# 37 Sconyers Bearoff & Backgame CDs (Commercial backgammon support software)

Volume 1: Bearoff Equities and Backgame Probabilities

INTRODUCTION:

This CD-ROM disk contains two large databases of equities and
probabilities. One database has the exact equities for all bearoff
positions when each side has 9 men or less. The other database
contains the probabilities for getting hit or hitting a man when one
side has a backgame of 4 men or less.

The bearoff database is over 400 MB and contains the answers to over
100,000,000 bearoff problems! In addition, you can do a MONTE CARLO
simulation on any bearoff position with more than 9 men on a side. The
program also has a feature which finds the best move given a specific
position and dice roll.

The backgame database is 90 MB and contains the answers to over
22,000,000 backgame positions (some of them are not legal positions).
There is a feature which finds the best move given a dice roll and
position.

These databases will help settle many questions about fair settlement
and the best moves.

BEAROFF:

Once the program has been loaded you can enter any bearoff position,
assuming that all men are in their home board. If both positions you
enter have 9 men or less, the program will give you the EXACT equities
for all 4 cube positions - NO CUBE, ROLLER'S CUBE, CENTER CUBE, AND
NON ROLLER'S CUBE. In addition, it will display the proper cube
decision. These cube equities, as throughout this bearoff program, are
the equities if you roll with the cube in that position.

To compute the proper settlement in any bearoff position(assuming you
are going to roll with the cube in that position) you would multiply
the equity times the value of the cube.

After the equities are displayed, you are given a chance to find the
best move for the position you have just entered. Keep in mind your
best move in the bearoff is the one that leaves your opponent with the
smallest equity. The best move will often be different depending on
the cube position.

If you enter a bearoff position where one or both side have more than
9 men you will enter the MONTE CARLO subroutine. You will first be
asked how many simulations you want to run. There is a limit of
30,000. This Monte Carlo subroutine rolls the dice and moves the men
until each side has 9 men or less. Then it looks up the exact answers
from the database. With a few hundred simulations the NO CUBE result
should be very close to exact. The other cube positions results will
be distorted by the fact that this subroutine assumes that there is no
doubling until the positions are back in the database (ie each side
has 9 men or less). For example, if you have 12 men and the cube is in
the center and your opponent has 12 men, the cube will stay in the
center until each side has 9 men or less. At that point, the
subroutine will retrieve the exact equity from the database.

BACKGAME:

position provided the position not bearing off has 4 men or less. The
side bearing off can have from 1 to 15 men. The program will return
two probabilities: one for each side being on roll. These results are
the probabilities that the side bearing off will have a man hit.

After the probabilities are displayed, you are given a chance to find
the best move for the position you have just entered. Keep in mind
that the best move for the position bearing off is the one that leaves
the other side with the smallest probability of hitting a man. The
best move for the side in the backgame is the one that gives it the
highest probability of hitting a man.

This program assumes that the side playing the backgame has infinite
timing; ie, he will never be forced to leave his opponent's home
board. It follows from this assumption that the backgame side can take
some, part or none of any roll.

Sony's MMCD Player:

This disc works on an MMCD player also. Sony makes this very small
CD-ROM player which takes special exe files. This disc works both for
dos and MMCD. The MMCD version is the same as the PC version except in
a few places. To start the program place the disc in the MMCD player
and turn the power on. If you plan to use the bestmove feature and the
MONTE CARLO routine you will need to put the Volume #1 disc in the
player after the program loads. The MONTE CARLO simulations are
limited to 20,000 games.

_________________________________________________________________

Volume 2: Bearoff Equities for 4 Points and 15 Men

INTRODUCTION:

This CD-ROM disk contains two databases of equities for the bearoff.
The first database(4X15) has the exact equities for all bearoff
positions when each side has 15 men or less on the first 4 points. The
second database(3X15) contains the exact equities for all bearoff
positions when each side has 15 men on the first 3 points. The second
database is a subset of the first. The smaller database(3X15) is
included for a number of reasons, which will be explained later.
Everything that follows applies to the 3X15 database when the 4's are
change to 3's etc.

The bearoff database for 4 points and 15 men is over 240 MB and
you can do a MONTE CARLO simulation for any bearoff position where one
or both sides have men on the 5 or 6 points(4,5 or 6 in the case of
the 3X15 database). The program also has a feature which finds the
best move given a specific position and dice roll.

These databases can help settle many questions about fair settlement
and the best moves.

BEAROFF EQUITIES:

Once the program has loaded you can enter any bearoff position,
assuming that all men are in their home board. If both positions you
enter have all their men on the first 4 points, the program will give
you the EXACT equities for all 4 cube positions - NO CUBE, ROLLER'S
CUBE, CENTER CUBE, and NON ROLLER'S CUBE. In addition, it will display
the proper cube decision and probability for winning in the no cube
case. These cube equities, as throughout this bearoff program, are the
equities if you roll with the cube in that position. If you find an
equity greater than 1.000 or less than -1.000 this is due to the fact
that a position with 15 men can still lose a gammon.

To compute the proper settlement in any bearoff position(assuming you
are going to roll with the cube in that position) you would multiply
the equity times the value of the cube.

After the equities are displayed, you have an opportunity to find the
best move for the position you have just entered. Keep in mind your
best move in the bearoff is the one that leaves your opponent with the
smallest equity. The best move will often be different depending on
the cube position.

If you enter a bearoff position where one or both side have men on the
5 or 6 points you will automatically enter the MONTE CARLO subroutine.
You will first be asked how many simulations you want to run. There is
a limit of 30,000. This Monte Carlo subroutine rolls the dice and
moves the men until each side has all men on the first 4 points. Then
it looks up the exact answers from the database. With a few hundred
simulations the NO CUBE result should be very close to exact. The
other cube positions results will be distorted by the fact that this
subroutine assumes that there is no doubling until the positions are
back in the database (ie each side has all men on the first 4 points).
For example, if you have 12 men on the one and 3 men on the 5 point
versus the same, the cube stays in the current position until both
sides have all their men on the first four points. At that point, the
subroutine will retrieve the exact equity from the database.

THE 3X15 DATABASE:

There are several reasons that this database is included. First, it is
small(only 10 MB!). This will allow it, if you desire, to be copied to
your hard disk(be sure to copy BEQT4X15.EXE, helvb.fon and tmsrb.fon).
Secondly, the 3X15 database has an advantage in speed when doing MONTE
CARLO simulations. Simulations will run faster at the expense of some
accuracy. If you have copied the 3X15 database to your hard disk it
will run MONTE CARLO simulations substantially faster.

_________________________________________________________________

Volume 3: Bearoff Equities for 6 Points and 10 Men

INTRODUCTION:

This CD-ROM disk contains a database of equities for the bearoff. The
database has the exact equities for all bearoff positions where one
side has 10 men in the home board and the other side has 10 men or
less in the home board.

The bearoff database for 6 points and 10 men is over 625 MB and
contains the answers to over 156,000,000 bearoff problems! In
addition, you can do a MONTE CARLO simulation for any bearoff position
where one or both sides have more than 10 men. The results of these
simulations will be more accurate than the results from Volume #1. The
program also has a feature which finds the best move given a specific
position and dice roll. You will need Volume #1 to use the MONTE CARLO
feature and you may need Volume #1 for the best move feature.

These databases can help settle many questions about fair settlement
and the best moves.

BEAROFF EQUITIES:

Once the program has loaded you can enter any bearoff position,
assuming that all men are in their home board. If you enter a position
where both positions have 9 men or less you will get an error message
because all these positions are on Volume #1. For positions where one
side has 10 men and the other side has 10 men or less, the program
will give you the EXACT equities for all 4 cube positions - NO CUBE,
ROLLER'S CUBE, CENTER CUBE, and NON ROLLER'S CUBE. In addition, it
will display the proper cube decision and probability for winning in
the no cube case. These cube equities, as throughout this bearoff
program, are the equities if you roll with the cube in that position.

To compute the proper settlement in any bearoff position (assuming you
are going to roll with the cube in that position) you would multiply
the equity times the value of the cube.

After the equities are displayed, you have an opportunity to find the
best move for the position you have just entered. Keep in mind your
best move in the bearoff is the one that leaves your opponent with the
smallest equity. The best move will often be different depending on
the cube position. For some positions you will need Volume #1.

If you enter a bearoff position where one or both sides have more than
10 men you will automatically enter the MONTE CARLO subroutine. You
will need Volume #1 to use this subroutine. You will first be asked
how many simulations you want to run. There is a limit of 30,000. This
Monte Carlo subroutine rolls the dice and moves the men until both
sides have 10 men on less. Then it looks up the exact answers from the
database. With a few hundred simulations the NO CUBE result should be
very close to exact. The other cube positions results will be
distorted by the fact that this subroutine assumes that there is no
doubling until the positions are back in the database (ie each side
has all men on the first 4 points). For example, if you have 12 men on
the six point and 3 men on the 5 point versus the same, the cube stays
in the current position until both sides have 10 men or less. At that
point, the subroutine stores that position and later retrieves the
exact equity from the database on Volume #3 or Volume #1.

Sony's MMCD Player:

This disc works on an MMCD player also. Sony makes this very small
CD-ROM player which takes special exe files. This disc works both for
dos and MMCD. The MMCD version is the same as the PC version except in
a few places. To start the program place the disc in the MMCD player
and turn the power on. If you plan to use the bestmove feature and the
MONTE CARLO routine you will need to put the Volume #1 disc in the
player after the program loads. The MONTE CARLO simulations are
limited to 20,000 games.

Available from Carol Joy Cole, The GAMMON PRESS and The Backgammon
Shop for \$99 per volume.

If you have any comments or questions, please forward them to the

Hugh Sconyers
sconyers@bga.com

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