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Main
Date: 01 Dec 2007 15:07:58
From: Kenneth Sloan
Subject: Re: Guy Macon on how many chess positions are possible
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Guy Macon wrote: ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Alas, your disproof is not sound. A significant percentage of the possible positions calculated by your method have multiple states that make them different positions. Let's start with: White to move/black to move (this alone multiplies your number by 2) White can/cannot castle queen side White can/cannot castle king side Black can/cannot castle queen side Black can/cannot castle king side (The possible can/cannot castle states only apply to positions where the king/rooks have not moved and the king is not in check.) The above states multiply all of your positions by x2 and some of them by as much as x32. Also, a smaller but still significant percentage of the possible positions calculated by your method have the following states: No en passant capture available by the player who has the move. One en passant captures available by the player who has the move. Two en passant captures available by the player who has the move. So your upper bound is demonstrably too low. One could also argue for (or argue against!) the following states implying different positions: Move allows/does not allow 50-move-rule claim. Move allows/does not allow repetition of position claim. ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ alas your demonstration that his upper bound is demonstrably too low is unsound. We have an estimate, plus: a) factors which make the estimate too low, and b) factors which make the estimate too high Unless one is willing to do some arithmetic to decide which factors predominate, we can only conclude that the original estimate is: a) too low, or b) too high, or c) just right of course, the chances of c) are remote - but no SOUND argument has yet been given for either a) or b). -- Kenneth Sloan [email protected] Computer and Information Sciences +1-205-932-2213 University of Alabama at Birmingham FAX +1-205-934-5473 Birmingham, AL 35294-1170 http://KennethRSloan.com/
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Date: 02 Dec 2007 11:42:21
From: Guy Macon
Subject: Re: Guy Macon on how many chess positions are possible
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Kenneth Sloan wrote: >alas your demonstration that his upper bound is demonstrably >too low is unsound. > >We have an estimate, plus: > >a) factors which make the estimate too low, and >b) factors which make the estimate too high All factors I mentioned make his stated estimate too low. Feel free to list which one does not if you disagree, There are, of course, factors that would make his estimate too high -- chief of which is his simplifying assumption that there are 128 kings available, 128 queens available, etc. -- but he and I rightly ignored them on the basis that he clearly stated that he was calculating a first-order upper bound for the number of possible chess positions as opposed to attempting to calculate the actual number. To digress a bit, I am glad that so far this discussion has been about calculating how many chess positions are possible and has not devolved into yet another attempt to show who is the alpha geek through personal attacks. My interest is in the result of the calculation, not in who is the best at making such calculations (a skill that consists priily of starting with the correct assumptions, and which I claim no exceptional prowess in). -- Guy Macon <http://www.guymacon.com/ >
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Date: 02 Dec 2007 11:12:43
From: Kenneth Sloan
Subject: Re: Kenneth Sloan on Guy Macon on reading comprehension
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Guy Macon wrote: > Kenneth Sloan wrote: > >> alas your demonstration that his upper bound is demonstrably >> too low is unsound. >> >> We have an estimate, plus: >> >> a) factors which make the estimate too low, and >> b) factors which make the estimate too high > > All factors I mentioned make his stated estimate too low. > Feel free to list which one does not if you disagree, > > There are, of course, factors that would make his estimate too > high -- chief of which is his simplifying assumption that there > are 128 kings available, 128 queens available, etc. -- but he > and I rightly ignored them on the basis that he clearly stated > that he was calculating a first-order upper bound for the number > of possible chess positions as opposed to attempting to calculate > the actual number. > > To digress a bit, I am glad that so far this discussion has > been about calculating how many chess positions are possible > and has not devolved into yet another attempt to show who is > the alpha geek through personal attacks. My interest is in > the result of the calculation, not in who is the best at making > such calculations (a skill that consists priily of starting > with the correct assumptions, and which I claim no exceptional > prowess in). > I agree with your last statement. -- Kenneth Sloan [email protected] Computer and Information Sciences +1-205-932-2213 University of Alabama at Birmingham FAX +1-205-934-5473 Birmingham, AL 35294-1170 http://KennethRSloan.com/
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