[std_throwaway]

Is there a known probability curve?

With so many actors it could be very steep. Like 51% capacity has 99% chance of success and 49% has 1% of success and 40% has practically zero chance (these are made up numbers).

It could also be quite shallow as in 1% capacity gives you 1% of success... that would actually be quite bad and invite malicious actors to test the system with regular attacks.

[im3w1l]

It's a race of who can get to N blocks first. The higher N the "steeper" it is. N is set by the merchant so as to balance security with quick transactions