Match Equities

 Turner formula

 From: Gregg Cattanach Address: gcattanach@prodigy.net Date: 24 February 2003 Subject: Re: What is the doubling window at 4 away 2 away? Forum: rec.games.backgammon Google: tGm6a.460\$Ly2.316@newssvr19.news.prodigy.com

```One great tool I found to help come up with the numbers on the MET
(Woolsey's) is the 'Turner Formula'.  This makes it unnecessary to memorize
all those numbers, and this simple algebraic formula gets you to the right
number on Woolsey's table within 1 percentage point for all scores up to
11-away, 11-away.

First, you must memorize the Crawford score numbers, so just memorize this
series:  30, 25, 17, 15, 10, 9, 6, 5, 3, 3.  These are the trailer's equity
at 2-away, 3-away, 4-away, etc. Crawford.

Turner Formula:
((24 / T + 3) * D) + 50  where:
T is the number of points the trailer has to go
D is the difference between the two scores.

This is quite easily done in your head, especially because 24 divides
evenly with so many numbers.  If T is 5, then I just round (24 / T) to 5,
if T is 7 I round (24 / T) to 3-1/2 and it T is 9 I use (24 / T) as 2-2/3.
After completing the formula  there are 5 'perverse' scores that need
adjustment at 2-away 5-away, 2-away 6-away, 2-away 7-away, 2-away 8-away,
2-away 11-away.  For 2-away 11-away subtract 3 points.  For the other 4 add
2 points to each, (or to be most precise actually at 3 points for 6-away
and 7-away).  Your final result for any score up to 11-away 11-away  is
always +-1 of the Woolsey number and 80% of the time exact.

For those that use 'Neil's Numbers' which is also an excellent system,
you'll see that the (24 / T + 3) part is exactly Neil's number.

This much math can be done in your head, and figuring out a take point is
often quite important in lots of match situations.  In my experience,
figuring the take point comes up 10 times more often than figuring the
minimum doubling point.  The reason is when I'm doubling, it is usually
true that I want to be near my opponent's take point.   So I'm either
figuring my take point (if being doubled) or my opponent's take point (if
I'm doubling.)

Take point:  (PS - TL) \ (TW - TL)
PS=ME if passed
TL=ME if take and lose
TW=ME if take and win

This is still the risk / (risk + gain) formula:  Risk = (PS - TL)  Gain =
(TW-PS)  but the - PS and + PS elements in the denominator cancel out.

Hope this helps.

Gregg C.
```

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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)
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)
ME Table: Big Brother  (Peter Fankhauser, July 1996)
ME Table: Dunstan  (Ian Dunstan+, Aug 2004)
ME Table: Escoffery  (David Escoffery, Nov 1991)
ME Table: Friedman  (Elliott C Winslow, Oct 1991)
ME Table: Kazaross  (Neil Kazaross, Dec 2003)
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)
ME Table: Zorba  (Robert-Jan Veldhuizen+, Dec 2003)
ME at 1-away/2-away (crawford)  (Fabrice Liardet+, Nov 2007)
ME at 1-away/2-away (crawford)  (Ian Shaw+, Apr 2003)
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)
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)
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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