except the bank will lock your online access after a set number of failed logins, typically three.
the only limit to how many guesses you can try for bitcoin private key is your computational power.
True, but let's put some math to that for any newbies reading this who might be worried.
Let's say my online bank password is truly random and drawn from the full 95 character ASCII set. Something along the lines of c"AQ+K78[={2W+9t, for example. (In reality, this is significantly more secure than the VAST majority of passwords which are being used, but we will error on the side of caution.) If someone has 3 attempts, then the probability of them guessing my password is 3 out of 95
16, which is a probability of 6.8*10
-32. Given that there are 2
256 private keys, for someone to have the same probability of finding my private key, they would have to check 7.9*10
45 private keys. Even checking a trillion
trillion keys every second, it would still take 250 trillion years for them to do so. I'm happy to take those chances.
Also worth pointing out that the chance of someone guessing your credit card PIN or even your long credit card number is astronomically more likely than either of the above scenarios.
If someone finds one of your private keys (still impossible, but), he won't be able to steal an entire balance of HD-wallet.
It's always worth noting the caveat to this - if you have revealed your extended public key (as you might do when setting up a watch only wallet), then the additional knowledge of the private key of one single address in that wallet would allow an attacker to calculate
all the private keys in that wallet.