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Subject: Re: Is this solvable by brute force?

Author: Omid David Tabibi

Date: 07:32:44 09/18/03

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On September 18, 2003 at 10:02:33, Edward Seid wrote:

>I'm learning how to program by reading Deitel's Visual Basic.NET How to Program.
> I'm eager to try out my new skills on a chess-related project.
>
>The Pawn Game - as presented by GM Lev Alburt in Comprehensive Chess Course, Vol
>1
>
>[D]8/pppppppp/8/8/8/8/PPPPPPPP/8 w - - 0 0
>
>The game is won by:
>1- capturing all of the opponent's pawns
>2- reaching the last rank first
>3- 'stalemating' the opponent, while still having at least one move for yourself
>
>The game is drawn if:
>1- both sides' pawns are blocked so that neither side can make any moves
>
>The programming exercise I've assigned to myself it to try to solve this game
>using brute-force minimax.  My question to you... can this game be solved on
>today's typical desktop computer using brute-force?
>
>I've been thinking about this and have made the following observations:
>1- while classical chess has a branching factor of around 30, the Pawn Game
>branching factor is 16 in the initial position, and around 8 in the
>'middlegame', and goes down with each capture.
>2- the longest 'game' is certainly less than 81 ply, and is probably around
>60-65 (81 ply is calculated by the impossible scenario of each side taking 40
>ply each to march all pawns to the 7th rank + 1 ply to promote)
>
>I'm not planning to use anything fancy like hashtables or board rotation.  I'd
>be happy if I'm successful in coding a 10x12 board representation (practice for
>writing a classical chess engine in the future), a valid pawn move generator,
>and a correct implementation of the minimax algorithm.
>
>I'm very curious what the solution to this game is.  Is it a win/loss/draw for
>White?  Of the 16 possible White moves, which ones win/lose/draw?  How long is
>the longest game?  How long is the shortest game?  What is the distribution of
>wins amongst the 3 methods of winning?
>
>Any thoughts or suggestions are appreciated.

The branching factor is at most 8 (initial position) and in the 'middlegame'
about 4. It seems to me that the average game would be no more than 32 moves,
and I think 50 would be a realistic upper bound.

So, assuming a branching factor of 4, and game length of 50 plies, there are
about 4 ^ 50 = 1267650600228229401496703205376 positions to search. Assuming you
can search 100 million positions per second, it will take you about
401969368413314 _years_ to finish the computation!

However, there will be a huge hash table hit rate (about 99% I guess), and you
can also benefit from many symmetrical positions (which arise by mirroring
another position). So, I think this position is solvable by brute force. Good
luck!



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