# [MUD-Dev] [DGN] Subjective randomness (was: The psychology of random numbers)

Robert Zubek rob at cs.northwestern.edu
Wed Jan 28 18:57:43 New Zealand Daylight Time 2004

```From: Brian Hook

> What people equate with randomness isn't true randomness, it's
> even distributions based on some percentage.  E.g. if you have a
> 75% chance of success, people expect to see:

>   T T T F T T T F T T T F T T T F

> Or at least something approximation that.  If they occasionally get a:

>   F F F F F F T T T T T T T F F F

> They freak out because it's "impossible" to get 6 failures in a
> row (when, in fact, it's guaranteed to happen at some point).

Subjective randomness is a notorious psychological effect - in a
series of random events, people seem more sensitive to the
*probability of change* than the probability of the event itself.

binary process (e.g. coin flips) we can compute the probability of
alternation Pr as the ratio Pr(sequence) = (r-1)/(n-1), where n is
the number of elements in the sequence, and r is the number of runs
(consecutive results).

For a fair coin, Pr ends up being about 0.5. However, people don't
perceive a fair coin sequence as really random, and consistently
prefer overalternating sequences - they judge as most random
sequences with Pr ~= 0.6! And the fair coin ends up being judged as
less random than even Pr ~= 0.7 (really overalternating).

This suggests a simple algorithm to approximate a perceptually
random coin:

bool perceptually_random_coin (bool previous_result)
{
if ( rand_normalized () < 0.6 )
return !previous_result
else
return previous_result
}

which produces a sequence with Pr ~= 0.6.

Rob

[1] http://www.umass.edu/srri/serg/papers/subjective%20randomness.pdf

--
Robert Zubek
http://www.cs.northwestern.edu/~rob
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```