Are there algorithms for generating psychologically random numbers? [closed]

Question

True random numbers often don't seem random to the average person since randomly generated sequences will be interpreted as structure. Are there any algorithms that generate a set of numbers that psychologically "seem" random, even though they are not?

Answer 1

Here is an algorithm:

1. Use any Pseudorandom Number Generator to create a sequence of numbers that are not random (because they are pre-determined by the seed and algorithm).

2. Use a bunch of statistical tests from the Diehard battery (source) to disqualify sub-sequences that are subjectively and historically considered biased.

The output would be "numbers that psychologically "seem" random, even though they are not".

Also, there are cognitive models of human randomness judgement. One such model (of binary sequences) is based on Kolmogorov complexity, but it won't give you an algorithm because Kolmogorov complexity in not computable. However, it might give you more ideas on finding "psychologically random numbers".

Abstract

We present a statistical account of human randomness judgments that uses the idea of algorithmic complexity. We show that an existing measure of the randomness of a sequence corresponds to the assumption that non-random sequences are generated by a particular probabilistic finite state automaton, and use this as the basis for an account that evaluates randomness in terms of the length of programs for machines at different levels of the Chomsky hierarchy. This approach results in a model that predicts human judgments better than the responses of other participants in the same experiment

Griffiths, T. L., & Tenenbaum, J. B. (2003). Probability, algorithmic complexity, and subjective randomness. In R. Alterman & D. Kirsh (Eds.), Proceedings of the 25th Annual Conference of the Cognitive Science Society (pp. 480-485). Mahwah, NJ: Erlbaum. [PDF]