Besides, suppose you happen to remember that your equity
at 11-away, 3-away is 10%. What do you do with that
priceless morsel of information? How do you estimate what
your chances of winning the game at hand are? Here's the
way Bill Robertie says to handle it (partial quote from
ADVANCED BACKGAMMON, Volume 1):
Over-the-board, aside from guesswork and intuition, only a
case-by-case analysis offers any chance of lending some
insight to this position. Let's see how this might proceed.
White's replies to this play fall into three pretty clear
groups: rolls which hit back (14), rolls which enter one man
without hitting (13), and bad shots which enter at most one
man (9). When White hits back...(analysis)...I'll give
Black only 25% of these games, or 3.5 games out of 14.
White enters both men but doesn't hit...(analysis)...I'll
make Black 50% in this variation, giving him 6.5 games out
of 13. White rolls badly...(more analysis)...I'll give
Black 5 games out of 9. Totals for Play (a): Black gets 3.5
games in the first group, 6.5 in the second group, and 5 in
the last group, a total of 15 games out of 36.
Once you've figured out Play (a), you do similar
calculations for Plays (b), (c), (d), and (e), total the
results, take the cube root, mulitiply by the distance from
the sun to Jupiter in parsecs, divide by the angle at the
tip of Madonna's bra in radians, and you come out with an
equity of 13%. You compare that to the match equity of...
ummm, ummm. Keep in mind that all this time your opponent,
back from his walk around the playing area, is tapping his
fingers and mumbling semi-intelligible comments about chess
Maybe top players actually do those calculations during a
game and memorize all kinds of odds and tables. For those
of us mere mortals who actually have lives, however, I have
created an Equity/Action Table. This greatly simplified
table not only considers match equity, but also tells you
what to do in many real-life situations. It is a lot easier
to memorize than Kit's table, because it's smaller (if
you're 1-away, 13-away and don't know what to do, I don't
want to tell you), uses letters instead of numbers, and has
recognizable patterns. Here it is:
"Unrevised Equity/Action Table"
1 2 3 4 5
1 TD DD DD DD DD
2 DS WD PC NT DM
o 3 DS PC QE PC NT
4 DS NT PC QE PC
5 DS DM NT PC QE
TD - Tactical Double. Double. Your opponent might drop, or
he might get steamed. You have nothing to lose, unless you
dread getting flamed on r.g.b.
DD - Don't Double. Whatever you do, hold the cube. The
Tactical Double reasoning does not apply.
DS - Double, Stupid! If you have to refer to the chart in
these situations, I'd be interested in playing you for money
at your earliest opportunity.
WD - Woolsey double. Kit says you should double in this
situation as soon as you have an actual chance to roll. If
you believe him, double.
PC - Pretty close. If you think you're a better player than
your opponent, you have to pay more attention or get
luckier. If you're an underdog, just keep doing what you've
NT - Not Too. The situation you're in is either not too bad
or not too good. Act accordingly.
DM - Desperate Maneuvers. If you are ahead, expect your
opponent to make maniacal plays and cube turns. If you're
behind, make maniacal plays and cube turns.
QE - Quite Even. Equity here is easy to evaluate. Also
applies at the beginning of 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
as for WD, some people advocate doubling on first roll at -2:-2 but
kit isn't one of them (unless he's changed his mind since his book);
i think he wants to have at least one market loser before he lets it
Kit Woolsey (kwoo...@netcom.com) wrote:
: 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
well hell, i'll recommend it. you can order kit's book from Gammon
Press (see the FAQ). now if i only had the time to learn
that darn table :)
** Gerald E. Mortensen (Jay) Syracuse Research Corp. ***
** Research Engineer Merrill Lane ***
** (315)426-3269 -- j...@syrres.com Syracuse, NY 13210 ***
> thanks for the table, durf. i like it! especially the TD :)
> as for WD, some people advocate doubling on first roll at -2:-2 but
> kit isn't one of them (unless he's changed his mind since his book);
> i think he wants to have at least one market loser before he lets it
Just to put this in perspective....
I had a pretty graphic illustration of what exactly a market loser consitutes
in my first Fall Tournament match (which I went on to lose after this game).
The game: Score: -2,-2.
4-2: 24-20, 13-11 3-3: 8-5(2), 6-5(2)
6-4: (0) Double
Correct strategy here, obviously: 3-3/Dance is a market loser, so I should
double before I roll 3-3.
Lesson learned by me: any attempt to split back men at -2,-2 should be doubled.
Robin Davies Standard disclaimer for the self employed:
Software Consultant This message does not neccessarily reflect
Windows, NT, OS/2, DOS the views of the author.
Applications and Device Drivers
I, John Bazigos, who have no vested interest in the sale of Kit's
aforesaid book (in fact, it makes almost all of its readers, including my
opponents in tourneys, stronger match-players), entirely my own
initiative, and with no remuneration therefor, hereby recommend Kit
Woolsey's book "How To Play Tournament Backgammon" (1993), published by
and available from
The Gammon Press
P.O. Box 294
Arlington, MA 02174
for $20 US
(USA, $3; Canada or foreign surface, $3; European or South-American airmail,
$7, Pacific Airmail, $8)
as an introductory text on issues related to backgammon match-play per se.
Here is an outline of the book:
1. Crawford Game Strategies
2. Post-Crawford Play
2.1. The Free Drop
2.2. Mandatory Doubling
3. The Two-Away versus Two-Away Score
4. The Match-Equity Table
5. Learning the Table
5.1. The Janowski Formula
6. Using the Table
6.1. Gain-Loss Tables
6.2. The Doubling Window
7. Initial Cube-Decisions at Various Scores
8. Redoubles and Cube-Leverage
9. Cube-Leverage in Gammonish Positions
10. Gammon Potential and Checker Play
11. Five Practical Examples
12. An Illustrative Game: Woolsey-Robertie, Reno 1993
-- John Bazigos ("doc" on FIBS)
>There is a school of thought that says once you reduce backgammon to
>this...you've become a peer of fatboy...unless you have desires to be a
>professional...why not just play as well as you can by gut feel.
>Otherwise...it's ONLY a dice game.
One of the great appeals of backgammon is that it can be enjoyed so soon
after learning the bare rules of the game. And it is true that the game can
offer hours of pleasure without ever appealing to any science beyond "gut
. . . But I would bet that those players who do pursue the mathematical
subtleties of the game, as I do do some extent, take a very real aesthetic
pleasure in the shifting patterns of nu,mbers, the surges of equities, the
paradoxical violations of "common sense" that constantly arise in the game.
I have heard a sentiment similar to yours expressed about music and poetry.
"It spoils it if you study it." ---And yet this sentiment is expressed more
often by persons who HAVEN'T undertaken serious study than by those who
So by all means, ignore lengthy posts hashing out match equities and and
take/drop points, but don't make the assumption that those who are
interested enought to write such treatises are robotic drones. There may be
some professional BG drudges out there, but I've never met one. The best
players I know take delight in the numbers.
"When it was proclaimed that the Library contained all books,the
first impression was one of extravagant happiness. All men felt
themselves to be the masters of an intact and secret treasure.
-Jorge Luis Borges, "The Library of Babel"
There is another school of thought which says that people with that attitude
lose money in the long run to those with the opposite attitude.
Stephen R. E. Turner
Stochastic Networks Group, Statistical Laboratory, University of Cambridge
e-mail: sr...@cam.ac.uk WWW: http://www.statslab.cam.ac.uk/~sret1/home.html
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