Based on checksum length, the chance is 1 in 2^4 for 12 words and 1 in 2^8 for 24 words. If you want 1 in 4 billion chance, the checksum length should be 36-bit which equal 3.2727 4 words.
wait so it is useless as an error detection tool? any mistake you make in one of the words there's a 1 in 16/1 in 256 chance it will not raise any flag and be happy to let you use that set of words. if that's the case then i'm not sure what purpose it serves.