From [0] we can see that there are 10 banks founded before 1700 and 24 from 1700 to 1800.

So it might not be that far fetched, assuming that the banks keep your accounts open after more than 100 years without use.

[0] https://en.wikipedia.org/wiki/List_of_oldest_banks_in_contin...

Probably tiny?

Lloyds bank founded 1765

Barclays founded 1736

I doubt any banks in the new world are as old.

That's not the right question, though, because the expected rate of failure isn't constant throughout the lifetime of a bank. See, e.g., https://en.wikipedia.org/wiki/Lindy_effect

Seems like your best bet would be to park your money with several very old banks: https://en.wikipedia.org/wiki/List_of_oldest_banks_in_contin...

Also might want to think about purchasing bonds: https://en.wikipedia.org/wiki/List_of_oldest_banks_in_contin...

Bitcoin! :)

As pointed out by other commenters: a non zero number have survived. A small investment made with many different institutions would substantially increase your chances of a massive return upon... return.