It has been published that checkers has been solved. See:

http://www.sciencemag.org/cgi/conten.../317/5844/1518

However, I am hearing that checkers has not been solved at all. Only
free-style checkers has been solved. Tournament style checkers where
there is a drawing to determine the first three moves is still an
actively contested game.

Which is true? Does anybody know?

Sam Sloan

The abstract states "The game of checkers has roughly 500 billion
billion possible positions (5 x 10 ^ 20)" Walter Trice calculated
about 1.8 x 10^19 positions for backgammon http://www.bkgm.com/rgb/rgb.cgi?view+371.
His calculation is actually a little too large because he did not
worry about if the positions could actually arise or not but that is
probably an insignificant factor.

I am surprised that checkers has more possible positions than
backgammon. I figure that the 30 backgammon pieces instead of 24 for
checkers would about balance 33 locations in checkers forthose pieces
instead of only 26 locations for them in backgammon. Backgammon would
then pull way ahead becuase there can be up to 15 checkers at a
location as opposed to 2 for the all the checker locations except "off
the board".

Am I missing something in my intuitive argument or is one of the
calculations incorrect? The Trice argument looks solid to me.

Bob Koca

One factor to be considered is that the number of possible moves in a
backgammon games is infinite. The players could easily just keeping
hitting each other to infinity.

The number of possible chess games, while very large, is not infinite.
After a few billion moves the 50-move rule becomes a factor.

Except for the fact that checkers does not have a 50-move rule, the
number of possible checker games is relatively small.

None of this addresses the basic question being asked here, of course.

Sam Sloan

in the recent ICGA Journal ( www.icga.org) was a lengthy article about
checkers being solved. And AFAIK tournament checkers is a subset of
freestyle so if the later is solved....

ciao
Frank

BTW: Have you read "one jump ahead" If you either interested in
checkers or in programming board game AIs it's a good book to read.

On Mar 16, 1:32*pm, wrote:
in the recent ICGA Journal (www.icga.org) was a lengthy article about
checkers being solved. And AFAIK tournament checkers is a subset of
freestyle so if the later is solved....


Suppose that it has been discovered that with a certain opening
play that the first player can force a win. One might then say that
checkers has been solved. This knowledge though does not say what the
theoretical status of the game is if a different opening play is
forced.


Bob Koca

Checker pieces can be crowned to make kings. That accounts for the
extra positions.

Tom

On Mar 16, 11:27 am, bob wrote:
The abstract states "The game of checkers has roughly 500 billion
billion possible positions (5 x 10 ^ 20)" Walter Trice calculated
about 1.8 x 10^19 positions for backgammonhttp://www.bkgm.com/rgb/rgb.cgi?view+371.
His calculation is actually a little too large because he did not
worry about if the positions could actually arise or not but that is
probably an insignificant factor.

I am surprised that checkers has more possible positions than
backgammon. I figure that the 30 backgammon pieces instead of 24 for
checkers would about balance 33 locations in checkers forthose pieces
instead of only 26 locations for them in backgammon. Backgammon would
then pull way ahead becuase there can be up to 15 checkers at a
location as opposed to 2 for the all the checker locations except "off
the board".

Am I missing something in my intuitive argument or is one of the
calculations incorrect? The Trice argument looks solid to me.

Bob Koca

IIRC all tournament openings are shown to be a draw. IIRC further the
other openings are not selected in tournament play because they gave
one player a too large advantage.

All from the memory...

On Mar 16, 2:55 pm, wrote:
IIRC all tournament openings are shown to be a draw. IIRC further the
other openings are not selected in tournament play because they gave
one player a too large advantage.

Almost.

First, what Schaeffer did is to show that freestyle (unrestricted)
checkers is an absolute draw.

He has not analyzed all of the 3-move restriction openings so he has
not proven that tournament checkers is a draw. He has proven that
some of the 3-movers are a draw, and will likely eventually show that
all 156 of the accepted tournament choices are a draw (the other few
are almost certain losses and are not used). Of course, there could
be a deeply-buried surprise in one or more of the 156, but with the
amount of other computer analysis done to date, it's not very likely
--- but it hasn't been categorically proven yet.

But translate this over to human players, and checkers is certainly
not a draw when played by real people, even at the very highest
current level of human skill. So people are going to keep playing.

On Mar 17, 10:39*am, "
wrote:
On Mar 16, 2:55 pm, wrote:

IIRC all tournament openings are shown to be a draw. IIRC further the
other openings are not selected in tournament play because they gave
one player a too large advantage.

Almost.

First, what Schaeffer did is to show that freestyle (unrestricted)
checkers is an absolute draw.

He has not analyzed all of the 3-move restriction openings so he has
not proven that tournament checkers is a draw. *He has proven that
some of the 3-movers are a draw, and will likely eventually show that
all 156 of the accepted tournament choices are a draw (the other few
are almost certain losses and are not used). *Of course, there could
be a deeply-buried surprise in one or more of the 156, but with the
amount of other computer analysis done to date, it's not very likely
--- but it hasn't been categorically proven yet.

But translate this over to human players, and checkers is certainly
not a draw when played by real people, even at the very highest
current level of human skill. *So people are going to keep playing.

My recollection is slightly different. I remember looking at results
from the highest level of checkers play and a player would win a match
by 1 game to 0 with 20 draws. However, that's an impression from
memory only -- I haven't been able to check it. Can you back up your
claim with hard stats? If the world no. 1 plays the world no. 2,
would they draw less than 95% of their games? (I doubt it.) I think
it's a pretty dead game at the highest level.

Paul Esptein

* Am I missing something in my intuitive argument or is one of the
calculations incorrect? The Trice argument looks solid to me.


Are you the one who used to play with username "Bob" at GetClub? I was
searching for Bob for long time. You left playing long before. Play a
few games at GetClub and see how well it plays now.

Play Chess at: http://www.GetClub.com/Chess.html

Help Bot used to say that you use Computer's help while playing
against GetClub is that True?

Your games are remarkable. Only Zebediah matches your game style.

Bye
Sanny

Play Chess at: http://www.GetClub.com/Chess.html