Interesting to see this incorrect line of reasoning about risk laid out so explicitly.

If you're around people who do extreme sports with serous risk, you'll know many people who have this attitude and you'll also know many people who incurred life-altering injuries or died because of this attitude.

A friend of mine who's reasonable and has a higher risk tolerance than me used to paddle with a group of whitewater kayakers who were doing the hardest stuff. 4 out of 7 of them died. She says

the reason she's still alive and so many of her compatriots are not is how she thinks about risk.

People would say things like "there's a 99% chance this will be fine", where "not fine" is fatal and they would then run something that had a 99% chance of working out. She wouldn't do that because, of course, if you regularly take a 1% chance of death, you're going to end up dead unless you're extremely lucky.

Another one is that she would never run something she hadn't observed before, whereas

most people around her would, using the same reasoning as the above. But if you do that often enough, you're not likely to live.

She has a similar attitude when backcountry skiing and would never take a drop of more than a few feet without having inspected it first, which is why she's never been seriously injured in the backcountry, but she's had to carry a partner back who landed on unexpected terrain and broke both legs, a rare occurrence per instance but not unlikely in the long run.

She is also not dead after many years of fairly serious mountaineering where partners would be extremely upset that she wanted to turn back because she thought that were a small chance of weather that would cause an attempt at summitting to be fatal.

If you're around a lot of mountaineers or other people doing high-risk activities, you'll hear about deaths every year because the cumulative impact of summing up small risks is counterintuitive and default human intuition for this is wrong.

@danluu I think people are not so much bad at estimating these things as just talking themselves into doing very risky stuff because otherwise many of the things they want to do are impossible.

@samth If that's the reasoning, that also seems wrong to me because being crippled or dying really puts a damper on both skill development and future chances to accomplish something, e.g., if you look at what people are doing in whitewater today vs. 20 years ago, people are now doing stuff that would've been considered impassable 20 years ago. It would've been more effective to not take fatal risks.

And for things like blind drops / runs, there's no upside in terms of what you can accomplish.

@danluu Sure, but (a) if you're 23 and want to accomplish something big "wait 20 years" doesn't really work. And (b) for some things like base jumping or alpine-style mountaineering on big mountains accceptable levels of risk aren't really possible.
@danluu For example, consider Alex Honnold's free soloing. The way he talks about it is exactly what you criticize. But there's no way to do what he does "safely".