On Friday, May 6, 2022 at 12:23:20 AM UTC+1, Simon Woodhead wrote:
> 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
> +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 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.
> XGID=-b----E-C---eE---c-e----B-:0:0:1:00:0:0:3:0:10
> Position ID: 4HPwATDgc/ABMA Match ID: cAkAAAAAAAAA
>
> +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.
> XGID=-b---BC-C---eE---c-e----B-:0:0:1:00:0:0:3:0:10
> Position ID: 4HPwATCwc/ABMA Match ID: cAkAAAAAAAAA
>
> Note by SW: this should really be
> XGID=-b---BD-B---eE---c-e----B-:0:0:1:00:0:0:3:0:10
> Position ID: 4HPwATCwZ/ABMA Match ID: cAkAAAAAAAAA
>
> +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.
> XGID=-b--BBB-B---eE---c-e----B-:0:0:1:00:0:0:3:0:10
> Position ID: 4HPwATDYZvABMA Match ID: cAkAAAAAAAAA
>
>
> +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
> XGID=-b-B-BB-B---eE---c-e----B-:0:0:1:00:0:0:3:0:10
> Position ID: 4HPwATDMZvABMA Match ID: cAkAAAAAAAAA
>
> +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 157
>
> X wins 64%
>
>
>
>
>
> If you have the 52 combo you add 8 + 2 -1 because of the decreased
> priming potential.
> XGID=-bB--BB-B---eE---c-e----B-:0:0:1:00:0:0:3:0:10
> Position ID: 4HPwATDGZvABMA Match ID: cAkAAAAAAAAA
>
> +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 155
>
> 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%.
> XGID=-b----E-C---eE---c-eB-----:0:0:1:00:0:0:3:0:10
> Position ID: 4HPwATDgc/ABAw Match ID: cAkAAAAAAAAA
>
> +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 159
>
> 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.
> XGID=-b----E-C---dE---bbe----B-:0:0:1:00:0:0:3:0:10
> Position ID: 4NvgATDgc/ABMA Match ID: cAkAAAAAAAAA
>
> +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
>
>
>
>
> -----------------------------------------------
> XGID=-b----E-C---dE---bbeB-----:0:0:1:00:0:0:3:0:10
> Position ID: 4NvgATDgc/ABAw Match ID: cAkAAAAAAAAA
>
> +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 159
>
> 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.

Thanks Simon, very kind of you!
--
BD