Using the gun analogy - it depends on what those odds INCREASE to. If they increase by .1% and go from 0.01% to 0.11%, it's a DRAMATIC increase - 10 fold. However, what that really means is the odds of hurting someone go from 1 in 10,000 to 11 in 10,000 - it's not a big deal. Put it another way - if the odds of losing your money in vegas were 11 in 10,000 versus 5002 in 10,000, why would you ever leave?
It's not just understanding the odds change, but how much they change and where they change from - everything has to be understood as much as possible to make a value decision. That includes probability and impact. Just one isn't sufficient to make an informed decision.
BTW, if you've seen a cop show, you know how to fire a gun - insert clip, rack it back, and start firing. The bullets come out going very fast, so be careful where you point it.
Regarding an overhead environment - one thing we have to remember is we effectively dive with an overhead environment on dives below 40 feet. That surface looks really tempting when you breathe all 3000 psi from your 100s at 75 feet, but that's just as lethal as out of air in a cave - and a situation well within the OW parameters. I'll leave the "worse way to go" discussion for another thread.
Having gotten back from cenote diving in an overhead environment, I'd say the factors for danger for me would be:
Max and min visibility
Bottom conditions
Map availability
Route marking and familiarity
Quality and experience of guide
Previous safety/track record of site
Previous safety/track record of diving organization
All of these factors were determined by me before I got on the plane. I memorized the routes and had my own back up gear that I knew and trusted, and did field checks prior to the dives. In fact, the dive guide used my materials to do the group briefing because I accessed information that wasn't easily available to them.
That being said, I'll get cave certified before I try a serious wreck penetration course. But for cavern dives, even in low vis? Give me my lights, a line, compass, and the natural experience of 6 inch vis in the lake in my backyard, and I'm good.