Message-ID:

The very ink with which all history is written is merely fluid prejudice. -- Mark Twain

On 6/05/2022 4:55 am, BlueDice wrote:

> Great stuff!
> I've only just come across this while searching for something else...
> I see that you have included the GNUBG ID for the first position diagram but not the others.
> Try as I might I cannot display the others so that they become intelligible.
> I have copied and pasted elsewhere and used an equi-spaced font but no joy.
> If you do happen to have the GNBG ID's for these please post.
> Any other advice will be greatly appreciated.
> Thanks
> --
> BD

Here's the original post, not munged by google groups...
-----------------------------------------------------------------------

Example of a reference system.

Let me start by saying that this kind of method for learning has worked
for me in a very nice way, but I understand that this method might or
might not be suitable for use from other players. I believe that
everyone should study with the way that he feels more comfortable. After
all backgammon is a game. I write this post as another reply to crf's
post. He stated there:

"A few of us at the local club have started down this path as well --
tweaking positions we don't understand well to get at their key aspects.
But mostly it feels like we are just guessing and feeling our way
around in the dark, sometimes almost randomly moving checkers around,
then making up stories to go along with how the numbers change."

Through the example below, I try to show how you can create meaningful
systems based upon 1 position (BP), that convey a lot of information and
are not that hard to remember. I try to explain my thought process step
by step as I create a simple reference system. I encounter a few of the
problems that can come up with reference systems and I state what I
believe can be done to overcome these problems. Maybe this can help you.
I am sorry if I left out some things, or if this text has other
problems, but this post is eventually too long for me and It had been
quite a long time since I last produced a text of this size in English.

What I call a reference system is a number of positions that are all
associated between them and their purpose is to help you in making
correct estimations about your win and gammon percentage. You can use
those estimations OTB for cube decisions in matches, but also as
guidelines for checker play at some occasions. Serving that purpose, a
reference system has some similar features with reference positions, but
it also has some differences.

From MCG's article on reference positions at gammonvillage:

"Reference positions are both precise and easy to remember.

The best kinds of reference positions are ones where a decision is
either always right or is
borderline."

Reference systems certainly need to be easy to remember.
But they do not need to be precise and always right or borderline. The
player needs to memorize BP'S winning and gammon percentages rounded to
the nearest integer. As the player later makes changes to the position
trying to understand the reference system, the player tries to remember
the value of each change. Maybe all this sounds too complicated and
maybe you do not have a strong memory. Well neither do I, but I can
remember the reference systems. The reason is that there are shortcuts
available for every step.

An example of a huge reference system that someone can find for free and
online is Kit's excellent article around the 5 point holding games.

http://www.bkgm.com/articles/GOL/May01/hold.htm

Personally I do find it hard to remember, but let's examine what can
make a reference system easy to remember.

1) The reference system is based around a simple position. The easier it
is to remember this position the easier to remember the whole system.

For example, what if this position was used as a BP for 5 point holding
games?

GNU Backgammon Position ID: 4HPGBwDgc/ABAw

+13-14-15-16-17-18------19-20-21-22-23-24-+ O: O
| X O O | | O X | 0 points
| X O O | | O X |
| X O | | O |
| X | | O |
| X | | O |
v| |BAR| | (Cube: 1)
| O | | X |
| O | | X |
| O X | | X |
| O X | | X | On roll
| O X | | X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X: X
Pip counts: O 139, X 159

The race difference is 20 pips here and according to XG mobile's 3 ply,
X wins 75% here. For sure this is far from a late game 5 point position
as Kit's position is.
But I believe that there is a reason why Kit chose his position and I
chose mine. Our minds work differently and we define a 5 point holding
game in a different way. I guess that Kit's position carries for him all
the necessary elements of a 5 point holding game. Therefore I believe
that he would be able to reconstruct this position easily just by making
sure that his position has all these elements, even if he did not
remember the exact position.

Same goes for me. I can remember this position very easily, because I
know the logical way that I created it. Even if that way was "let's put
X's checkers on the 5 point and let's throw O's back checkers wherever
we have to in order to make a 20 pip difference." I do not really have
to remember this position, because my mind will work the same way next
time and recreate it from the beginning if it has to. Maybe Kit's system
has more value than the one I propose, still mine has much value as well
and I can remember it easily by asking my self: "what would be a good BP
to start with for this system?" As you will see, such an approach can
give to the reference systems a personal characteristic. They might be
easy for everyone to remember but for sure they will be easy to remember
for the player who makes them.

2) The changes that you make to the BP follow a pattern and the value of
the changes follows a pattern as well. If this happens great. You can
memorise it easily. If the pattern deviates instead, then you know that
something is happening that you do not understand and this can prove a
great learning tool.

The system I will use as an example is a small one, is not full and can
certainly be expanded. The reason I present this system and not another,
is that it is the only one that I have rolled out positions from it and
I feel strange at presenting positions without rollouts. It examines the
winning percentage of the player on roll (WP) who has an anchor X points
away from an anchor of the opponent, where X equals 6, 5, 4, 3, 2, 1.

First let's talk about the BP of the system. To create it, I thought
along those lines:

1) Let's focus on the WPP when there is no racing equity for the
opponent. This can help in general cube decisions, if the racing chances
of the player can also be calculated.
2) Only 2 checkers of X and 2 checkers of O are necessary to form the
condition I want to study. As the most common variant found in normal
holding games is the one below, I will use it for the BP

+13-14-15-16-17-18------19-20-21-22-23-24-+ O:
| X | | | OOO 0 points
| X | | | OOO
| | | | OOO
| | | | OO
| | | | OO
v| |BAR| | (Cube: 1)
| | | | XX
| | | | XX
| | | | XXX
| O | | | XXX On roll
| O | | | XXX 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X:

3) I want to create a huge pip difference between X and O, but not give
X a crunched position as in games usually X's board is not crunched. I
also want to form a prime with O's checkers to make sure that when he
hits it works.

+13-14-15-16-17-18------19-20-21-22-23-24-+ O:
| X O O O O O | | O | 0 points
| X O O O O O | | O |
| O | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| | | X |
| O | | X X X X X X | On roll
| O | | X X X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X:

Now, I am a bit afraid that GNU will not recognise the outside prime, so
I will move it up forward up to the 4 point. The pip difference is still
very big, 51 pips.

+13-14-15-16-17-18------19-20-21-22-23-24-+ O:
| X O O O O | | O O O | 0 points
| X O O O | | O O O |
| | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| | | X |
| O | | X X X X X X | On roll
| O | | X X X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X:

Pips O: 125 X: 74

Is this reference system too personal? Maybe, but the ones you make will
be as well.

Once you have the BP, it is easy to visualise the rest of the positions
, if you know the parameters that you want to examine.

In any type of positions, usually you can make positional changes by

a) Creating points
b) Placing new blots on points
c) Changing the position of checkers, by either moving a blot from a
point to another or by changing the distribution of the spares on
already made point.
d) Changing the timing available for a task. I.e how long can you last
without breaking the back anchor.

It might look like normal that the race should be included in the list
as well, but this is not usually the case, as by making the changes
above you will change the race as well inevitably. Only in positions
were the positional changes have no or little effect it makes sense to
examine the effect of the race on its own.

If you really want to get into the details of a reference system it
might be useful to spot even the small changes that are worth 1%. Such
changes can come from moving a blot or a spare by just 1 pip.

So there we go for the first 6 positions of this system:

___________________6 pips distance_____________________

X wins 62.4 O wins 37.6 These are the winning
percentages for each player.

Cube analysis
Rollout cubeless equity +0.239

Cubeful equities:
1. Double, take +0.346
2. Double, pass +1.000 ( +0.654)
3. No double +0.343 ( -0.004)
Proper cube action: Double, take

___________________5 pips distance_____________________

GNU Backgammon Position ID: 2LaNwADbtgMDAA
Match ID : cAkAAAAAAAAA
+13-14-15-16-17-18------19-20-21-22-23-24-+ O: O
| O O O O | | O O O | 0 points
| O O O | | O O O |
| | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| | | X |
| X O | | X X X X X X | On roll
| X O | | X X X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X: X
Pip counts: O 126, X 72

X wins 73.3 O wins 26.7

Cube analysis
Rollout cubeless equity +0.478

Cubeful equities:
1. Double, take +0.860
2. Double, pass +1.000 ( +0.140)
3. No double +0.658 ( -0.203)
Proper cube action: Double, take

___________________4 pips distance_____________________

+13-14-15-16-17-18------19-20-21-22-23-24-+ O: O
| O O O | | O O O | 0 points
| O O O | | O O O |
| | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| | | X |
| X O | | X X X X X X | On roll
| O X O | | X X X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X: X
Pip counts: O 127, X 70

X wins 79.1 O wins 20.9

Cube analysis
Rollout cubeless equity +0.641

Cubeful equities:
1. Double, pass +1.000
2. Double, take +1.168 ( +0.168)
3. No double +0.838 ( -0.162)
Proper cube action: Double, pass

___________________3 pips distance_____________________

+13-14-15-16-17-18------19-20-21-22-23-24-+ O:
| O O O | | O O O | 0 points
| O O O | | O O O |
| | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| | | X |
| X O | | X X X X X X | On roll
| O X O | | X X X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X:
Pip counts: O 128, X 68

X Wins 87.7 O wins 12.3

___________________2 pips distance_____________________

X Wins 94.1 O 5.8

___________________1 pip distance_____________________

+13-14-15-16-17-18------19-20-21-22-23-24-+ O: O
| O O O | | O O O | 0 points
| O O O | | O O O |
| | | |
| | | |
| | | |
v| |BAR| | 4 point match (Cube: 1)
| | | |
| | | |
| | | X |
| X O | | X X X X X X | Rolled 13
| O X O | | X X X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X: X
Pip counts: O 129, X 64

X wins 98.0 O wins 2.0

___________________________________________________________________________

The rest of the positions will be based upon those 6.

Let's try to summarise the data of the winning percentages.

6pt --> 37
5pt --> 27
4pt --> 21
3pt --> 12
2pt --> 5
1pt --> 2

Note: The percentage for the 6 point distance, is rounded down instead
of rounded up instead. This will make numbers for some positions we will
see below easier to remember.

I cannot see a clear pattern here. On the upside, it is not that
difficult to memorise these numbers. However if you really want to, you
could always make it easier somehow For example you can remember the
sequence below and add 2 to the first 2 entries of the sequence.

6pt --> 35 +2
5pt --> 25 +2
4pt --> 20
3pt --> 10
2pt --> 5
1pt --> 2

So what if X had a little help with 1 or 2 extra anchors (steps) at the
outfield just in front of O's anchor. The positions of the steps is
where I believe they would most commonly be in a game.

First let's check for the 6 point.

6 pips _____________ With 1 step ______________

+13-14-15-16-17-18------19-20-21-22-23-24-+ O: O
| X O O O O | | O O O | 0 points
| X O O O | | O O O |
| | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| | | |
| X O | | X X X X X | On roll
| X O | | X X X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X: X
Pip counts: O 125, X 78

X wins 67.6 O wins 32.4

Cube analysis
Rollout cubeless equity +0.337

Cubeful equities:
1. Double, take +0.552
2. Double, pass +1.000 ( +0.448)
3. No double +0.442 ( -0.110)
Proper cube action: Double, take

6 pips _____________ With 2 steps ______________

+13-14-15-16-17-18------19-20-21-22-23-24-+ O: O
| X O O O O | | O O O | 0 points
| X O O O | | O O O |
| | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| | | |
| X X O | | X X X X | On roll
| X X O | | X X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X: X
Pip counts: O 125, X 85

X wins 72.2 O wins 27.8

Cube analysis
Rollout cubeless equity +0.428

Cubeful equities:
1. Double, take +0.759
2. Double, pass +1.000 ( +0.241)
3. No double +0.605 ( -0.154)
Proper cube action: Double, take

If we deduct 4% from the BP for each step then we get 33 and 29. Those
percentages are close enough to the real ones. This pattern continues,
with some exceptions around the 5 and 4 point. Specifically the 5
distance with 2 steps position and both the 4 distance positions deviate
from this pattern. For all the rest positions the pattern works just
fine. I believe that all the exceptions have something in common. I
could be wrong of course, but here is what I think. Creating 2 steps for
the 5 distance position and creating 1 or 2 points for the 4 distance
position gives X at least 3 of 6 numbers to break the anchor. The
increase in rolls from 2 to 3 or from 3 to 4 is quite a significant one.
Also the difficulty to clear the back anchor is much higher when the
anchor is 4 or 5 pips away. Both parameters together are only found in
these 3 positions. In these positions deduct an extra 2% for each step
and again your estimation is very close to the real one.

As we check for the other positions, a pattern will emerge. The winning
percentage of X will be within a 2% from the winning percentage of the
position without the steps - 4% for each step. There are a few
exceptions, but they are logical exceptions and if you understand the
why, then it is easier to remember them (if you are lazy you can ignore
them of course).

5 pips _____________ With 1 step ______________

+13-14-15-16-17-18------19-20-21-22-23-24-+ O: O
| O O O O | | O O O | 0 points
| O O O | | O O O |
| | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| | | |
| X X O | | X X X X X | On roll
| X X O | | X X X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X: X
Pip counts: O 126, X 76

X wins 77.7 O wins 22.3

Cube analysis
Rollout cubeless equity +0.551

Cubeful equities:
1. Double, pass +1.000
2. Double, take +1.029 ( +0.029)
3. No double +0.840 ( -0.160)
Proper cube action: Double, pass

5 pips _____________ With 2 steps ______________

+13-14-15-16-17-18------19-20-21-22-23-24-+ O: O
| O O O O | | O O O | 0 points
| O O O | | O O O |
| | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| | | X |
| X X X O | | X X X X | On roll
| X X X O | | X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X: X
Pip counts: O 126, X 100

X wins 83.9 O wins 16.1

Cube analysis
Rollout cubeless equity +0.667

Cubeful equities:
1. Double, pass +1.000
2. Double, take +1.275 ( +0.275)
3. No double +0.984 ( -0.016)
Proper cube action: Double, pass

4 pips _____________ With 1 step1 ______________

+13-14-15-16-17-18------19-20-21-22-23-24-+ O: O
| O O O | | O O O | 0 points
| O O O | | O O O | Cube offered at 2
| | | |
| | | |
| | | |
v| |BAR| |
| | | |
| | | |
| | | |
| X X O | | X X X X X |
| O X X O | | X X X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X: X
Pip counts: O 127, X 74

X wins 86.0 O wins 14.0

4 pips _____________ With 2 steps ______________

+13-14-15-16-17-18------19-20-21-22-23-24-+ O: O
| O O O | | O O O | 0 points
| O O O | | O O O |
| | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| | | |
| X X X O | | X X X X | On roll
| O X X X O | | X X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X: X
Pip counts: O 127, X 81

X wins 90.8 0 wins 9.2

3 pips _____________ With 1 step ______________

+13-14-15-16-17-18------19-20-21-22-23-24-+ O: O
| O O O | | O O O | 0 points
| O O O | | O O O |
| | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| | | |
| X X O | | X X X X X | On roll
| O X X O | | X X X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X: X
Pip counts: O 128, X 72

X wins 93.2 O wins 6.8

3 pips _____________ With 2 steps ______________

X wins 95.1 O wins 4.9

2 pips _____________ With 1 steps ______________

X wins 97.7 O wins 2.3

Examining the reference system further, lets check what happens if you
use the checkers from the 1 point to make the first step? How does this
extra timing affect the winning percentage? You will see the same
pattern as before. It seems that if you deduct an extra 2% total 6% in
all cases with the same exception of the 4 point where you should deduct
an extra 2% as before for a total of 8%, then your estimations will be
very close to reality.

The only real exception this time is when the anchors have a 2 pip
distance for obvious reasons as you cannot just deduct 6% from 5%.
Deducting an extra 2% probably feels intuitive and will not be hard to
remember. Someone could question that time was lost rolling out such a
parameter - detail. Ok, fair enough. If your gut feeling is strong, the
position is easy, the parameter is small and the 3 or 4 ply agrees with
you do not spend time rolling everything out.

6 pips _____________ With 1 step & more timing ______________

+13-14-15-16-17-18------19-20-21-22-23-24-+ O:
| X O O O O | | O O O | 0 points
| X O O O | | O O O |
| | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| | | X |
| X O | | X X X X X | On roll
| X O | | X X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X:
Pip counts: O 125, X 88

X wins 69.9 O wins 30.1

Cube analysis
Rollout cubeless equity +0.383

Cubeful equities:
1. Double, take +0.652
2. Double, pass +1.000 ( +0.348)
3. No double +0.564 ( -0.088)
Proper cube action: Double, take

5 pips _____________ With 1 step & more timing ______________

+13-14-15-16-17-18------19-20-21-22-23-24-+ O:
| O O O O | | O O O | 0 points
| O O O | | O O O |
| | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| | | X |
| X X O | | X X X X X | On roll
| X X O | | X X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X:
Pip counts: O 126, X 86

X wins 80.4 O wins 19.6

4 pips _____________ With 1 step & more timing ______________

+13-14-15-16-17-18------19-20-21-22-23-24-+ O:
| O O O | | O O O | 0 points
| O O O | | O O O |
| | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| | | X |
| X X O | | X X X X X | On roll
| O X X O | | X X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X:
Pip counts: O 127, X 84

X wins 88.0 O wins 12.0

3 pips _____________ With 1 step & more timing ______________

X wins 93.8 O wins 6.2

2 pips _____________ With 1 steps & more timing ______________

X wins 97.7 O wins 2.3

However, if you try to create 2 steps as before with checkers from the 1
and 2 points you will find that things are not that clear. Why? I
believe it is because the race just got closer and this has quite a
different effect depending on the distance of the anchor. The pattern
breaks as the race pattern comes in which I have not examined or rolled
out positions for it. It looks like I would have to work more on that
system before I can expand it and get real use from the rollouts below.

6 pips _____________ With 2 steps & more timing ______________

+13-14-15-16-17-18------19-20-21-22-23-24-+ O:
| X O O O O | | O O O | 0 points
| X O O O | | O O O |
| | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| | | X |
| X X O | | X X X X | On roll
| X X O | | X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X:
Pip counts: O 125, X 102

X wins 74.6 O wins 25.4

Cube analysis
Rollout cubeless equity +0.485

Cubeful equities:
1. Double, take +0.862
2. Double, pass +1.000 ( +0.138)
3. No double +0.755 ( -0.107)
Proper cube action: Double, take

5 pips _____________ With 2 steps & more timing ______________

+13-14-15-16-17-18------19-20-21-22-23-24-+ O:
| O O O O | | O O O | 0 points
| O O O | | O O O |
| | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| | | X |
| X X X O | | X X X X | On roll
| X X X O | | X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X:
Pip counts: O 126, X 100

X wins 83.9 O wins 16.1

4 pips _____________ With 2 steps & more timing ______________

+13-14-15-16-17-18------19-20-21-22-23-24-+ O:
| O O O | | O O O | 0 points
| O O O | | O O O |
| | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| | | X |
| X X X O | | X X X X | On roll
| O X X X O | | X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X:
Pip counts: O 127, X 98

X wins 90.2 O wins 9.8

3 pips _____________ With 2 steps & more timing ______________

X wins 93.2 O wins 6.8

There are some other parameters that you can look at. Like what if X had
more timing with a third checker on his anchor for example. There is a
pattern here as well. For the 6 point difference deduct 4 for the 5
point deduct 3 for the 4 point deduct 2, for the 3 point deduct 1 and
for the 2 point deduct nothing.

6 pips _____________ With 3 checkers back ______________

+13-14-15-16-17-18------19-20-21-22-23-24-+ O:
| X O O O O | | O O O | 0 points
| X O O O | | O O O |
| X | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| | | |
| O | | X X X X X X | On roll
| O | | X X X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X:
Pip counts: O 125, X 81

X wins 67.0 O wins 33.0

Cube analysis
Rollout cubeless equity +0.337

Cubeful equities:
1. Double, take +0.533
2. Double, pass +1.000 ( +0.467)
3. No double +0.470 ( -0.063)
Proper cube action: Double, take

5 pips _____________ With 3 checkers back ______________

+13-14-15-16-17-18------19-20-21-22-23-24-+ O:
| O O O O | | O O O | 0 points
| O O O | | O O O |
| | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| X | | |
| X O | | X X X X X X | On roll
| X O | | X X X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X:
Pip counts: O 126, X 78

X wins 76.2 O wins 23.8

Cube analysis
Rollout cubeless equity +0.537

Cubeful equities:
1. Double, take +0.966
2. Double, pass +1.000 ( +0.034)
3. No double +0.863 ( -0.103)
Proper cube action: Double, take

4 pips _____________ With 3 checkers back ______________

+13-14-15-16-17-18------19-20-21-22-23-24-+ O:
| O O O | | O O O | 0 points
| O O O | | O O O |
| | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| X | | |
| X O | | X X X X X X | On roll
| O X O | | X X X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X:
Pip counts: O 127, X 75

X wins 81.3 O wins 18.7

3 pips _____________ With 3 checkers back ______________

X wins 89.2 O wins 10.8

2 pips _____________ With 3 checkers back ______________

X wins 94.9 O wins 5.1

Do you really need to know this? As I understand it, it is quite
unlikely that you will need this kind of information OTB. At holding
games the favorite player will try to clear the spares from his back
points early in the game. So this information will not be very useful.
Still if you wanted to have expert understanding of the system, it would
make sense to note this. Kit's reference system has many small details
as well. The more experience you gain, the more you will be able to
understand how important is each piece of information around a reference
system. However, working with reference systems tends to sort the
problem out on its own.

After you learn a reference system, every time you make a wrong
estimation while playing you go back to the reference system and try to
find again the why your estimation was wrong. Do not be lazy and only
check the number, try to understand what was wrong in your thinking
process. If there is a part of your reference system that does not come
up while playing for a while, then for sure you will not revise it and
next time you see it within your reference system you can move it at the
bottom or even hide it. While it is nice to know the exact value of each
change, sometimes knowing just the size of the value (small, medium ,
large , XL) is enough to help you make correct decisions OTB. It is up
to you how deep you want to learn a reference system.

SUMARRY

Summary of findings For 1 step deduct For 2 steps deduct For 1
step with more timing For a third checker back deduct

6pt --> 37 4 2*4 As for 1 step +2% 4
5pt --> 27 4 1*4 +1*6 " 3
4pt --> 21 6 2*6 " 2
3pt --> 12 4 2*4 " 1
2pt --> 5 4 "
1pt --> 2

Note: Where you add 6 instead of 4 it is because the player gets 3 or
more numbers of the dice to clear an anchor and the value of clearing
the anchor is quite high at that position.

Is this an easy reference system to remember? Maybe if the positions and
the parameters you examine come out naturally from you it is.

If anyone wants a zip folder with all the rollout files emailed to him,
let me know. Below I post the rollout settings that were used for all
the rollouts. Only the seed probably differs.

Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 732794327 and
quasi-random dice
Play: 2-ply cubeful
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful

Does this system have any practical value? I would say that it has some.
It is not one that you will meet positions of this kind often, but they
do come up once in a while and the system is quite easy to remember. I
used this system a number of times and it always worked well. Is this
system incomplete? Certainly yes. More parameters can be checked. Do you
find it big? Kit's reference system was very big as well, so this is
normal with reference systems. Do not be afraid to start a huge
reference system. I have found out that as the size of a reference
system grows, so does its importance, its generality and usefulness. The
most useful and interesting reference system I have discovered is based
around the initial position.

+13-14-15-16-17-18------19-20-21-22-23-24-+ O:
| X O | | O X | 0 points
| X O | | O X |
| X O | | O |
| X | | O |
| X | | O |
v| |BAR| | (Cube: 1)
| O | | X |
| O | | X |
| O X | | X |
| O X | | X O | On roll
| O X | | X O | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X:
Pip counts: O 167, X 167

X wins 52.6%

Do you know the winning percentage if you are on roll and you have made
your 5 pt while your opponent did not move at all.

+13-14-15-16-17-18------19-20-21-22-23-24-+ O:
| X O | | O X | 0 points
| X O | | O X |
| X O | | O |
| X | | O |
| X | | O |
v| |BAR| | (Cube: 1)
| O | | |
| O | | |
| O X | | X |
| O X | | X X O | On roll
| O X | | X X O | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X:
Pip counts: O 167, X 165
X on roll

X wins 60.8% **************** This and all winning percentages
below are based upon XG mobile's 3 ply

The value of the 5 point for positions with little development from both
sides equals 60.8 - 52.6 or about 8%. To find the approximate value of
the 4,3,2 points, all you have to do is deduct 2% each time you make a
step. The 4 pt has a 6% value the 3 pt 4% and the 2 pt 2%.

Winning chances

5 pt 60
4 pt 58
3 pt 56
2 pt 52

Note: While XG's mobile winning estimation when you have the 5 pt is
closer to 61 than 60, whenever you make other changes to the position
that decrease the priming potential of X, then the value of the 5 pt is
closer to 60 and therefore I kept this estimation.

What if you had 2 points inside? The counting still works.

If you have the 54 combo you add 8 for the 5 6 for the 4 and an extra 1%
for the extra priming potential.

+13-14-15-16-17-18------19-20-21-22-23-24-+ O:
| X O | | O X | 0 points
| X O | | O X |
| X O | | O |
| X | | O |
| X | | O |
v| |BAR| | (Cube: 1)
| O | | |
| O | | |
| O | | |
| O X | | X X X O | On roll
| O X | | X X X O | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X:
Pip counts: O 167, X 159

X wins 67%

If you have the 53 combo you add normally 8 + 4

X wins 64%

If you have the 52 combo you add 8 + 2 -1 because of the decreased
priming potential.

X wins 61

How far can this counting go? Pretty far, if you keep adjusting the
value of each point and spare according to a logical way you can count
pretty complicated positions. But this is another subject and the
message is already too long.

Just a small example of what I mean by adjusting.

The value of having the opponent's 5 point and being on roll is 7%.

X wins 59.7

But if the opponent has his bar formed, and you hold his 5 point then
this takes away part of the opponent's advantage of having the bar
point. Therefore in that case,you should adjust the value of opponent's
5 point and increase it by 2.6, the 5 point is now worth 9.6.

+13-14-15-16-17-18------19-20-21-22-23-24-+ O:
| X O O | | O X | 0 points
| X O O | | O X |
| X | | O |
| X | | O |
| X | | O |
v| |BAR| | (Cube: 1)
| | | X |
| O | | X |
| O X | | X |
| O X | | X O | On roll
| O X | | X O | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X:
Pip counts: O 160, X 167

X wins 46.5

-----------------------------------------------

X wins 56.1

Learning this difference as an integer of 2 or 3 is quite easy as many
adjustments have this typical value around 2%. And if you understand the
why, then you can also very easily understand that the correct play for
43 after an opponent's 61 is 24/20 24/21.

Subject	Replies	Author
Re: An example of a reference system ... unfortunately quite long ... By: BlueDice on Thu, 5 May 2022	5	BlueDice

The very ink with which all history is written is merely fluid prejudice. -- Mark Twain

interests / rec.games.backgammon / Re: An example of a reference system ... unfortunately quite long ... maybe even too long