### Analysing humanly generated random number sequences: a pattern-based approach.

OPEN PloS one | 30 Jul 2012

###### MA Schulz, B Schmalbach, P Brugger and K Witt

##### Abstract

In a random number generation task, participants are asked to generate a random sequence of numbers, most typically the digits 1 to 9. Such number sequences are not mathematically random, and both extent and type of bias allow one to characterize the brain’s “internal random number generator”. We assume that certain patterns and their variations will frequently occur in humanly generated random number sequences. Thus, we introduce a pattern-based analysis of random number sequences. Twenty healthy subjects randomly generated two sequences of 300 numbers each. Sequences were analysed to identify the patterns of numbers predominantly used by the subjects and to calculate the frequency of a specific pattern and its variations within the number sequence. This pattern analysis is based on the Damerau-Levenshtein distance, which counts the number of edit operations that are needed to convert one string into another. We built a model that predicts not only the next item in a humanly generated random number sequence based on the item’s immediate history, but also the deployment of patterns in another sequence generated by the same subject. When a history of seven items was computed, the mean correct prediction rate rose up to 27% (with an individual maximum of 46%, chance performance of 11%). Furthermore, we assumed that when predicting one subject’s sequence, predictions based on statistical information from the same subject should yield a higher success rate than predictions based on statistical information from a different subject. When provided with two sequences from the same subject and one from a different subject, an algorithm identifies the foreign sequence in up to 88% of the cases. In conclusion, the pattern-based analysis using the Levenshtein-Damarau distance is both able to predict humanly generated random number sequences and to identify person-specific information within a humanly generated random number sequence.

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- Concepts
- Fibonacci number, Scientific method, Randomization, Futurology, Prediction, Mathematics, Hardware random number generator, Randomness
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