Must argue why she shouldn't be killed. It is a complex game.

There are a group of 12 people locked in a cage. Each round one will die, chosen by the group.. if they can figure out who the traitor is, they all go free.

Told through the eyes of a prisoner.