From: darse@cs.UAlberta.CA (Darse Billings)
Subject: Re: Awari? (Re: rec.games.strategic)
Keywords: checkers, shogi, othello, hex, etc.
Organization: University of Alberta, Edmonton, Canada
Date: Fri, 21 Aug 1992 04:12:17 GMT

elkies@ramanujan.harvard.edu (Noam Elkies) writes:
>In article <darse.714354066@silver-vly> darse@cs.UAlberta.CA (Darse Billings) writes:
>>Awari, Chase, 8x8 Checkers, 10x10 Draughts, Chinese Chess, Connect
>>Four, Dominoes, Hex, Go-Moku, Renju, Reversi (Othello), Nine Men's
>>Morris, Nim, Qubic (4x4x4 Tic-Tac-Toe), Scrabble, Shogi

>I've heard of most of these except Awari and Chase (and may need
>a refresher course on Renju).  Are these games simply enough defined
>that you can post the specs to rec.games.chess?

Awari is one of a family of games, called Mancala, which has more than
1000 variants.  Awari is common in Africa, and is nicely described in
articles [1] and [2].

Very briefly:  There are two rows of six pits, each pit having four stones:

   f e d c b a     player 1
-----------------
| |4|4|4|4|4|4| |
| |-----------| |
| |4|4|4|4|4|4| |
-----------------
   A B C D E F     player 2

A move consists of taking all the stones from a pit, and sowing them one
at a time clockwise into the other pits.  Stones are captured whenever
the last stone sown fills that pit to a total of two or three stones.

The goal is to capture more stones than your opponent (ie. 25 stones).
If your opponent has no move (ie. all of the pits on her side are empty),
then you capture all of the remaining stones.

There are a few other special case rules, so I recommend reading one or
both of the following articles.

[1] "Awari Tournament Report", in _Heuristic Programming in Artificial
Intelligence -- The First Computer Olympiad_, D.N.L. Levy and D.F. Beal
(editors), Ellis Horwood Limited, 1989, pp 17-20.

[2] L.V. Allis, M. van der Meulen, and H.J. van den Herik, "Databases in
Awari", in _Heuristic Programming in Artificial Intelligence 2 -- The Second
Computer Olympiad", Ellis Horwood Limited , 1990, pp 73-86.

-----

Chase (TM) is a chess-like game played on a hexagonal board, using two
colours of six-sided dice for men.  The range of mobility of the men is
defined by the value on each die, and certain moves allow you to change
those values during the game.  Thus the nature of the playing pieces may
vary, and this must be taken into account when computing moves and
strategies.

>Note that Dominoes falls under the nondeterministic category as well,
>though that's no reason to exclude it from your list.

Yes.  The list is comprised of games with relatively simple rules and
materials, but that are strategically very rich.  This is perhaps the
most important distinguishing feature from the complex board games such
as Advanced Squad Leader and the plethora of other fine Avalon Hill
games discussed in rec.games.board.

>Nine Men's Morris!?  Surely *that* is completely solved by now?
>There are only about 18 billion possible positions modulo the
>8 board symmetries.

Well, not to my knowledge.  Umm, I count 3^24 = 282429536481 or about
10^12 board positions without symmetries -- am I missing something?
I'm not sure if anyone has fully investigated and capitalized on board
symmetries, as was done for Qubic.  But there has been some interesting
work on database construction toward the goal of solving the game.  See
[3] for more information.

Connect Four and Qubic have been solved, but this certainly does not mean
that they are not worth discussing (in fact the stories of how they were
solved are very interesting).  For more on this, see my earlier posting
in response to a question about checkers (subject: "Checkers match").

[3] R. Gasser, "Applying Retrograde Analysis to Nine Men's Morris",
in _Heuristic Programming in Artificial Intelligence 2 -- The Second
Computer Olympiad", Ellis Horwood Limited , 1990, pp 161-173.

Follow-ups to rec.games.chess and rec.games.board only, please.  (And
to rec.games.strategic, when it is created :^)
--

 - Darse Billings, 2100 CM, 7 kyu.

Go is better than Chess.  Poker is more lucrative.  Sex is more fun.
Newsgroups: rec.games.chess