A Memory Efficient Retrograde Algorithm and

Its Application To Chinese Chess Endgames

Reference ： MSRI Publications Volume 42, 2002 Writer ： Ren Wu. Department of Computer Scienc

e, Queen Mary & Westfield College

Reporter ： 梁秦宜

Outline

Introduction Fast, Memory Efficient Retrograde

Algorithm Reducing the Size of the Database Results from the Database Conclusion

Introduction

Endgame databases have several benefits.

Goal --- new retrograde algorithm and reducing the size of the database

Previous Work --- retrograde with burst force

Fast, Memory Efficient Retrograde Algorithm

Previous ： 帥、炮、兵 vs 將、象

帥、兵 vs 將、象

帥、炮 vs 將、象

帥、炮、兵 vs 將

帥、兵 vs 將

帥 vs 將、象

帥、炮 vs 將

帥 vs 將

New ： difference

1. use only one bit per position to generate

full information for both sides

2. generate a pair databases, one for each

side

Example ： construct a 5-men pawn-less chess endgame database, 15MB RAM is sufficient to avoid random disc access

Algorithm ：

Reducing the Size of the Database

Limiting the Pieces' Placement to Legal Squares. ( Table 1. )

Vertical Symmetry. ( Table 2. )

Multiple Piece Symmetry. ( Table 3. )

Piece Grouping. ( Table 3. )

90n is too large, n is the number of pieces

Table3 ： 1. there is more than one piece of the same

type, we can exchange these pieces'

places without altering the position

2. consider a few different type of pieces

together

maximum savings is incorporating the symmetry reduction

Results from the Database

One Major Piece. One Major Piece Plus a Pawn. Two Major Pieces. One Gunner, One Pawn Plus Some Minor P

ieces. Two Gunners Plus Some Minor Pieces. Two Pawns Plus One Major Piece. Some of the Hard Subgames. ( Table 4.)

Table 4 ：

Special case ： The aegp-aaee Endgame

Human Analyses ： Draw Game!

1.Shi Qin Ya Qu

2.Pao Bin Endgames

the aeegp-aaee endgame is theory win for

the stronger side

Use 95 moves to capture the first piece, and prove the Pao Bin Endgames theory.

aegp-aaee ：

Conclusion

improved, memory efficient retrograde

algorithm

prove that the aegp-aaee is a winning endgame, which maximum number of moves the stronger side need to capture the first piece is 95