[wahern]

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...

[wahern]

2nd link was supposed to be https://en.wikipedia.org/wiki/Perpetual_bond with information about a bond from 1648 with the issuer still paying annual interest.