Author: martin fierz
Date: 03:33:05 02/01/01
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On February 01, 2001 at 05:57:58, Tony Werten wrote: >On January 31, 2001 at 08:13:52, martin fierz wrote: > >>hi, >> >>i recently corrected some code in my connect 4 program and now it is able to >>solve connect 4 in less than a day on a fast PC with a large hashtable (of >>course, connect 4 has been solved long ago). i tried again with a smaller >>hashtable and >>got some strange results, for very long searches (billions of nodes) i don't get >>the same value for >>the root position. for not-so-deep searches i get the same values for both >>versions. i am wondering, [if this is not just a bug :-)] could this be some >>hashcollision-problem? can anybody give me a probability for a hash collision >>occuring when using B-byte key & lock, with a hashtable with S entries after >>searching N nodes? (i am using 4 byte ints for the key and the lock) >>also, i think i remember somebody mentioning here that one can choose the random >>numbers for the XORs in a clever way making hashcollision probabilities >>smaller - can somebody tell me how? > >Ideal would be if every number would change half of the number of bits. > >Currently I'm working on connect 4,5,6 and 7, using hash scheme of 64bits. I >have found no problems. The advantage of using zobrist is you can handle >mirroring very easy. You just have to keep 16 hash values and store the lowest. >It sounds slow, but getting a hashhit saves such a lot of nodes that it's worth >it. you are probably right. i used symmetries to solve solitaire a long time ago with exactly that scheme - i thought in connect4 they would be less important since there is only 1 symmetry operation (flip the board left/right), but i never tested it. why do you use 16 values? >Using this hashscheme and some intelligent recognisers (recognizing >win-in-5-moves is a big winner), solving 4 in a row shouldn't cost you more than >2M nodes (with boards >= 6 by 5, wich is the minimum size for a first player >win). i'm using the standard 7x6 board. i can't really imagine solving that with 2Mnodes - what makes you think you can do it with so few nodes? cheers martin
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