Example of a reference system.feels more comfortable. After all backgammon is a game. I write this post as another reply to crf's post. He stated there:
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
"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 almostrandomly 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 simplereference 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
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 inmatches, 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: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
"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
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?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.
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
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 pipdifference." 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
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 donot 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 presentingpositions 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 bylittle effect it makes sense to examine the effect of the race on its own.
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
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_____________________
+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: boo
Pip counts: O 125, X 74
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_____________________
+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 128, X 66
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 2entries 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 the4 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
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 exceptionsand 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 ______________
+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 128, X 79
X wins 95.1 O wins 4.9
2 pips _____________ With 1 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 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 70
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 youdeduct 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 waslost 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 ______________
+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 128, X 82
X wins 93.8 O wins 6.2
2 pips _____________ With 1 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 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 128, X 80
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 ofthe 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 ______________
+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 128, X 96
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 ______________
+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 72
X wins 89.2 O wins 10.8
2 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 129, X 69
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 informationwill 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
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 waswrong 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
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
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
I've added ids. All positions are assumed to be money, as the OP didn't indicate that this system applies to match scores and match scores
aren't mentioned anywhere.
This post can be viewed with a graphical board at https://bglog.org/rgbnews.html
------------------------------------------------------------------------- [OP: Sunday, November 24, 2013 at 7:27:20 PM UTC, smcrtorchs wrote:]
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?
XGID=------E-C---eE-b-c-eB-----:0:0:1:00:0:0:3:0:10
Position ID: 4HPGBwDgc/ABAw Match ID: cAkAAAAAAAAA
+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 XGID=-------b-----B------------:0:0:1:00:0:0:3:0:10
Position ID: AAAGAIABAAAAAA Match ID: cAkAAAAAAAAA
+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.
XGID=-BBBBBCb-----Bcbbbbb------:0:0:1:00:0:0:3:0:10
Position ID: YNt2wADbtgMGAA Match ID: cAkAAAAAAAAA
+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.
XGID=-BBBBBCb-----Ba-bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LZNwADbtgMGAA Match ID: cAkAAAAAAAAA
+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_____________________ XGID=-BBBBBCb-----Ba-bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LZNwADbtgMGAA Match ID: cAkAAAAAAAAA
+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: boo
Pip counts: O 125, X 74
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_____________________ XGID=-BBBBBCb----Ba--bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LaNwADbtgMDAA Match ID: cAkAAAAAAAAA
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_____________________ XGID=-BBBBBCb---Ba---bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwQDbtoMBAA Match ID: cAkAAAAAAAAA
+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_____________________ XGID=-BBBBBCb--Ba----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwgDbtsMAAA Match ID: cAkAAAAAAAAA
+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_____________________ XGID=-BBBBBCb-B-a----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwgDbtmMAAA Match ID: cAkAAAAAAAAA
+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 128, X 66
X Wins 94.1 O 5.8
___________________1 pip distance_____________________ XGID=-BBBBBCbB-a-----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNxADbtjMAAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=-BBBBBAbB----Ba-bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LZNwADbtgwGAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=-BBBBA-bBB---Ba-bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LZNwADbFhsGAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=-BBBBBAbB---Ba--bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LaNwADbtgwDAA 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 | 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 ______________ XGID=---BBBCbBB--Ba--bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LaNwABsOxsDAA 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 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 ______________ XGID=-BBBBBAbB--Ba---bbbbbb----:0:0:1:D:0:0:3:0:10
Position ID: 2LYNwQDbtowBAA Match ID: cBEAAAAAAAAA +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 ______________ XGID=-BBBBA-bBB-Ba---bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwQDbFpsBAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=-BBBBBAbB-Ba----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwgDbtswAAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=-BBBBA-bBBBa----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwgDbFtsAAA Match ID: cAkAAAAAAAAA
+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 128, X 79
X wins 95.1 O wins 4.9
2 pips _____________ With 1 steps ______________ XGID=-BBBBBAbBB-a----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwgDbtmwAAA Match ID: cAkAAAAAAAAA
+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 70
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 ______________ XGID=--BBBBCbB----Ba-bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LZNwAC27QwGAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=--BBBBCbB---Ba--bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LaNwAC27QwDAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=--BBBBCbB--Ba---bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwQC27YwBAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=--BBBBCbB-Ba----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwgC27cwAAA Match ID: cAkAAAAAAAAA
+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 128, X 82
X wins 93.8 O wins 6.2
2 pips _____________ With 1 steps & more timing ______________ XGID=--BBBBCbBB-a----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwgC27WwAAA Match ID: cAkAAAAAAAAA
+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 128, X 80
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 ______________ XGID=---BBBCbBB---Ba-bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LZNwABsOxsGAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=---BBBCbBB--Ba--bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LaNwABsOxsDAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=---BBBCbBB-Ba---bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwQBsO5sBAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=---BBBCbBBBa----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwgBsO9sAAA Match ID: cAkAAAAAAAAA
+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 128, X 96
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 ______________ XGID=-BBBBBBb-----Ca-bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LZNwADbtgEHAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=-BBBBBBb----Ca--bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LaNwADbtoEDAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=-BBBBBBb---Ca---bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwQDbtsEBAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=-BBBBBBb--Ca----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwgDbtuEAAA Match ID: cAkAAAAAAAAA
+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 72
X wins 89.2 O wins 10.8
2 pips _____________ With 3 checkers back ______________ XGID=-BBBBBBb-Ca-----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNxADbtnEAAA Match ID: cAkAAAAAAAAA
+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
I've added ids. All positions are assumed to be money, as the OP didn't indicate that this system applies to match scores and match scores
aren't mentioned anywhere.
This post can be viewed with a graphical board at https://bglog.org/rgbnews.html
------------------------------------------------------------------------- [OP: Sunday, November 24, 2013 at 7:27:20 PM UTC, smcrtorchs wrote:]
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?
XGID=------E-C---eE-b-c-eB-----:0:0:1:00:0:0:3:0:10
Position ID: 4HPGBwDgc/ABAw Match ID: cAkAAAAAAAAA
+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 XGID=-------b-----B------------:0:0:1:00:0:0:3:0:10
Position ID: AAAGAIABAAAAAA Match ID: cAkAAAAAAAAA
+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.
XGID=-BBBBBCb-----Bcbbbbb------:0:0:1:00:0:0:3:0:10
Position ID: YNt2wADbtgMGAA Match ID: cAkAAAAAAAAA
+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.
XGID=-BBBBBCb-----Ba-bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LZNwADbtgMGAA Match ID: cAkAAAAAAAAA
+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_____________________ XGID=-BBBBBCb-----Ba-bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LZNwADbtgMGAA Match ID: cAkAAAAAAAAA
+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: boo
Pip counts: O 125, X 74
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_____________________ XGID=-BBBBBCb----Ba--bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LaNwADbtgMDAA Match ID: cAkAAAAAAAAA
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_____________________ XGID=-BBBBBCb---Ba---bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwQDbtoMBAA Match ID: cAkAAAAAAAAA
+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_____________________ XGID=-BBBBBCb--Ba----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwgDbtsMAAA Match ID: cAkAAAAAAAAA
+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_____________________ XGID=-BBBBBCb-B-a----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwgDbtmMAAA Match ID: cAkAAAAAAAAA
+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 128, X 66
X Wins 94.1 O 5.8
___________________1 pip distance_____________________ XGID=-BBBBBCbB-a-----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNxADbtjMAAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=-BBBBBAbB----Ba-bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LZNwADbtgwGAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=-BBBBA-bBB---Ba-bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LZNwADbFhsGAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=-BBBBBAbB---Ba--bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LaNwADbtgwDAA 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 | 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 ______________ XGID=---BBBCbBB--Ba--bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LaNwABsOxsDAA 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 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 ______________ XGID=-BBBBBAbB--Ba---bbbbbb----:0:0:1:D:0:0:3:0:10
Position ID: 2LYNwQDbtowBAA Match ID: cBEAAAAAAAAA +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 ______________ XGID=-BBBBA-bBB-Ba---bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwQDbFpsBAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=-BBBBBAbB-Ba----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwgDbtswAAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=-BBBBA-bBBBa----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwgDbFtsAAA Match ID: cAkAAAAAAAAA
+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 128, X 79
X wins 95.1 O wins 4.9
2 pips _____________ With 1 steps ______________ XGID=-BBBBBAbBB-a----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwgDbtmwAAA Match ID: cAkAAAAAAAAA
+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 70
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 ______________ XGID=--BBBBCbB----Ba-bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LZNwAC27QwGAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=--BBBBCbB---Ba--bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LaNwAC27QwDAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=--BBBBCbB--Ba---bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwQC27YwBAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=--BBBBCbB-Ba----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwgC27cwAAA Match ID: cAkAAAAAAAAA
+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 128, X 82
X wins 93.8 O wins 6.2
2 pips _____________ With 1 steps & more timing ______________ XGID=--BBBBCbBB-a----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwgC27WwAAA Match ID: cAkAAAAAAAAA
+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 128, X 80
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 ______________ XGID=---BBBCbBB---Ba-bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LZNwABsOxsGAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=---BBBCbBB--Ba--bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LaNwABsOxsDAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=---BBBCbBB-Ba---bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwQBsO5sBAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=---BBBCbBBBa----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwgBsO9sAAA Match ID: cAkAAAAAAAAA
+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 128, X 96
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 ______________ XGID=-BBBBBBb-----Ca-bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LZNwADbtgEHAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=-BBBBBBb----Ca--bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LaNwADbtoEDAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=-BBBBBBb---Ca---bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwQDbtsEBAA Match ID: cAkAAAAAAAAA
+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 ______________ XGID=-BBBBBBb--Ca----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNwgDbtuEAAA Match ID: cAkAAAAAAAAA
+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 72
X wins 89.2 O wins 10.8
2 pips _____________ With 3 checkers back ______________ XGID=-BBBBBBb-Ca-----bbbbbb----:0:0:1:00:0:0:3:0:10
Position ID: 2LYNxADbtnEAAA Match ID: cAkAAAAAAAAA
+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
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.
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