So if you have a 51 to 49 percent bias on all your picks it still to the 24th power.
What number are you raising to the 24?
If there is 50.8% chance for heads and 49.2% for tails, then you can calculate the entropy like that:
H(X) = - P(heads) * log2(P(heads)) - P(tails) * log2(P(tails)) = - 0.508 * log2(0.508) - 0.492 * log2(0.492) = 0.999815327
So tossing a coin gives you 0.999815327 bits of entropy. If you toss it 256 times, it will give you 255.95 bits which are sufficient.