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.
Dan Luu
Taiki