Urquhart's Pip counting system, adapted

I think I finally found a pip counting system I can use.

I am using a modified version of Urquhart's Absolute Pip Count (UAPC) which was described in Gammon Village in January 2013.


His system is based on the two point and takes four steps to get an exact count.

1: Count # of crossovers times six (This moves all checkers to home board)

2: Count # of semi-crossovers ** times three (This moves all checkers to near half of the home board)

3: Add 30 pips (this assumes all 15 checkers are stacked on the two point)

4: Adjust for Unit crossovers (add one pip for checker at far edge and subtract one pip for checker at leading edge of triad)


** Semi-crossover means moving from the far side of quadrant to near side of quadrant.



Here is my adapted version:


For You:
1: Count # of crossovers

2: Count # of semi-crossovers. Count each as 1/2

For Opponent:

1: Count # of crossovers

2: Count # of semi-crossovers. Count each as 1/2


Difference times six is the approximate pip count difference.


So by omitting the conversion to absolute count I only get the difference.

And also by skipping the last step the difference is not exact. The count may be off be a few pips if checkers are not centered in each triad.

For my purposes, I mainly want to know ...

Is the race about even?
Am I ahead some or a lot?
Am I behind some or a lot?

and this method seems a quick and easy way to determine the status of the race with confidence.


An exact count is usually not needed. If it is, in a race scenario for example, I can use other methods to determine the exact count. Usually I try to get the raw count for each side.



*****************

Here is an example using the method:

is tanzsox score: 0 pip: 129

7 point match

pip: 167 score: 0 is Chutzpah

XGID=----ABCaB---cC---eBdAb--A-:0:0:1:00:0:0:0:7:10

on roll, cube action?

eXtreme Gammon Version: 2.10

I (yellow) have:

crossovers, starting from opponent's home board ... 3,6, plus 5x2 or 16, +2 is 18 crossovers.
Plus semi-crossovers, again starting from opponent's home board ... 18.5, 19, 19.5, 20, none on my outer board, plus 3 more from my home board or 23 Total crossovers.

Opponent (black) has:

crossovers ... 0, 2-4-6-8, plus 5 is 13
semi-crossovers ... 13.5, plus 3 from home board or 16.5 total crossovers.

So I am behind approximately 6.5 crossovers or about 39 pips.

Actual is 38 pips.  Not bad.  And this is actually pretty quick to do in your head.  Much quicker than writing it out long hand.

****************

Here is one more for practice:

is tanzsox score: 5 pip: 160

7 point match

pip: 116 score: 4 is Chutzpah

XGID=-a--BbEBC---cBA--cac-b----:0:0:1:00:4:5:0:7:10

on roll, cube action?

eXtreme Gammon Version: 2.10

Me / Yellow:

2-4-6, plus 5 is 11 crossovers
plus semis in the home board, 12,13,14,14.5 total crossovers

Opponent / Black:
3-6-9, 11-13-15, plus 4 is 19 crossovers
plus semis 19.5, 20.5-21.5-22 total crossovers

I am up 7.5 crossovers or about 45 pips.   (Actual 44)

Chris Yep, post 2

Continuing to look at match against Chris Yep from Michigan vs. Ohio Challenge.  Here are some positions from the first game of the match from the other point of view.


******************

55 to play.

is Chris Yep score: 0 pip: 183

7 point match

pip: 162 score: 0 is Bill

XGID=-c-a--E-C--AcD---b-db-AA--:0:0:1:55:0:0:0:7:10

to play 55

1.	XG Roller++	23/18 13/3* 8/3	eq: +0.284
	Player: Opponent: 54.85% (G:21.36% B:2.16%) 45.15% (G:12.34% B:0.53%)
2.	XG Roller++	23/13 8/3*(2)	eq: +0.232 (-0.052)
	Player: Opponent: 53.67% (G:20.64% B:2.04%) 46.33% (G:12.94% B:0.55%)
3.	3-ply	13/3*(2)	eq: +0.226 (-0.057)
	Player: Opponent: 53.15% (G:21.85% B:2.43%) 46.85% (G:12.35% B:0.59%)

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

I played 23/13, 8/3(2)*

which escapes and points on head.  I think I was paranoid about leaving good sixes from the bar.


The computer likes 23/18, 13/3*/8/3.  The distro looks much better to the eye this way, whether I am hit or not.


***************

Chris doubles from the bar.  Take or Drop?

is Chris Yep score: 0 pip: 152

7 point match

pip: 131 score: 0 is Bill

XGID=ab-BA-F--A---D--abccc---A-:0:0:-1:00:0:0:0:7:10

on roll, cube action?

Analyzed in XG Roller++	No double	Double/Take
Player Winning Chances:	63.19% (G:24.51% B:1.42%)	63.31% (G:24.73% B:1.45%)
Opponent Winning Chances:	36.81% (G:11.64% B:0.87%)	36.69% (G:11.62% B:0.87%)
Cubeless Equities	+0.401	+0.835
Cubeful Equities
No double:	+0.568 (-0.009)
Double/Take:	+0.576
Double/Pass:	+1.000 (+0.424)
Best Cube action: Double / Take

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

So this is an easy take, barely a double. But it is a very *scary* double which I could easily see myself passing. I did take, but it was not an insta-scoop for me like the computer suggests. I had to talk my way through it.

Let's look at our old friend Position Pips and Threats.

Position: Advantage Chris. He has a 4.5 budding prime on his side of the board while I have six nasty stacked checkers on the six point. I do have better outfield control though and the potential to put these guys to work later.

Pips: Advantage Bill. With three men back to one man back I have to be up. A full count shows I am up about 20.

Threats: Chris hits with any four plus 53 23 13 and 22 or 17 numbers.


That's a lot of hitters. But he doesn't always hit and I certainly in the game if he misses. even if he hits he can't do everything in one roll. He only has a two point board so I have good chances of anchoring somewhere. With an anchor, I can play for a long time. And Chris still needs to maneuver his three back men all the way around the board.

******************

65 to play.

is Chris Yep score: 0 pip: 117

7 point match

pip: 180 score: 0 is Bill

XGID=-a-BaBC------AAAAbccbBbBa-:1:1:1:65:0:0:0:7:10

to play 65

1.	XG Roller++	15/4*	eq: +0.094
	Player: Opponent: 49.86% (G:13.06% B:0.58%) 50.14% (G:24.21% B:1.64%)
2.	XG Roller++	16/10 15/10	eq: +0.027 (-0.067)
	Player: Opponent: 47.25% (G:11.17% B:0.46%) 52.75% (G:22.59% B:1.22%)
3.	XG Roller+	21/16 21/15	eq: -0.046 (-0.140)
	Player: Opponent: 46.58% (G:10.42% B:0.40%) 53.42% (G:24.96% B:1.43%)

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

I made a blocking point six away with 16/10, 15/10. Apparently this was the wrong strategy. It looks like I should take a shot a t winning going forward by hitting 15/4*.

If I get hit I may hit his loosie on the ace point. And even if I don't I now have a very reasonable 2-4 backgame to fall back on so the downside is small. Again, it looks like I have a "free" shot at winning going forward so I should just go for it.

***************

11 to play

is Chris Yep score: 0 pip: 108

7 point match

pip: 169 score: 0 is Bill

XGID=---B-BCb--B--AA--bccbBbBa-:1:1:1:11:0:0:0:7:10

to play 11

1.	XG Roller++	14/13 6/4 5/4	eq: -0.022
	Player: Opponent: 45.66% (G:9.32% B:0.35%) 54.34% (G:21.80% B:0.98%)
2.	XG Roller++	14/12 13/12 6/5	eq: -0.085 (-0.064)
	Player: Opponent: 43.25% (G:8.63% B:0.33%) 56.75% (G:21.27% B:0.98%)
3.	XG Roller++	14/13 10/9(2) 6/5	eq: -0.142 (-0.120)
	Player: Opponent: 41.90% (G:7.88% B:0.28%) 58.10% (G:22.59% B:1.00%)

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

I don't understand this one.

I moved 14/13, 10/9(2), 6/5. Holding the board and making a reasonable block.

The computer says this is a whopper, preferring 14/13, 6/4, 5/4. Giving up the five point didn't cross my radar. I suppose the priority here is maximum containment against Chris's checkers so you hold the two point as far back as possible. Even seeing how wrong my play is I will probably do it again. I am too afraid about misapplying this logic .... breaking the 5 point must be wrong more often than it's right!

**********

I lead 5 away 7 away and am on roll. Cube action?

is Chris Yep score: 0 pip: 144

7 point match

pip: 143 score: 2 is Bill

XGID=--aB-BBaCA--cB-bAb-dB--b--:0:0:1:00:2:0:0:7:10

on roll, cube action?

Analyzed in XG Roller++	No double	Double/Take
Player Winning Chances:	67.37% (G:24.92% B:0.80%)	67.11% (G:25.75% B:0.81%)
Opponent Winning Chances:	32.63% (G:5.98% B:0.20%)	32.89% (G:5.92% B:0.20%)
Cubeless Equities	+0.531	+1.085
Cubeful Equities
No double:	+0.700
Double/Take:	+0.688 (-0.012)
Double/Pass:	+1.000 (+0.300)
Best Cube action: No double / Take
Percentage of wrong pass needed to make the double decision right: 3.7%

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

I doubled and Chris took.

This is a Double all day long for money (.85 Double / Take) but with a modest lead this turns into a borderline No Double. I liked it since I have some threats and own the 5 point if things go bad.

***********

54 to play.

is Chris Yep score: 0 pip: 151

7 point match

pip: 135 score: 2 is Bill

XGID=a-aB-BBBC---cA-bAb-dB--b--:1:-1:1:54:2:0:0:7:10

to play 54

1.	XG Roller++	16/11 13/9	eq: +0.591
	Player: Opponent: 73.23% (G:29.68% B:0.87%) 26.77% (G:4.26% B:0.16%)
2.	XG Roller++	20/16 13/8	eq: +0.589 (-0.002)
	Player: Opponent: 74.41% (G:27.14% B:0.98%) 25.59% (G:4.61% B:0.16%)
3.	XG Roller++	13/9 7/2*	eq: +0.535 (-0.056)
	Player: Opponent: 69.47% (G:38.26% B:0.87%) 30.53% (G:6.96% B:0.32%)

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

I played it big, going for the gammons, and hit with 13/9, 7/2*. While it does win more gammons it's simply too big.

Better was the solid 16/11, 13/9. If Chris doesn't anchor I may attack yet anyway. And if he does anchor his game still blows. Basically what I am saying is the solid play scores a decent number of gammons without risking too much.

**************

As you can see the attack didn't go so well. I now have six men back and 64 to play.

is Chris Yep score: 0 pip: 127

7 point match

pip: 172 score: 2 is Bill

XGID=-aAB-BB-B---b---cb-eBBBb--:1:-1:1:64:2:0:0:7:10

to play 64

1.	XG Roller++	20/10	eq: -0.595
	Player: Opponent: 45.38% (G:11.02% B:0.43%) 54.62% (G:19.23% B:0.72%)
2.	XG Roller++	22/18 8/2	eq: -0.695 (-0.100)
	Player: Opponent: 41.85% (G:10.20% B:0.33%) 58.15% (G:18.84% B:0.46%)
3.	XG Roller+	21/11	eq: -0.587 (+0.008)
	Player: Opponent: 44.46% (G:10.31% B:0.39%) 55.54% (G:17.40% B:0.53%)

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

I moved 8/2, 22/18. This makes the board and aims for maximum contact but violates my newly formed "superbackgame rules."

First off, the two point is hardly critical here.

Timing is the most important thing and I lack it. Time to vacate one of my backgame points and my rule "always vacate from the front" should apply here. Therefore 20/10. Note I am in no danger of getting primed.

**************

I trail 5 away 3 away and am on roll. Cube action?

is Chris Yep score: 4 pip: 131

7 point match

pip: 130 score: 2 is Bill

XGID=---BaBCBBAA-c-a--c-cbb-AA-:0:0:1:00:2:4:0:7:10

on roll, cube action?

Analyzed in XG Roller++	No double	Double/Take
Player Winning Chances:	57.30% (G:27.64% B:0.75%)	57.50% (G:28.53% B:0.70%)
Opponent Winning Chances:	42.70% (G:12.67% B:1.05%)	42.50% (G:12.95% B:1.06%)
Cubeless Equities	+0.220	+0.756
Cubeful Equities
No double:	+0.537 (-0.110)
Double/Take:	+0.648
Double/Pass:	+1.000 (+0.352)
Best Cube action: Double / Take

eXtreme Gammon Version: 2.02, MET: Kazaross XG2

I rolled. This is a strong "scoreboard" double. Trailing I activate the gammons which favor me and give the opponent a crippled cube. Chris will have a late recube given the match score. Plus he might drop, you never know.

It all adds up to a good double which I missed.