The probability of 8 consecutive heads in 128 coin flips is about 1 in 5. I checked a SHA-2 256-bit hash in binary and indeed saw 8 consecutive 0s in the output

The probability of 8 consecutive heads in 128 coin flips is about 1 in 5. I checked a SHA-2 256-bit hash in binary and indeed saw 8 consecutive 0s in the output. If what you are saying were true than one could expect the probability of one bit in the key to depend on the previous bit.