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This math is based on having 100% of the existing hash power (the network is 500H/s, you would need 500H/s) - in most cases you would probably purchase enough to give yourself a decent buffer above the existing hashing power. The numbers are meant as very rough estimates to give people a better idea of the costs.

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OK, so by 51% you really mean at least 50%. Do you happen to have a background in finance? It's quite unusual to say 51% in math/engineering.

"51% attack" is the name of the attack, but you don't actually need 51% of the hash-rate to do it, just 50% plus a small margin.

You dont need 50%. You can do it on 1% with luck.

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.

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

"51% attack" is a term of art in the blockchain field.

I see, the number in the name is not to be taken too literally.

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