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January 29, 2012

Bill's Match Equity Table

The traditional match equity table shows your win percentage at any given score.  From there, you should be able to calculate takepoints and gammon values during live play.  However, I really struggle with the math calculations.   I made a different version which includes the takepoints and gammon values within the table itself.

It is a bit cumbersome to look at, but it is mainly for reference anyway.  For each score, I have placed four pieces of information.

Upper left corner is Traditional Match Equity, like you would find in any other match equity table.

Upper right corner is the Gammon Value on a 2 cube, or once the cube is turned.  I further color coded the GV according to MCG's terminology. 

Red = Dead cube or gammon value of 0
Light Red = Crippled cube or low gammon value less than money
Yellow = Moneyish or gammon value near .5
Light Green = Elevated gammon value or gammon value larger than money
Green = Gammon Go or gammon value near 1

Bottom left corner is Takepoint on initial cube.  Value is raw or gammonless.
Bottom right corner is Takepoint on recube.  Again value is raw or gammonless.

I'm not sure how this will look on a blog post.  My orginal work was done in Excel, and is in nice proportion.  I sized it to print very small, so small I taped it to a credit card which I carry in my wallet.  Alternatively you could size it to fit on an index card or a whole sheet of paper, whatever. 

Finally, imagine a line cutting through the chart flowing from top left to bottom right.  Scores are listed twice from both the Leader and Trailer perspectives.  The Top half is from the Leader point of view and Bottom half from the Trailer point of view.

For the Crawford scores, only the match equity is shown.

7 Pt Match L E A D E R
1 2 3 4 5 6 7
TRAILER 1 50 68   75   81   84   89   91  
2 32 50 0 60 0 67 0 74 0 80 0 84 0
  32 - 26 32 20 50 17 41 23 33 22 36
3 25 40 .48 50 .5 57 .45 65 .46 71 .36 76 .37
  25 - 29 25 20 40 18 33 21 28 22 30
4 19 33 1.0 43 .97 50 .98 58 .82 64 .67 70 .60
  19 - 21 19 19 33 17 30 21 25 21 26
5 16 26 .69 35 .74 42 .77 50 .66 57 .61 63 .55
  23 - 19 16 21 26 18 24 21 23 21 24
6 11 20 .51 29 .54 36 .56 43 .57 50 .55 56 .54
  22 - 20 11 22 20 22 16 21 21 20 22
7 9 16 .56 24 .57 30 .56 37 .56 44 .54 50 .54
  23 - 18 9 21 26 21 24 21 18 20 20

Remembering the Match Equity values.

Crawford equities I remember going down. 
32, 25, 19, 16, 11, 9.   The odd away equities are the anchors in my mind. 
3 away Crawford is 25, and 5 away is about 15 and 7 away is about 10. 
Not exact, but I seem to remember the odd away and the nice round numbers 25,15,10 (even though these are off a bit I usually can get to 16 and 9 from there)

I remember the Two-away equities this way.
2 away 3 away is 40%, or 2 / (2+3).
2 away 4 away is about one third, or 33%, or 2 / (2+4).
2 away 5 away is about 25,

As MCG showed in his Gammon Village article, two-away equities are close to Crawford (shift two).
For the out 2-away scores, I approximate using MCG's method. 

For example, 2 away 6 away is similar to 1 away 4 away Crawford or about 19 (actually 20).
And 2 away 7 away is similar to 1 away 5 away Crawford or about 15 (actually 16).

3 away equities are already covered by Crawford and 2 away notes above.

The only remaining 4 away equity is 3 away 4 away.
at 3 away 4 away one player has 43%  (nice trick from Turz on BGO)

For 5 away equities..
at 3 away 5 away one player has 35% (also from Turz).
4 away 5 away is either halfway btwn 35 and 50 or 42.5%, or use Neils Number of 8 to get ~42.

For 6 away equities ... use Neils Number of 7.

For 7 away equties .. use Stick's trick.
Start with 7 away Crawford at 9%, then add 7% in steps up for the other scores.
Or start with 44% for 6 away 7 away and subtract 7% in steps down for other scores.

I remember that Neils Numbers as applied to the old Woolsey table use the key number 13 for the near-in values.  For 7 away through 3 away you take 13 minus the points away to get to Neils Number.
For example, 3 away is 13-3 or Neils Number of 10.  4 away is 13-4 or Neils Number 9, etc through 7 away.

Remembering the Gammon Values

Cube is dead for Leader at 2 away scores (obvious)

Cube is crippled for Leader at 3 away 6 away and 3 away 7 away.  Think Stick's rule (the rule is never double as Leader at 3 away 6 away or more but it should also prompt you to remember that gammon value is crippled for the leader).

Gammon value is moneyish for the Leader at other 3 away scores. (including 3 away 3away which is exactly .50)

Gammon value is also moneyish for the Trailer at 2 away 3 away.

Gammon Value is 1.0 at 4 away 2 away for the trailer and almost 1.0 at 4 away 3 away for the trailer and for both sides at 4 away 4 away.

Gammon values are elavated for both sides at 4 away 5 away but actually higher for the leader.

Gammon values are elevated for the leader at other 4 away scores ( 4 away 6 away and 4 away 7 away) since the leader needs exactly four points to win the match.

At 6 away and 7 away scores, Gammon Values are moneyish for the trailer, regardless of exact score. (slightly higher than money but not too much to worry about)

Remembering the Initial Takepoints

Takepoints on initial cubes are moneyish at most scores.

TP 32% or about 1/3 at 2 away 2 away.

TP 26.5% for the leader at 2 away 3 away, which is high.
TP 25% for trailer at 3 away 2 away, which is also high.

TP is 30% at 3 away 3 away, which is VERY HIGH.  The highest in the whole chart.

TP is about 19% for both sides at 2 away 4 away but beware this is gammonless!!  Leader should use use NeilKaz Rule of 80 to evaluate cubes.  Take if estimate Trailer Wins + Trailer Gammon Wins < 80%, otherwise DROP!!

TP is low for the leader at 5 away scores (17-18%).  Keep in mind again these are gammonless takepoints!!
2 away 5 away. I think the reason is you are getting a free shot at winning the match.
3 away 5 away. I think the reason is favorable risk/reward.... the trailer has tremendous cube leverage if you drop anyway (and go to 3a 4a) plus you get a free chance at advancing to Crawford so you might as well go for it.. again this assumes gammons are low.
4 away 5 away.  Not sure on this one.  Guessing losing a plain game not too bad since then you are behind but will have tremendous cube leverage next game as the trailer (where your GV is almost 1.0 at 4a 3a).  Also your gammon value is as leader at (4a 5a) is actually higher than the trailer and you might just win the match this game.

Initial takepoint is moneyish for all 6 away and 7 away scores (assuming low gammon games once gain).

Takepoint for Trailer is also moneyish for all 2 away scores.  Leader should only double a race or holding game but he doubles as per money and Trailer takes/drops as per money.  The rewhips for the trailer at 2a 5a and further back are just not that powerful.

Remembering the Recube Takepoints

Actually I don't have a way to remember these right now.  And this is a weakness for me at this time.

Generally speaking, the leader is hesitant to redouble to 4 as he may be putting the match on the line while simultaneously killing his own gammons.

On the other hand, the Trailer is eager to redouble to 4 - the value of the recube often justifies taking deep positions that you would otherwise pass for money.

If the recube puts the match on the line, then the takepoint is simply the match equity if you drop.  For example, the takepoint on a redouble at 4 away 4 away is 32% (the ME at 4a 2a).

For other scores, I attempt to do the takepoint calculation in my head - which I really struggle at!!

TP = EP - TL / (TL - TW)

EP equity if pass
TL equity if take&lose
TW equity if take&win

January 28, 2012


What follows are blunders from a match against SteamSax.

I trail 7 away 5 away and have just been doubled.  Take or Drop?


score: 2
pip: 140
7 point match
pip: 159
score: 0

is Chutzpah
on roll, cube action?

Analyzed in XG Roller+ No double Double/Take
  Player Winning Chances: 64.26% (G:42.00% B:0.53%) 64.18% (G:41.98% B:0.46%)
  Opponent Winning Chances: 35.74% (G:8.79% B:0.48%) 35.82% (G:8.85% B:0.49%)
  Cubeless Equities +0.596 +1.245
Cubeful Equities
     No double:+0.689 (-0.061)
     Double/Pass:+1.000 (+0.249)
Best Cube action: Double / Take
eXtreme Gammon Version: 2.01, MET: Kazaross XG2

I totally misjudged this position and dropped.

2 on the bar against a 3 point board, plus 10 men in the zone usually spells D-R-O-P for me.

And my judgment is correct as far as it goes.  XG++ gives this as a small pass for both money and at the 7 away 7 away score. 

I'm not sure I really understand it, but apparently the recube leverage to 4 is worth a lot here.  I suppose many of the games I win will often be on a 4 cube, which is good.

Also important to note is that I have both the 11 point and the 4 point made, so I have a good offense.  Also I have three flexible spares, which is unusual for a blitz. 

Also worth noting is that Steve has the ace point and his builder distro is not ideal.  While not huge, it helps my equity here.

Lesson?  Well my mental reference (2 on the bar against 3 point board with 10 in zone equals DANGER) is actually pretty good.  But this is not the end of the story.  I need to be on my toes and refine my initial judgments to consider the score as well as the location of all the checkers on the board.  In this particular case my offense was unusually good and I need to note his ace point is bad.

In the next position I am on roll trailing 7 away 4 away.  Cube action?


score: 3
pip: 155
7 point match
pip: 160
score: 0

is Chutzpah
on roll, cube action?

Analyzed in XG Roller+ No double Double/Take
  Player Winning Chances: 70.18% (G:23.44% B:1.41%) 70.22% (G:23.78% B:1.46%)
  Opponent Winning Chances: 29.82% (G:6.89% B:0.32%) 29.78% (G:6.92% B:0.33%)
  Cubeless Equities +0.583 +1.246
Cubeful Equities
     No double:+0.902 (-0.098)
     Double/Take:+1.166 (+0.166)
Best Cube action: Double / Pass
eXtreme Gammon Version: 2.01, MET: Kazaross XG2

This is an obvious double and a big pass.  Unfortunately I didn't double here.  Not sure what I was thinking as I have better board and prime plus 2 blots to shoot at.  Steve has an anchor and a close race.  Not much to hang your hat on.

These first two positions remind me of my chess days, which were often plagued by fear and lack of confidence.  I overestimate my opponent's attacks while underestimating the strength of my own attacks.  How frustrating.


Here I trail 5 away 2 away and have 52 to play.


score: 5
pip: 83
7 point match
pip: 84
score: 2

is Chutzpah
to play 52

1.XG Roller+20/13eq: -0.337
38.88% (G:2.15% B:0.02%)
61.12% (G:2.91% B:0.06%)
2.XG Roller+6/1 3/1eq: -0.507 (-0.170)
34.36% (G:0.96% B:0.01%)
65.64% (G:2.95% B:0.05%)
3.4-ply20/15 3/1eq: -0.366 (-0.029)
38.11% (G:6.54% B:0.17%)
61.89% (G:7.54% B:0.15%)
eXtreme Gammon Version: 2.01, MET: Kazaross XG2

I made the howler 6/1, 3/1.  Looking at this match a week later, the right play seesm obivous.  Run Forrest Run!!  Why the heck am I staying put?  The race is close, he has two inner board blots, and I have a 4 point board. 


Next position I trail 3 away 2 away and have a 32 to play.


score: 5
pip: 131
7 point match
pip: 150
score: 4

is Chutzpah
to play 32

1.XG Roller+13/8eq: +0.089
47.94% (G:13.83% B:0.38%)
52.06% (G:10.92% B:0.21%)
2.XG Roller+22/20 13/10eq: -0.104 (-0.193)
44.03% (G:9.32% B:0.24%)
55.97% (G:7.22% B:0.10%)
3.4-ply13/11 13/10eq: +0.047 (-0.043)
47.12% (G:12.71% B:0.32%)
52.88% (G:12.02% B:0.22%)
eXtreme Gammon Version: 2.01, MET: Kazaross XG2

I played 22/20, 13/10.  This is big error in concept.  I am behind in the race and need the contact.  13/8 is much better.  I have a strong 4 point board and Steve is a bit stripped here.  My guy on the 3 point is annoying Steve and I certainly shouldn't lift it out of the way so he play his awkward rolls behind me.

Last position. Same game.  I trail 3 away 2 away and have 33 to play.


score: 5
pip: 95
7 point match
pip: 124
score: 4

is Chutzpah
to play 33

1.XG Roller+13/7 5/2 4/1eq: -0.650
31.02% (G:2.81% B:0.04%)
68.98% (G:3.19% B:0.07%)
2.XG Roller+20/17(2) 13/7eq: -0.943 (-0.293)
26.13% (G:1.09% B:0.02%)
73.87% (G:1.96% B:0.02%)
3.4-ply13/4 5/2eq: -0.633 (+0.017)
30.36% (G:2.44% B:0.03%)
69.64% (G:2.28% B:0.02%)
eXtreme Gammon Version: 2.01, MET: Kazaross XG2

I made the same error in concept, advancing the anchor with 20/17(2), 13/7. 
Down in the race, make pace!  Or stay back when behind.  Painful to admit, but I am still making elementary errors.