This directory contains a program which does exhaustive-search analysis
of bearoff positions in backgammon. Because searching a tree takes
exponential time in the depth of the tree, you really don't want to
use this on "large" positions; exactly what "large" means depends on
the computer you're using and how long you're prepared to wait!

The program is written in CWEB, a literate programming system. If you
haven't a clue what that means, have a look at comp.programming.literate,
or read Knuth's book "Literate Programming". CWEB source gets munged to
produce C (program) and TeX (documentation). Since many users don't have
CWEB, this directory contains the C and TeX too. It also contains a DVI
file produced from the TeX, and the macro file "cwebmac.tex" needed to
make the TeX work.

Warning: This is a slightly non-standard version of CWEB, called CWEB 3.x.
You can get a copy by anan ftp to ftp.cwi.nl, in directory pub/cweb.

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Caveats:

Er, this may not work properly if you have 64-bit integers. It certainly
won't work at all if you have 16-bit integers.

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Using the program:

Invoke it as "race position1 - position2 [-r roll]"

A position is a list of up to 6 non-negative numbers whose total is
at most 15. It indicates the number of men on the 1-point, 2-point etc.
You specify first of all the position of the player who's on move,
and then that of the other player. The numbers should be separated by
spaces.

A roll is a list of either 2 or 4 numbers from {1,2,3,4,5,6}.

The output from the program should be pretty self-explanatory; perhaps
I should mention that the after-one-roll equities it gives when you don't
specify a roll are in the order no-cube,p1-has-cube,p2-has-cube.

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Why you should use this program:

There is another program floating about the net which does much the same
as this, called "race2". Its main drawback is that it is about 5 times
slower, and gives less information. If you don't mind that, fine. It may
on occasions be more accurate, with a difference of about 10^-6 at most,
because it uses double-precision reals everywhere and mine uses integers.

This isn't quite fair: on machines with fast floating-point arithmetic,
the speed difference is much less. My program is still faster, though.

Gareth McCaughan 27/6/1995