Author: Russell Reagan
Date: 21:01:45 11/28/02
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Generally the number of chess positions is estimated at about 10^40, but it is not possible (currently) to know exactly how many there are. It will probably not be possible within our lifetime to know exactly how many there are, and quite possibly never possible at all. Even a search, such as perft, couldn't determine this piece of data. You would need to store every position, and make sure you don't count duplicates that arise in the search more than onces, which means you would have to store all of the positions. If you take the approach of generating endgame tablebases, you might have some positions that are not actually possible to reach in a legal game of chess, so that number could be wrong. So now we're back to doing one giant search and storing each position we come across in a giant array capable of storing every possible chess position (both legal and illegal) and then seeing which ones you can find. Perhaps set each array element to 1 if the position is found, and initialize the array with 0's. Then count the number of 1's in the array, and you have your answer. So you would need a computer capable of doing this giant search (and none is even close to existing) and you'd need some medium capable of storing such an array, using a godel number (I think that's what it's called) as the index into that array. So you could do this computation needing only 1-bit per position, but, that number is not terribly useful even if you could compute it, and I don't know of anyone that has 10^40 bits laying around. You would need about 1,164,153,218,269,348,144,531,250,000,000 gigabytes of memory. I only have 20 gigs, but my birthday is coming up, so maybe someone will give me a new hard drive with this much storage :)
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