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Subject: Re: Fhourstones benchmark -- solving Connect-4

Author: john tromp

Date: 14:14:11 12/03/04

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Hi Martin,

>i read your post with interest, because i wrote a bitboard-based connect 4
> about 2 years ago (www.fierz.ch/4inarow.htm).

Welcome to the club:-)

> my test for a win is not very elegant,
>and so i checked out your version. cute! i am using the concept of threats to
>evaluate intermediate positions so my program can play a sensible game without
>calculating to the end. but your win-test is really nice. perhaps i can work out
>some better way to detect threats with this...

The heuristic connect-4 program I once wrote kept track of threats
and incrementally computed a 12-bit value for each column,
such that adding all these values for different columns together
modulo 4095 could be used to lookup the theoretical outcome.

However, I found that the program still lacked in strength, since
it failed to see that some new threats would inevitably arise
that would change its perceived outcome. This turned out practically
impossible to correct, so I gave up on that approach.

>>The solver is currently being used to solve connect-4 on bigger
>>board sizes. Unfortunately, avoiding collisions while storing only
>>32-bit locks requires a lot of memory, more than I have access to.
>>For instance, 7x8 and 9x6 boards both require 63-bit keys, which
>>means the table size must exceed 2^(63-32)=2G, taking 10Gb memory.
>i don't understand this part. why don't you just increase your key/lock sizes?
>ok, you might have one collision in a bazillion read/store operations, but does
>it matter?

You are right. Increasing the lock to 40+ bits would also solve that problem.
And that is pretty much unavoidable when trying to solve 8x8 (where the
key becomes 72 bits, and a 32-bit lock would leave you needing 5 Terabyte:().

But since 10Gb is not quite unheard of for big servers these days,
I figured I might as well see if such computing power is available.
Exhaustively searching a 7x8 or 9x6 game seems sufficiently mammoth
a task that you'd want to use such a big transposition table anyway.

regards,
-John



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