Did you know that if you're colorblind, you might actually be able to find the blue ball more easily than someone who can see colors? Let me teach you a trick: ask someone to assign a number to each ball, then apply a hash function to each number, and stick a label with the hash on the ball (the hash function must not be rigged).

Then, ask that person to give you the hash of the red ball, the winning one! Of course, since you're colorblind, you can't see colors, you can only read the hashes, but now you know which one is the winner.

At that point, to find the blue ball, you divide the N balls into blocks. When you find a hash in a block that starts with the same first X bits as the winning one's hash, you discard that whole block, because that prefix was already used in the block, and it's very unlikely that another ball in the same block would share it, unless the hash function is rigged.

With this method, you'll find the blue ball faster, thanks to uniform distribution, 1st grade math, and probabilistic search. But it works only if you’re not checking all the balls, because if you do that, then you don't gain any statistical advantage. And it only works if you're colorblind and can use hash functions and prefixes, if you can see colors, then you're stuck with the classic, old, and outdated probabilities of a uniform distribution.