You got 23 of your mother's 46 chromosomes, and your half-brother got a different set of 23 of your mother's 46 chromosomes. On average 11.5 of those chromosom

You got 23 of your mother's 46 chromosomes, and your half-brother got a different set of 23 of your mother's 46 chromosomes. On average 11.5 of those chromosomes will be the exact same ones -- that's 25% of your total DNA. With a full sibling of the opposite sex, you share about 11.5 of your mom's chromosomes (half of the 23 each of you got from mom will be the same) and 11.0 of your dad's chromosomes (11 of 22; you know the 23rd is different), for a total of 22.5 out of 46 which is 49%. If you're both the same sex, you share on average 11.5 of your mom's chromosomes and 12.0 of your dad's chromosomes (11 of 22, and you know the 23rd is the same), which makes you around 51% similar.