Kenneth Sloan wrote:
David Richerby wrote:
Guy Macon http://www.guymacon.com/ wrote:
I wonder if some variation on the backgammon doubling method of
forcing a losing player to resign might work...

Doubling only works in matches. In a tournament, the correct
procedure would be for each player to double every move so that
whoever wins gets the highest possible score.

Not if you change the basic scoring to [-1, 0, +1] and you double
BOTH the positive gain for a win and the negative score for a loss.

That still doesn't quite work. In the last round, two middle-of-the-
field players may as well double to infinity because they've nothing
to lose and whoever wins the game will win the tournament. Perhaps
one could invent some sort of Crawford's rule analogue to deal with
this? (Crawford's rule says that a player cannot double in the first
game where his opponent needs just one point to win the match, though
he can redouble if his opponent is foolish enough to double. This is
to prevent the person who's trailing in a match using the `nothing to
lose' argument and doubling as soon as his opponent needs a single
point to take the match.)

Even without this sort of repeated doubling, suppose player A believes
he's in a won position and doubles. B, his stronger opponent redoubles
immediately because he can see that A is actually lost. Even assuming
that A takes the hint, the game is still worth four points and more
because of A's incompetence than B's skill.

I suspect the actual effect would be to increase the number of
draws. After a few doubles, it becomes too expensive to take a risk
and play for the win.

For really good players, yes. But it's hard to imagine really good
players doubling and redoubling -- games of chess don't tend to have
the to-ing and fro-ing that backgammon does.

Imagine how backgammon would change if you allowed players to agree
to a draw.

I've played a bit of backgammon but mostly against the computer. I
can't see any circumstances under which one might agree a draw -- if
the game looks level, you'd just wait and not double, since it'll
surely unbalance itself after a while. Since the men can only move
forwards in Backgammon, progress of a sort must be made all the time
so I don't see a situation comparable to the sort of honest draw in
chess where neither player can make progress by any means other than a
gross blunder from the opponent. I've not played backgammon except
socially and against the computer -- am I missing something?


Dave.

--
David Richerby Beefy Spoon (TM): it's like a piece
www.chiark.greenend.org.uk/~davidr/ of cutlery that's made from a cow!