Author: Omid David Tabibi
Date: 07:36:38 09/18/03
Go up one level in this thread
On September 18, 2003 at 10:32:44, Omid David Tabibi wrote: >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! Of course alpha-beta will reduce the complexity from b^d to b^(d/2), so this position is very easily solvable in brute force.
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