[net.games] Is it logical to make random decisions?

desj@brahms.BERKELEY.EDU (David desJardins) (03/25/86)

In article <2293@jhunix.UUCP> ins_akaa@jhunix.ARPA (Ken Arromdee) writes:
>The point is that randomly does NOT mean "without logic", that in fact 
>the most logical move can be a random decision.  I am cross-posting this to
>net.math to see if any game theorists can confirm this...  (can you?)

   Yes, in fact in almost all hidden-information games (that is, games where
you do not know exactly what your opponent is doing) random moves are often
part of the optimal strategy.
   In games like chess with no hidden information the optimal strategy never
requires random decisions, but some random decisions can nevertheless be
useful in real, non-optimal strategies (for example, to avoid repeating
previous defeats).

   -- David desJardins

kort@hounx.UUCP (B.KORT) (03/28/86)

David desJardins is correct.  In certain games, the optimal strategy
is to randomly select a move among a set of alternatives.

This leads to an interesting point.  To a disinterested observer,
a random strategy may be perceived as an "irrational" strategy.
(Hence the phrase, "there is method to his madness.)  In general,
if someone is evidently following a nondeterministic (hence
unpredictible) strategy, is it decidable whether the person is
using a logical random strategy or merely behaving erratically?
It seems to me that it would be very difficult to decide the issue
unless one had many repetitions of the play upon which to cumulate
statistics.

--Barry Kort   ...ihnp4!houxm!hounx!kort

desj@brahms.BERKELEY.EDU (David desJardins) (03/29/86)

In article <768@hounx.UUCP> kort@hounx.UUCP (B.KORT) writes:
>...  In general, if someone is evidently following a nondeterministic
>(hence unpredictible) strategy, is it decidable whether the person is
>using a logical random strategy or merely behaving erratically?  It
>seems to me that it would be very difficult to decide the issue unless
>one had many repetitions of the play upon which to cumulate statistics.

   A related point is:  If God manipulates the universe by affecting
random events (QM wavefunction collapse), it is impossible to prove
that intervention is taking place.  In fact, it is not clear if there
is any distinction at all between intervention by an incomprehensible
God and "true" randomness.

   -- David desJardins