How I generate random numbers without any tools: come up with a sequence of ~5 digits, take their sum and look at its parity/remainder. (Alternatively, take ~5 words and do the same with their lengths.) I think I’d pretty quickly notice a bias in using just a single digit/word, but taking many of them gives me something closer to a uniform distribution.
Also, note that your “More than two options” method is non-uniform when the number of sets is not a power of two. E.g. with three sets the probabilities are 1⁄2, 1⁄4 and 1⁄4.
How I generate random numbers without any tools: come up with a sequence of ~5 digits, take their sum and look at its parity/remainder. (Alternatively, take ~5 words and do the same with their lengths.) I think I’d pretty quickly notice a bias in using just a single digit/word, but taking many of them gives me something closer to a uniform distribution.
Also, note that your “More than two options” method is non-uniform when the number of sets is not a power of two. E.g. with three sets the probabilities are 1⁄2, 1⁄4 and 1⁄4.