Subject: 'dead-end' Abalone positions

From: [email-masked] (Michael P. Frank)
Date: Sun, 19 Jul 92 18:08:25 EDT

As some of you know already, it turns out that there are reachable
Abalone positions for which the side to play cannot make a move.
Let us call these positions 'dead-end' positions.

For example, here is a dead-end position we discovered a few months
ago:

                           . . . . . 
                          . . . . . . 
                         . . . . . . .       @ = white
                        @ . . . . . . @      O = black
                       O @ . . . . . @ O     . = empty
                        O @ . . . . @ O   
                         O @ . . . @ O     
                          O @ @ @ @ O       
                           O O O O O        
                    
                         Black to move

Note that black cannot move, unless he is allowed to 'suicide' by
moving one of his own pieces off the board.

We have found that this position is indeed reachable from the initial
position, if the players cooperate to reach it.  Probably white could
not force black into this position.  But for random or cooperating
players, the position is theoretically possible.

Thus, the Abalone rules are incomplete, in that they do not provide
for a 'suicide' move, nor do they specify what happens if there are no
legal moves.  I called the American Federation of Abalone about this,
and they were unaware of the existence of dead-end moves and did not
know of any official Abalone rules that would resolve the conflict.

Note that in the above position, only 13 marbles are left on each
team.  It turns out that there are dead-end positions that use all 28
of the marbles.  Let us call such dead-end positions 'complete'
dead-end positions.  Here at MIT, we've come up with 3 different
complete dead-end positions.

Puzzle for the reader: find some different dead-end positions.  See if
you can find some that are complete.  Send your answers to this
mailing list.  (You can use the above diagram as a template.  If
you've already seen the answers we came up with at MIT, please refrain
from answering for a while so as not to spoil the puzzle for others.)

-Mike