🚀 go-pugleaf

In <1992Sep28.114530.7475@cbnewsl.cb.att.com> ed@cbnewsl.cb.att.com (edward.m.hummel) writes:

>In article <xeno.717656375@pv34ad.vincent.iastate.edu> xeno@iastate.edu (Gary L Snethen) writes:
>>>Well, of course!  Once you ASSUME this, the rest is trivial.  The point
>>>was that an additional assumption is NEEDED.
>>
>>No, an additional assumption is not needed.
>>
>>Let me rephrase:  If you wish to apply the theorems we have used
>>so far from game theory, this assumption has ALREADY been made...  

>Speak for yourself.  I had not made this assumption, AND the game
>can be proven "solvable" even without making the assumption.  In
>the "real" game of chess, the rules do not make the assumption.

Please prove the game is solvable without the assumption.
I would VERY much like to see it.  The very term "solvable" assumes
against a player does not make mistakes.

Here's why:
  Let's say you cannot force a win with ANY move, but you can force a draw
  with e4, and I will make no mistakes in that variation, so the game will
  always draw.
  Let's say that I can force a win if you move d4...  but that I will
  always make a mistake in response to d4 that allows you to force a win.
  Against a perfect player you would NEVER move d4, because you know that
  you would lose.  Against me, however, you should ALWAYS move d4, because
  the outcome of your game will be maximal (ie., you will always win instead
  of draw).

  You MUST make an assumption about your opponent before you can analyze your
  'best move'.

>>In other words, the assumption is:  We don't take chances and assume our
>>opponent will be blind to our weaknesses.  We assume that if he CAN force
>>a win, he WILL, and that if he CAN force a draw, he WILL do that
>>in preference 
>>to allowing you to force a win against him.  This is an assumption we (who
>>support 'solvability') have been making all along.

>I also "support solvability", and I managed to do it without making
>the assumption.

Do it.


>>Summary of my position:
>>  Making the assumption that our opponent will not make mistakes, chess is
>>  solvable and the 'loops' presented do not interfere with the analysis.
>>
>>  Without this assumption, the version of game theory we are trying to
>>  apply does not hold, anyway...  And indeed, I feel it's very
>>  provable that optimal play cannot be obtained without insight
>>  into your opponent's 'algorithm' or 'psychology'.

>I would be interested in such a proof.  I think there is a solution
>to the "chess problem" that does not involve psychology or "insight
>into your opponents algorithm".

Take my example above as a demonstration.  You can not predict your optimal
play at d4, although that IS your optimal move.


---Xeno