Human Random Number Generation

By making use of Amazon’s Mechanical Turk I was able to obtain large quantities of random numbers generated by people.

I used http://www.fourmilab.ch/hotbits/ to obtain 310 bytes of random numbers obtained from radioactive decay. The following text shows various statistics obtained using a program called ‘ent’.


Entropy = 7.256475 bits per byte.

Optimum compression would reduce the size
of this 310 byte file by 9 percent.

Chi square distribution for 310 samples is 282.93, and randomly
would exceed this value 25.00 percent of the times.

Arithmetic mean value of data bytes is 130.4645 (127.5 = random).
Monte Carlo value for Pi is 2.901960784 (error 7.63 percent).
Serial correlation coefficient is 0.071475 (totally uncorrelated = 0.0).


The following shows the entropy of 310 bytes of random numbers based on those from humans.

Entropy = 7.322698 bits per byte.

Optimum compression would reduce the size
of this 310 byte file by 8 percent.

Chi square distribution for 310 samples is 253.20, and randomly
would exceed this value 50.00 percent of the times.

Arithmetic mean value of data bytes is 116.3226 (127.5 = random).
Monte Carlo value for Pi is 3.294117647 (error 4.86 percent).
Serial correlation coefficient is -0.017168 (totally uncorrelated = 0.0).

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