If the car oversteers, just let go of the steering wheel. The car will probably sort itself out for you. If you still hit something, then you would have hit it using the advice given in the above videos, so you're no worse off.
I think 90% of people that would actually lose control in the first place on the road would not be capable of recovering, so to tell them to just hit the brakes and slow the car as much as possible is probably the right thing to do.

Lots of dubious advice posted about fwd cars being able to "power out" of an excessive oversteer moment and not to countersteer at all. Maybe if you're in some 200bhp+ hot hatch. Try "powering out" of a situation like that in a typical 80bhp family car at 70mph. The weight transfer when you press the go pedal at those speeds is next to nothing, let alone the idea that you could spin the front wheels like a touring car driver to straighten up.
Quote from tristancliffe :If the car oversteers, just let go of the steering wheel. The car will probably sort itself out for you.

That's a little gem of information that I'm surprised isn't emphasized more. You always hear about countersteering and this and that, but no one ever seems to make mention of the fact that the car will DO the countersteering FOR you if you just let the wheel slip through your hands. The only time people ever learn this is when I sit them down in front of LFS, lol.

Pretty sure if more people learned that, there'd be fewer accidents.
The ideia of letting go the steering wheel looks scaring I understand the idea, but as Tristan says, probably it will sort itself, or not

Anyway, most people on the road simply don't react and do nothing because they were never in a situation like that. Here, in driving classes they don't talk or practice emergency situations... so no experience whatsoever
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