It is incredibly unlikely that you will ever even see a wild mountain lion (a.k.a. cougar or puma), let alone be put in the position of negotiating your way out of an encounter safely. Pumas are incredibly reclusive creatures. They also aren't stupid: the vast majority of close encounters between pumas and humans end with a dead cat, and the pumas know it.
Since 1909, just 20 people have died as a result of puma attacks in North America, including Canada and Mexico. Five of those have been in California. That's an average of one person killed by a puma about every five years. For comparison's sake, about 62 people die each year from lightning strikes in the US: you're thus more than 300 times more likely to be killed by lightning than by a puma.
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This indicates that most people killed by pumas have acted in ways that make them attractive prey to big cats, whether by being small, noisy children moving in unpredictable ways, or by moving at a rapid clip. This is essentially the equivalent of dressing up as a bright red laser pointer dot, triggering reflexes in the lions with potentially unhappy results.
And thus the best way to avoid trouble with mountain lions is to avoid putting on that laser pointer dot costume. Keep from tripping those prey reflexes and you drastically reduce your chances of unpleasant encounters with North America's native lion. In other words:
- Don't hike, bike, or jog alone, especially during dawn, twilight, and nighttime hours.
- Stick to wide, established trails to reduce your chances of inadvertent ambush.
- Keep any small children close at hand and under control.
- Leash your dog.
- Absolutely do not run. Nothing triggers this predator's reflex like fleeing.
- Pick up small children.
- Stare the puma down. Make loud noises and try to look bigger by waving your arms. Put the kid you just picked up on your shoulders. Throw rocks or other objects, though be careful not to crouch down near the puma to pick up that rock, as I found out the hard way once.
- If the puma attacks you, fight back. Kick it, hit it with branches or hiking sticks or rocks, punch it.