Match Equities

Forum Archive : Match Equities

Neil's numbers

From:   Kit Woolsey
Date:   9 October 1994
Subject:   Re: Equity/Action Table

Come on, Durf.  Match equities aren't all that complicated, and they
really are important if you are to maximize your chances to win matches.

First of all, it might surprise you to know that I have never been able
to memorize my own table -- my memory isn't too good either.  Fortunately
there are formulas around which help those of us with poor memories.  The
best one I know was developed by Neil Kazaross -- called Neil's numbers.
It is as follows:

   3    4    5    6   7   8   9   10   11   12   13   14   15

  10    9    8    7       6             5                   4

The numbers on top represent the number of points the trailer has to go.
The numbers on bottom represent what each point the leader is leading is
worth over 50%.  If there isn't a whole number there, interpolate.  For
example, suppose you are ahead 3-0 in a 7 point match.  The trailer has 7
points to go, so each point of lead is worth 6 1/2 points over 50% to you
-- thus your equity is about 69 1/2% (my table says 70%).  That's all
there is to it!  The above table is easy even for us dumbbells to
remember -- after the trivial start all you need to remember is "8 is 6, 11
is 5, 15 is 4" and you're done.  Also, the calculations involved are
pretty simple to do in your head quickly.  Neil's numbers are incredibly
accurate if the leader has 3 or more points to go, but tend to break down
when the leader has 2 or 1 points to go.  Thus it is best to memorize
that part of my equity table (even I was able to do that), and you're all

As far as using the table to make cube decisions, it isn't as complicated
as people make it to be.  For example, suppose you are ahead 2-0 in a 7
point match, and a 4-cube comes sailing your way.  If you pass, it is 2-2
for 50% equity.  If you take and are right (i.e. you win) you will be
ahead 6-0 for 91% equity.  If you take and are wrong (i.e. you lose) you
will be behind 4-2 for 34% equity.  Thus you are risking 16% to gain 41%,
so you are getting 41 to 16 odds on your take (somewhere between 2 to 1
and 3 to 1), so you can act accordingly.

As for estimating your chances of winning a given position, maybe
there are players who can actually go through the calculations which
Robertie describes.  I'm not one of them!  When I am presented with a
cube decision, I make an old fashioned seat of the pants estimate of my
winning chances, based on my experience and intuition.  I then compare
this estimate with the odds I am getting on my take (calculated as I
described above), and that is what I base my decision on.  Crude, and my
estimate of my winning chances in a position might be way off, but at
least once I have made that estimate I know what to do with it.  If you
don't know how to use match equities you might be able to make a very
accurate estimate of your winning chances and still not be able to make a
sensible cube decision.

If anybody is interested in learning more about match equities and
tournament play I could immodestly recommend a certain book, but that
might be construed as *shudder* advertising, so maybe I shouldn't do


Paul Money  writes:

The book which Kit modestly fails to mention is "How To Play Tournament
Backgammon", author K. Woolsey. It is essential reading for anyone who
aspires to handle the cube with confidence in match situations. I cannot
recommend it too highly. This is an unsolicited testimonial!

rew  writes:

(23 August 2011)

Accuracy of Neils numbers in relation to Kazaross XG2 MET:

I did a little excercice of trying to write down the MET for a 7 point
match using Neils Numbers as a tool. A side result is that I found which
scores Neils Numbers fail, and by how much.

Note 1) For 1 away and 2 away scores I didn't using NN because it is known
not to work for those scores. Instead you need to rely on memorization

Note 2) Always rounding upwards, for instance 56.5 is 57.

Most scores yielded a correct results. Those who didn't:

  -3,-4: NN says 59. Correct is 57.
  -4,-3: (The reverse score of course gives the same error.)
         NN says 41. Correct is 43.
  -3,-5: NN says 66. Correct is 65.
  -5,-3: NN says 34. Correct is 35.
  -6,-7: NN says 57. Correct is 56.
  -7,-6: NN says 43. Correct is 44.
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Match Equities

Constructing a match equity table  (Walter Trice, Apr 2000) 
Does it matter which match equity table you use?  (Klaus Evers+, Nov 2005)  [GammOnLine forum]
Does it matter which match equity table you use?  (Achim Mueller+, Dec 2003) 
Does it matter which match equity table you use?  (Chuck Bower+, Sept 2001)  [GammOnLine forum] [Long message]
ME Table: Big Brother  (Peter Fankhauser, July 1996) 
ME Table: Dunstan  (Ian Dunstan+, Aug 2004)  [GammOnLine forum]
ME Table: Escoffery  (David Escoffery, Nov 1991) 
ME Table: Friedman  (Elliott C Winslow, Oct 1991) 
ME Table: Kazaross  (Neil Kazaross, Dec 2003)  [GammOnLine forum]
ME Table: Kazaross-XG2  (neilkaz, Aug 2011) 
ME Table: Rockwell-Kazaross  (Chuck Bower+, June 2010) 
ME Table: Snowie  (Chase, Apr 2002) 
ME Table: Snowie  (Harald Retter, Aug 1998) 
ME Table: Woolsey  (Raccoon, Apr 2006) 
ME Table: Woolsey  (Kit Woolsey, May 1994) 
ME Table: Woolsey  (William R. Tallmadge, Jan 1994) 
ME Table: Zadeh  (Jørn Thyssen, Mar 2004)  [GammOnLine forum]
ME Table: Zorba  (Robert-Jan Veldhuizen+, Dec 2003) 
ME at 1-away/2-away (crawford)  (Fabrice Liardet+, Nov 2007)  [GammOnLine forum]
ME at 1-away/2-away (crawford)  (Ian Shaw+, Apr 2003)  [GammOnLine forum]
Match equities--an alternate view  (Durf Freund, Oct 1994) 
Neil's new numbers  (neilkaz, Aug 2011) 
Neil's numbers  (Kit Woolsey+, Oct 1994) 
On calculating match equity tables  (Neil Kazaross, July 2004)  [GammOnLine forum]
Turner formula  (Gregg Cattanach, Feb 2003) 
Turner formula  (Stephen Turner, June 1994) 
Using a match equity table  (Michael J. Zehr, June 1992) 
Value of free drop  (Neil Kazaross, Oct 2002)  [GammOnLine forum]
Which match equity table is best?  (Martin Krainer+, Oct 2003) 
Which match equity table is best?  (Ian Shaw+, Dec 2001) 
Why use a match equity table?  (Kit Woolsey, Feb 1999) 
Worth memorizing?  (Alef Rosenbaum+, Feb 2003) 

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