There are (on average) 128 words which will be a valid checksum for a 12 word seed phrase. It is 8 words (on average) for 24 word seed phrases.
Thanks for the correction.
But isn't that 128 words for the 12 word seed phrase and 8 words for the 24 word seed phrase?
Let's say I have the first 11 words of a 12 word seed phrase and the last word is unknown.
There are 256 possibilities for the first 8 bits of the last word and 16 possibilities for its last 4 bits.
There's
1/
256 chance that the first 8 bits of the last word I choose are 00000000.
There's
1/
256 chance that the first 8 bits of the last word I choose are 00000001.
There's
1/
256 chance that the first 8 bits of the last word I choose are 00000010.
.......
.......
.......
If the first 8 bits are 00000000, there are 16 possibilities for the last 4 bits that make the seed phrase valid.
If the first 8 bits are 00000001, there are 16 possibilities for the last 4 bits that make the seed phrase valid.
If the first 8 bits are 00000010, there are 16 possibilities for the last 4 bits that make the seed phrase valid.
......
......
......
The chance of having a valid BIP39 seed phrase in which the first 8 bits of the last word are 00000000 is
1/
256 *
1/
16.
The chance of having a valid BIP39 seed phrase in which the first 8 bits of the last word are 00000001 is
1/
256 *
1/
16.
The chance of having a valid BIP39 seed phrase in which the first 8 bits of the last word are 00000010 is
1/
256 *
1/
16.
......
......
......
Therefore the chance of having a valid BIP39 seed phrase is (
1/
256 *
1/
8) * 256.
That's always 1/16. (128 out of 2048 words)