I'd argue that a colony at the bottom of our own ocean would survive literally any event of any magnitude, maybe except for a direct asteroid strike. In terms of survivability of the human race, that's a better project to start with - and of course then move on to other planets, but underwater/underground colonies would give us lots of insights into living in such environments permanently.

The pressure range range between vacuum, mars atmosphere and earth atmosphere is 10⁵Pa. The pressure at the bottom of the ocean is 10⁸Pa. Humans can survive the former with little more than strong tensile garment and a breathing apparatus, the latter requires massive, crumple-resistant pressure vessels around everything.

Finally someone with the sense to realize what difference an order of magnitude can make to a decision. Now lets compute how likely we are to die by an asteroid vs how likely we are to die being stranded on a barren, frozen rock 60M Km away from the nearest source of critical supplies.

That depends on your time horizon. Probabilities of catastrophic events tend towards 1.0 individually. But within the same time horizon you can keep it close to 0 with sufficient redundancy and recovery.

So the tradeoff would be risking a finite amount of human lives in the short term to reduce the risk of a total loss in the long term. I.e. over time it becomes fixed vs. fractional cost.

Fair point, but then we forgo learning how to build a rocket to leave this rock should there ever be a need.

Just....do both? Have a proper, city-size, self-sustaining colony on the bottom of the ocean, and at the same time keep developing rockets and vehicles to bring as much material and and many robots over to Mars as physically possible. Like, I don't think getting to Mars is an issue - we probably could send and even land someone on Mars within a couple years if we absolutely had to. But then the question is - what then? That's the hard problem.