Amazons is a fascinating game.
Some of its tactical and strategical aspects remind of Chess and Go.
Amazons is particularly challenging for humans and computers because of
its huge amount of possible moves
(more
than 1000 at the beginning). Like most good games Amazons has simple
rules and is easy to learn (see below).
Amazong is a program that plays Amazons. If you want to play
against Amazong, just select your color ("human"
with white or black) and press "New game". Then make your moves by
draging & dropping an amazon from her source square to her
destination
square and by clicking at a square to shoot. You can take back moves
and
review the game by using the scrollbar to
the
left of the game notation.
It is also fun to watch Amazong playing against itself (white and black
= "computer") with various styles as black and white player and on different levels.
Newsletter:
In case of major changes of this page (e.g. new versions of Amazong) I
am sending a newsletter to all subscribed visitors.
Rules of the
game Amazons:
- The game amazons is played with four white and four black amazons
on a
board of size 10 x 10 as shown above.
- A move of an amazon consists of two steps: moving an amazon and throwing an arrow.
- An amazon moves like a
Queen in chess - that means diagonally, vertically
or horizontally as far as she wants and no obstacle (an arrow or
another
amazon) blocks her way.
- In the second step of the move the amazon has to throw an arrow.
Arrows move according to the same rules as amazons do, but arrows stay
at their destination square for the rest of the game.
- Starting with white, the players make moves in alternating order
with an
amazon of their color.
- The game ends when one player cannot move. The player who made
the last
move wins the game.
Revision history
of Amazong:
- Amazong v3.3 was released on September 13, 2004. The main new feature is the "Deep Analysis" mode for analyzing a single position for several hours or days. The search algorithm in the "Deep Analysis" mode was also used to generate an opening book. Since the size of the opening book is ~100KB it is not submitted to your browser by default, but it can be activated under "White Settings" and "Black Settings". In the "Help"-mode, it is now possible to choose from a list with Amazong's six favorite moves. This list can be used to simplify input of moves while playing a game and also to navigate through variations of the "Deep Analysis" mode and through the opening book.
- Amazong v3.2 is publicly accessible since November 28, 2003. It has won the gold medal at the 8th Computer Olympiad on Nov. 27, 2003 (see under 'Tournaments' below). Amazong v3.2 is faster than the old version (by a factor 2 in the opening and by a factor 4 in the endgame). This speedup is "wasted" again by adding new features to the evaluation function: Amazong now knows more about huge areas of potential territory and about the distribution of amazons on the board. Some more time is spent doing a quiescence search. In the download section of this page you can find more details.
- Amazong v2.7 was finished on October 20, 2003. It has a user manual and a highscore list. You can load and replay the games from the highscore list.
- Amazong v2.6 was released on October 13, 2003. Again, all changes concern the user interface.
New features are 'Turn board'- and 'Print game'-buttons, independent parameters of white and black computer opponents, and a 'Help'
option. The source code of parts of the user interface is available for download (see below).
- Amazong v2.5 was finished on August 31, 2002. Except for an
improved
user
interface, it is identical with the version that has won the 7th
Computer Olympiad in Maastricht in July 2002. The search algorithm
uses pruning techniques and is slower than usual AlphaBeta because it
collects
more information about moves that do not belong to the main line. All
levels
are now of type 'time per move'. New features include 'search info',
'game
info', 'speed info' and the button 'Analyze' that can be used to review
the supplied games more conveniently than before.
- Amazong v2.2 was released on May 23, 2002. It is now possible to
load games
from an archive. I analyzed games from the jenazon cup 2001 and from
the
olympiad 2001 to improve the endgame capabilities of Amazong, but
Amazong
is still far from treating all examples from the paper 'Experiments
in Computer Amazons' correctly. The search algorithm has been changed
from NegaScout to a slightly modified version of ordinary AlphaBeta
with
iterative deepening together with a null-move heuristic.
- Amazong v2.1 was finished on October 23, 2001. It has an improved
evaluation
function, and it provides more search information.
- Amazong v2.0beta was finished on March 27, 2001. It has a
selective version
of NegaScout with iterative deepening and makes extensive use of
hashtables
for various purposes. The user can interpolate between two different
evaluation
functions ("Bob" and "Rob"). It is now possible to take back moves and
to review the game.
- Amazong v1.1 was finished on August 22, 2000. It plays faster and
has improved
graphics & user interface.
- Amazong v1.0 was finished on August 14, 2000. In first tests on
level
advanced
it competed well against the strongest existing programs.
Ideas for future versions of Amazong:
- Improve the endgame strength of Amazong (understand Zugzwang, guards, defective territory, squeezes).
- Try out simulations instead of (or in combination with) Minimax search, try out Realization-Probability-Search.
- Improve the memory management.
- Automatic tuning of MultiProbCut parameters.
- Allow playing versus other computers via a serial cable connection using the protocol of Yamazon & Invader.
Downloads:
- amazons_eval_xl.pdf
An extended version of the paper below. Submitted for publication in a special issue of TCS.
- amazons_evaluation.pdf, eval_amazons.ppt
The design of the evaluation function of Amazong is explained
in the paper and in the powerpoint presentation. The paper appeared in the book
Advances in Computer Games:
Many Games, Many Challenges, Proceedings of the 10th Advances in Computer Games Conference (ACG-10), IFIP Volume 263, edited by
H. Jaap van den Herik, Hiroyuki Iida, and Ernst A. Heinz, published by Kluwer Academic
Publishers/Boston, copyright 2004 by IFIP.
- amazons.ppt
This is a powerpoint presentation about the selective
search in Amazong. I used the presentation
in two talks about the program:
'Selektive Suche und Zugsortierung mit einstellbarer
Genauigkeit',
Universitaet Jena, Oct. 2002
'Selective search in Amazong', Games seminar, University
of Alberta,
Edmonton, Nov. 2002
It might be difficult to understand all details from this
presentation without the comments I gave in the talks.
- JBoardPanel
The source code of a part of the user interface of Amazong and an applet to test it.
You may freely download the source code and use it in your own non-commercial Amazons program.
- Amazong-PocketPC-Setup.zip
A toy version of Amazong for PocketPC (ARM, SH3, and MIPS processors) optimized for displays of size 240 x 320. It features the levels Beginner and Intermediate of the Amazong applet. The setup program is very large because it contains the Ewe Virtual Machine for PocketPC (see
www.ewesoft.com) that is required for this version of Amazong.
- amaz3_2.zip
An offline version of the applet Amazong 3.2. You can play against the offline version of Amazong in a browser or appletviewer without visiting this page. I would appreciate if you link to this page instead of installing the applet on your own web page. This page will always contain the most recent version of Amazong. In addition, the database containing the highscore list can only be accessed from this site.
Tournaments
(* means: see under 'Load Game' of Amazong)
Related links
(certainly an incomplete list):
last update : Nov. 14, 2004
