Well first I'm not sure you can quantify risk like a percentage.. it doesn't work like that. Next statistically speaking let's say it was 1%, after 50 dives it still is only 1%, but that 1% can hit you on the first diver the 49th or the 250th...
What you wrote is not what I said. Yes, your risk is still 1% each time, but your risk overall is greater with each repetition. These are difficult concepts to understand and to reconcile, but they are crucial for anyone engaging in risky activities. Think of a coin flip. Your odds of getting heads is 50% each time, but the odds of getting heads 10 times in a row is much smaller. Of couse, the odds of any set of outcomes (5 heads followed by 5 tails, alternating heads and tails, etc.) are equally slim, but half of the possible outcomes involve half heads, half tails, while 100% heads gets less and less likely the more times you do it. If tails means you die, you'd be a fool to take that bet even once, of course, but even if you did and got lucky, enough repetitions would surely kill you.
Now imagine you're playing Russian Roulette, but with a gun that has 100 chambers and just one bullet. And imagine you don't keep pulling the trigger, which would mean slightly higher odds each time as you use up the empty chambers, but rather you spin it each time, so you have a 1% chance of death each round. In 100 rounds, you would expect the gun to fire once. Maybe it wouldn't; maybe you'd get to round 150 without it going off. Maybe it would go off on the very first round. But even though your odds of death are still 1% each round, they're much higher over the long term if you keep doing it, just like your odds of getting at least one tail increase the more times you flip that coin.
I do think it's at least theoretically possible to quantify any risk as a percentage if you have enough data. I know I don't have anywhere near enough data to make even an educated guess regarding cave dives, and maybe nobody does. But I'm interested in hearing what the experts think.
One place in diving I've heard the 1% risk figure is in the use of dive tables or algorithms; supposedly the risk of getting bent if you dive right to the NDLs is about 1%. Of course, that's the generic you, as opposed to John with a hangover and an undiagnosed PFO, or Jane, with excellent bouyancy control and no history of injuries that might create nucleation sites for bubbles. But either of them would want to bear in mind that figure when planning their dives, because if they both dive 100 times per year and do each dive right up to the limits, they're both eventually going to get bent. If they keep their dives just a bit shorter and shallower, and increase their surface intervals a bit longer, they could reduce their odds to the point that you might expect only one incident per 10,000 or even 100,000 dives, which might give them a chance to die warm in their beds before their number is up.
Suppose for the sake of argument that a diver with good OW skills but no cave training had a 1% chance of dying in that particular cave, and suppose cave training would decrease his risk to .1%. But no one who goes through all that expensive training is going to stop at 10 cave dives. After 100 dives in that cave, the trained diver's risk profile might not be so good. (Of course, his risk would probably drop slightly each time as he gained experience with cave diving and with that particular cave especially, but at that point the math gets really complicated.) In some cases, a brief foray into a dangerous activity might be less risky than making it a regular thing. On the other hand, suppose training reduces your risk from 1% to .01% or even .001%. That would present a much stronger argument for getting the training rather than limiting your exposure, and I suspect that may be closer to the truth.
The other problem is, of course, that humans tend to be selectively rational about these things. Going back to the 1% for untrained vs. .1% for trained divers assumption, is the untrained diver really going to stop at one dive? Or is he going to go along, switching from "I'm managing my risk by not making this a regular thing" to "well, my risk is still only 1% each time," to "I've done this ten times already; I obviously know what I'm doing." That's what I was hinting at in the end of my post addressed to the OP. Being 1% right about risk can sometimes be more dangerous than being 100% wrong.