🚀 go-pugleaf

In article <1992Sep26.003838.14329@cbnewsl.cb.att.com> ed@cbnewsl.cb.att.com (edward.m.hummel) writes:
>In article <1992Sep25.185626.14074@ugle.unit.no> andreas@idt.unit.no (Andreas Lothe Opdahl) writes:
>>In article <1992Sep25.013439.1019@cbnewsl.cb.att.com> ed@cbnewsl.cb.att.com (edward.m.hummel) writes:
>>>The graph may be finite, but how do you assign a value to the loops?
>>>As far as I can see, they have undetermined value. 
>>
>>This is important, thank you for pointing it out.
>> ...
>>  Obviously, a "pure" game-theoretic evaluation can not make such 
>>an assumption about players behaviour (i.e. claiming a draw.)
>>
>>What is your reason why it can not be *proven* that closed loops have
>>the value of a draw?  
>
>It is easy enough to create a counter example.  I made up one for a
>simple game (only five nodes for the whole game tree) and could
>find no contradictions with the rules.
>
>>Perhaps we must add the *axiom* that closed loops 
>>are drawn to make chess solvable? 
>
>Yep.  That would do it, but it admits defeat.
>
>Another thought:  Can it even be proved that all undetermined loops
>have the same value?  I haven't worked this one out in any great detail
>but it is not obvious to me.  If it turns out that there are an infinite
>number of different undetermined values (to the infinite number of loops)
>then chess is not solvable.  If there are a finite number of values,
>then chess is solvable, but we can't determine the "optimal" strategy
>or assign a value to the initial position.
>
>

Would the people who talk about 'undetermined loops' be so kind to provide an
example, as I haven't the slightest idea what they mean. If at any point in
a loop one side can exit the loop and get on a winning path, then the loop is
a win for the side that can do it first. If neither side can do it, i.e. all
exits from the loop are draws, it is a draw.

And please don't respond 'philosophically'. If you claim that there are 
'undetermined' loops, give an example!

	Sven