The other person gets bit

I believe, you have to take turns pushing down individual teeth. By random chance, it will close the mouth when you do that. So, you lose when you get bitten.

they probably have a powerful immune system to deal with decaying matter, or carrion. also because they constantly replace thier teeth, caries and gum disease is less of an issue for them, as they wont get tartar or bacteria getting trapped in thier teeth.

At least one person gets it

Alligators are ornery because they got all them teeth and no toothbrush