Author: Tony Werten
Date: 04:01:49 02/01/01
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On February 01, 2001 at 06:33:05, martin fierz wrote: >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? Flip horizontally, vertically and on both diagonals. ( 2^4 ) > > >>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? I never tried the 7*6 board. If you find the win on 6*5 you can make exactly the same moves on a 7*6 board, but you have saved a lot of computingtime. Tony ps Aha erlebnis, you're talking about connect4 with a standing up board (stones falling down). I'm talking about a flat board. Could make some difference. I don't think the smaller board trick works, because in you're game zugzwang is very important. > >cheers > martin
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