True Random Number Service

Runs Statistics

RANDOM.ORG is a true random number service that generates randomness via atmospheric noise. This page gives statistics for the runs test. Click on a graph for the full-size image. More graphs are available via the statistics browser.

2008-05-10	2008-05-11	2008-05-12

The focus of the Runs Test is the number of runs in a given block of random numbers, where a run is an uninterrupted series of identical bits bounded on both sides by bits of opposite values (or the beginning or end of the block). The Runs Test measures whether the number runs of ones and zeroes of various lengths are as would be expected for a truly random sequence. Each graph shows how the generator performed on a particular day. New graphs are generated automatically shortly after midnight (UTC) every day. If RANDOM.ORG is running with more than one radio (this may vary), you will see several plots in each graph. Each radio has its own name (e.g., hw0), and each plot is labelled with the name of the radio to which it belongs.

The Runs Test works by examining the stream of numbers as a series of blocks. For each block, we iterate over the bits and count the number of transitions between values (i.e., 0→1 or 1→0). This value is used to compute a P-value, which indicates whether the number of runs in the block is as we would expect. A block fails the test if its P-value is too small, meaning that there were fewer or more runs than we would expect.

The graphs show the distribution of P-values across the range. In the configuration used here, blocks with P-values less than 0.01 failed the test. For a truly random sequence, we expect a relatively even distribution of P-values across the range. Remember that a good random number generator will also produce blocks that don't look random, so we expect some of the blocks to fail the test. (In fact, we should be suspicious if all blocks passed the test.) You will find more details about this on the analysis page.

Full details of the Runs Test are given on page K.4 of Charmaine Kenny's Analysis of RANDOM.ORG and on page 18 of NIST Special Publication 800-22 (PDF, 1.4 MB).