If a venomous snake and a lion/ big cat fight, who is likely to win?



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Let me answer one question at a time. 1. Yes they do encounter each other in the wild. Snakes mostly try to avoid lion/big cat. Lion/big cat, out of curiosity, and not with a motive to fight may piss off the snake. 2. If it comes down to both fighting with each other, as you already mentioned, venom will have a say. But, because of the size of lion/big cat, venom will take some time to have an effect on the lion/big cat. And by that time it will be curtains for the snake.
Recently a white tiger was killed by a snake bite(Indian Cobra) in a zoo in Indore. The zoo officials found that the snake was also paralyzed as a result of the encounter. (Story: Rare white tiger dies from snake bite in zoo - AOL.com). So if a venomous snake and a lion/ big cat fight, snake won't escape unharmed. But lion's fate will depend on how potent the venom is.