Does anyone have the exact numbers of how much protection you get using a 24 word seed vs using the conventional default standard that shows up automatically when you create a wallet in Electrum?
It's still not clear to me that you can trust this type of wallet, that could be bruteforced and then all of your keys are compromised forever as long as you keep creating them on that wallet. It still seems safer to use a wallet.dat file. I want to see the math.
Here's the basics. Using the 2048 word BIP39 list, each word represents 11 bits of entropy (2**11 = 2048). So a 12 word phrase has 132 bits of entropy, and therefore a 24 word phrase has 264 bits of entropy.
Looking at a 12 word phrase, that means there are 2**132 possible combinations = 5.444 x 10**39 possibilities.
A 24 word phrase has 2**256 possibililties, or 1.158 x 10**77
If you want to go the distance on this analysis, you can do the math as to how long either would take, assuming some # of guesses/second.
Either should give you comfort.
If you want to consider phrases other than 12 or 24 words, as long as you're using the BIP39 list just remember: #bits of entropy = #words * 11
and number of possible phrases = 2**(#bits of entropy)