Celebrating 15 years in backgammon games

Feature Columnists: Walter Trice - Tactics and Theory

Cubes After an Endgame Hit

21 Aug 2009 - by Walter Trice

Some of the most difficult doubling decisions in backgammon come up in games that you could have sworn were already over!

 

Rating:  4.94
"Tactics and Theory" Archive
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Endgame Hit Parade

22 Jul 2009 - by Walter Trice

An important class of endgame problems occurs when an opponent has been squeezed off an anchor and a player must decide whether to hit loose and incur the risk of getting hit back, or to play safe and play to win the race without taking on any additional tactical risk.

Rating:  4.83

Step Up or Leap Out?

18 Jun 2009 - by Walter Trice

A common backgammon checker play decision is whether to split a pair of back men, intending to relink them later, or to run one of them into the opponent's outfield. We examine some factors that influence this choice, and introduce a third possibility.

Rating:  4.91

Backgammon Bar Point Slotting Problems

15 May 2009 - by Walter Trice

This month's column is a continuation of last month's discussion of the common dilemma of 13/7 or 24/18. The old school told us, especially in the opening, to "forget the race and play for position." What is the modern way?

Rating:  5.00

Which Bar Point to Slot?

15 Apr 2009 - by Walter Trice

A common backgammon checker play choice, especially in the opening phase of the game, is whether to use a six to slot the player's own bar point (13/7) or the opponent's (24/18). Experts play many of these sixes differently now than 20 years ago as a result of strategic insights.

Rating:  4.68

Let's Hit Some Blots

15 Mar 2009 - by Walter Trice

Backgammon strategy in a nutshell: hit blots, make points, win the race. Almost all backgammon players below the expert level could improve their game simply by hitting blots and making points more often.

Rating:  4.41

A Time to Refrain from Priming

15 Feb 2009 - by Walter Trice

All backgammon players rely on rules of thumb for making checker play decisions. We also know, at least unconsciously, that our rules often conflict with one another. That is why backgammon is not a trivial game.

Rating:  4.71

Why 7n+1 ?

15 Jan 2009 - by Walter Trice

The mean number of rolls required to bear off a stack of checkers from the ace point can be expressed in a remarkably simple formula. Here is an explanation of why it works, together with some other surprising facts about backgammon races.

Rating:  4.73

Third Roll Slot/Split Problems after Opening 6-1 (Part 3)

15 Dec 2008 - by Walter Trice

This month we will conclude our survey of the slot-or-split checker play problems that occur on the third roll of the game for a player who opened with 6-1.

Rating:  5.00

More Opening Slot/Split Backgammon Problems

15 Nov 2008 - by Walter Trice

Continuing last month's survey of opening slot-or-split problems, we look at positions after doubles roll responses to opening 6-1.

Rating:  4.85

Opening Slot/Split Problems

15 Oct 2008 - by Walter Trice

Opening 6-1 is an example of a change to the starting position that produces a tilt toward slotting the five point with aces on the third roll. We consider some backgammon checker play problems that present the slot-or-split problem in this context.

Rating:  4.94

A Backgammon Opening Mystery

15 Sep 2008 - by Walter Trice

The neural network backgammon programs tell us that slotting the five point with an opening 2-1 is a more plausible play than slotting with a 5-1. Why?

Rating:  4.41

Saving Backgammon Sixes

15 Aug 2008 - by Walter Trice

Sixes must be played from the outfield before the bearoff, so rolls with a six are most likely to be troublesome. Most backgammon players pay attention to spare outfield checkers that can be used to play sixes safely. Is this always a good strategy?

Rating:  4.87

Primes, Gammons, and Backgammons

15 Jul 2008 - by Walter Trice

Prime versus prime positions often call for checker plays that appear to be very risky. As a result, beginners and less expert backgammon players can give away mountains of equity by refusing to take the necessary risks.

Rating:  4.89

Backgammon Checkers and Backgammon Pips

15 Jun 2008 - by Walter Trice

Standard formulas for racing cube action have always ignored the even/odd factor, which can be quite significant for crunched positions. Here we present a method for estimating effective pip count that accounts for this effect.

Rating:  4.30

Backgammmon Prime Problems

15 May 2008 - by Walter Trice

Priming is the backgammon game plan that most consistently rewards skillful play. It also produces some very difficult problems in checker play. This month we study six problems that call for a choice between prime-building and other objectives.

Rating:  4.84

Post-Holding Backgammon Game Races

15 Apr 2008 - by Walter Trice

Holding backgammon game positions often lead to races in which standard cube action formulas fail. This month's column shows how to estimate effective pip counts in such positions and use the results to make better cube decisions.

Rating:  4.25

Backgammon Bear-In

15 Mar 2008 - by Walter Trice

Many backgammon players consider the bearing-in phase of a race to be trivial or insignificant. But errors in these positions can add up to significant costs. This month we survey racing positions with one outfield checker.

Rating:  4.39

Audacious Backgammon Hits

15 Feb 2008 - by Walter Trice

Some of the most brilliant and bold plays in backgammon can be made when positional logic demands that a player hit a blot in the face of extremely daunting risks.

Rating:  4.93

Dynamic Backgammon

15 Jan 2008 - by Walter Trice

Backgammon checker-play blunders often arise out of a player's simple failure to think about the consequences of his play. The backgammon expert considers the future, and how his actions may affect that future, with at least as much effort as he devotes to the perception of what is presently visible on the board.

Rating:  4.80

Straggler's Dilemma

15 Dec 2007 - by Walter Trice

One of backgammon's most common strategic patterns is the holding game, in which one player has some combination of points and blots well back on his opponent's side of the board. This month we consider the problem of a straggling blot in a holding game.

Rating:  4.67

Gapped Crunched Bearoffs

15 Nov 2007 - by Walter Trice

Bearoff positions consisting of a heap of buried backgammon checkers plus another clump, separated by a gap, are often misevaluated by standard methods. This month's column presents a simple technique for estimating effective pip count in these positions.

Rating:  4.31

Fifteen Checker Racing Positions

15 Oct 2007 - by Walter Trice

Most backgammon players can do pretty well in 'normal' positions with no buried checkers and low wastage, just by considering the pip count. But one often sees difficult positions that have crunched even before contact is broken, or that have various gaps and positional defects.

Rating:  4.50

Holding Game Cubes

15 Sep 2007 - by Walter Trice

Only three books have been devoted exclusively to the backgammon doubling cube. Each of them has been designated "Volume I" by its author, but none has ever been followed by a second volume!

Rating:  4.88

Backgammon Breakaway II

15 Aug 2007 - by Walter Trice

Breakaway time, often the moment of truth in a game of backgammon, hangs on two key questions. What's the game plan? And if the game plan says break now, is it safe?

Rating:  4.91

Backgammon Breakaway

15 Jul 2007 - by Walter Trice

The crucial point in a game of backgammon often occurs when it comes time to "break away" from an advanced anchor. We consider the strategic principles that underlie this important recurring decision and look at a number of checker-play problems.

Rating:  5.00

'Blood' Resurrection

15 Jun 2007 - by Walter Trice

Walter Trice revisits a classic backgammon book from the 1970s. According to this review, learning backgammon from Bruce Becker is like learning to drive an automobile from someone who doesn't know what the steering wheel is for.

Rating:  4.67

Crazy Aces

15 May 2007 - by Walter Trice

Crazy Aces are the aces in the bearoff that should be played neither to minimize the height of your highest stack nor to maximize the number of points occupied in your home board. If you make one of these plays in a consulting chouette as captain, one of your teammates is going to question your sanity.

Rating:  4.18

Stack and Straggler Races

15 Apr 2007 - by Walter Trice

Walter Trice introduces a conceptual tool --- called Effective Pip Count -- to use when pip counting isn't useful on its own.

Rating:  4.83

Pittsburgh Finals

15 Mar 2007 - by Walter Trice

No one wins a backgammon tournament without some pretty fancy rolling. But one of the distinguishing features of the Pittsburgh Championships, Steve Hast's annual February classic, is the fact that you have to roll well just to get there!

Rating:  4.86

Early Match Cubes

15 Feb 2007 - by Walter Trice

I often find myself wondering, when I am trailing in a match, whether I may be hurting my chances by trying to double "on time, but not too soon". Are there scores where one should turn the cube right off the bat no matter what?

Rating:  4.20

Charlotte Finals

15 Jan 2007 - by Walter Trice

Walter Trice comments on 10 interesting backgammon positions from the recent Carolina Invitational Backgammon Tournament.

Rating:  5.00

Ace Race in Match Play

15 Dec 2006 - by Walter Trice

Walter Trice has updated his Match Equity Generator program and created a new match equity table for ace races--a bearoff in which both players have all their remaining checkers stacked on the ace point.

Rating:  4.33

Ace Race Revisited

15 Nov 2006 - by Walter Trice

Walter wins two trophies at the Las Vegas Backgammon Open, and analyses several positions encountered along the way.

Rating:  4.50

Squeeze Cubes

15 Oct 2006 - by Walter Trice

Walter Trice's latest article concerns cube positions when a defender's anchor begins to fall apart. Eventually, like a fresh watermelon seed squeezed between thumb and finger, the top anchor checker shoots off into the outfield, leaving its companion to come under attack. But first comes the cube!

Rating:  4.75

Hickey vs. Jacobs

15 Sep 2006 - by Walter Trice

I recorded the 2nd-round Indy 300 match between Mary and Jake. According to Snowie the players were well-matched, but as we shall see their dice were not! One-sided matches are not as exciting as the close ones, but any match between two top players turns up some interesting positions. We'll look at a small selection of checker-play problems from the match.

Rating:  4.90

Pure or Safe?

15 Aug 2006 - by Walter Trice

It is helpful to study complete games and matches to get a feel for just how frequently the obvious play is the best available. Each of this month's problems has at least one attractive and pure candidate play that may or may not be correct.

Rating:  4.67

Routine Purity

15 Jul 2006 - by Walter Trice

Often the decisive play in a game of backgammon, whether it is an error that loses or a brilliancy that leads to a win, passes by without notice because it occurs in a quiet position. Violations of purity principles can lead to inferior positions that seem, to the player who is less conscious of those principles, to come about just because of bad luck.

Rating:  5.00

The Most Common Error?

15 Jun 2006 - by Walter Trice

I can almost guarantee that any opponent below the expert level will make a certain type of error at least once in a match. Errors by better players, and quite a few of my own, also fall into the same category with some frequency.

Rating:  4.93

Gammicide in the Three Point Match

15 May 2006 - by Walter Trice

Readers who have followed my last three columns may be expecting a short treatise on the three point match between unequal opponents. I hope you are not disappointed to find that you are not reading one. Even between equal opponents, three-point-match play is a complex subject.

Rating:  4.57

The Practical Three Point Match

15 Apr 2006 - by Walter Trice

In this article we will discuss cube action in racing positions in the three point match. As we shall see, if you can quantify the difference between yourself and your opponent in accordance with an Elo-type scale then you can adjust your cube action with a fair degree of precision in some circumstances.

Rating:  4.80

Two-Point Match In Practice II

15 Mar 2006 - by Walter Trice

With some weaker opponents attempts to improve on 'optimality' become increasingly tenuous. An effort to squeeze more equity out of what is theoretically available can be easily nullified by certain doubles of an opponent.

Rating:  4.80

Two-Point Match In Practice

15 Feb 2006 - by Walter Trice

Much has been written about the theory of the two point-match, but its practical treatment against opponents who do not behave as theory says they should, remains fairly obscure.

Rating:  4.33

Cube Value II

15 Jan 2006 - by Walter Trice

The One Checker Model of the backgammon race can be used to shed light on cube strategy and cube value. It is a useful theoretical tool, simple to manipulate, and it seems to aptly predict significant features of racing positions.

Rating:  4.44

Slot Or Split?

15 Nov 2005 - by Walter Trice

Backgammon players have been grappling with the question of how to play the opening 2-1, 4-1 and 5-1 for as long as I have been at the game and the answers have never seemed less clear to me than they do right now!

Rating:  4.67

Blots And Boldness

15 Oct 2005 - by Walter Trice

To play boldly or safely, that is the question. It applies to nearly every checker play decision that comes up in contact positions and the ability to answer it is a very large part of what constitutes skillful play.

Rating:  4.85

Loose Hits In The Endgame

15 Sep 2005 - by Walter Trice

The decision comes up at least once in almost every match. The opponent has one man back in your home board and the choice is between hitting loose or making a safe play.

Rating:  4.89

Volunteering II

16 Aug 2005 - by Walter Trice

This month we will consider a couple of additional factors that influence the decision to volunteer a shot. Naturally if I told you what they are then the following problems would be much too easy!

Rating:  4.73

Volunteering I

15 Jun 2005 - by Walter Trice

Many of the most difficult checkerplay problems in Backgammon come late in the contact phase of the game. Those that trip me up with some regularity involve the basic decision of whether or not to volunteer a shot in a holding game.

Rating:  4.54

Struggle For Initiative

15 May 2005 - by Walter Trice

This time we will look at a collection of checkerplay problems in which the main issue is the initiative. Initiative-oriented plays are plays that gain time in the pursuit of constructive short-term goals.

Rating:  4.92

When To Play 6/5*

15 Apr 2005 - by Walter Trice

Playing 6/5* early in the game is almost always going to be right when the opponent still has only a one point board or alternatives are non-constructive and/or risky.

Rating:  4.79

2005 Pittsburgh Final

15 Mar 2005 - by Walter Trice

I got knocked out by Neil Kazaross in the fourth round and on the day of the finals I wandered into the tournament hall and spotted him playing Phil Simborg for the crown. A few games had already gone by but we got the rest.

Rating:  5.00

Son Of Smoothy

15 Feb 2005 - by Walter Trice

While playing around with Smoothy it occurred to me that the same capability for two-sided bearoffs would be an even more useful thing to have, thus the creation of Junior, the "Son of Smoothy". Download it here.

Rating:  5.00

Bearoff Smoothing Plays (III)

15 Jan 2005 - by Walter Trice

As promised, I am wrapping up this series on the one-sided treatment of bearoff checker plays with a downloadable computer program. Since the program, among other things, produces lists of smoothing plays I have dubbed it "Smoothy".

Rating:  5.00

Bearoff Smoothing Combos

15 Dec 2004 - by Walter Trice

Compared to one-sided bearoff positions in which it is possible but wrong to bear off a checker with a single number, a distinct category consists of non-transposing plays that achieve smoothing by playing the lower of two numbers first.

Rating:  4.80

When Not To Bear Off

15 Nov 2004 - by Walter Trice

A number that doesn't bear off can be used to prepare to bear off by filling in empty points. A number that neither bears off nor fills may be used to prepare to prepare to bear off by evening out stacks - here are some tactics.

Rating:  5.00

Shot For The Gammon?

15 Oct 2004 - by Walter Trice

Aggression to the extent of volunteering a shot to save a roll is quite often correct when playing for the gammon against a crashed board. The key skill required to find these plays is the ability to recognize when the gammon race is a close.

Rating:  5.00

Practical Endgame Calculations

16 Sep 2004 - by Walter Trice

In an important match a contact bearoff arises and your opponent redoubles. The score is lopsided enough that money-game cube action is not an adequate benchmark, so you will actually need to estimate your chance of winning the game. What to do?

Rating:  4.63

Fifteen Versus One

15 Aug 2004 - by Walter Trice

A backgammon enthusiast, intrigued by the mathematical intricacies of bearoffs and endings, risks falling into the "specialist" trap: he may wind up knowing everything about nothing.

Rating:  4.43

Inside The Contact Database

16 Jul 2004 - by Walter Trice

Bearing in and off against contact remains one of the more difficult phases of backgammon strategy. What makes these problems so thorny? Why haven't they all been completely solved by computer programs?

Rating:  5.00

Closeout Bearoffs

15 Jun 2004 - by Walter Trice

Recently a reader expressed interest in a tutorial on the subject of the contact bearoff, and especially on the issue of "when to take an extra risk for the gammon and when to play safe". This is an excellent topic!

Rating:  4.94

Getting The Nack II

16 May 2004 - by Walter Trice

Backgammon checker plays tend to fall into characteristic groups, distinguished by their different strategic objectives and by the different types of positions in which they may or not be appropriate.

Rating:  5.00

Getting The Nack

20 Apr 2004 - by Walter Trice

Nackgammon games last longer than regular Backgammon games and they tend to produce more complex positions. As a result the skill factor becomes somewhat more significant increasing the stronger player's edge.

Rating:  4.47

Who's The Favourite?

20 Mar 2004 - by Walter Trice

This month Walter answers a query from GammonVillage subscriber Brian Busfield who wonders how the player with the higher error rate, in a Snowie-analyzed match between Mads Andersen and Mario Kuhl, is calculated as the favourite?

Rating:  4.62

Robertie Vs. Grandell - Part 6

20 Feb 2004 - by Walter Trice

This match is the Final of the 1987 Monte Carlo World Championship which pitted former World Champion Bill Robertie against Jerry Grandell, who would win in 1997. This is the sixth and final instalment of this series with Games 20 to 23.

Rating:  4.50

Robertie Vs. Grandell - Part 5

20 Jan 2004 - by Walter Trice

This match is the Final of the 1987 Monte Carlo World Championship which pitted former World Champion Bill Robertie against Jerry Grandell, who would win the title in 1997. This is the fifth instalment of this series with Games 16 to 19.

Rating:  5.00

Robertie Vs. Grandell - Part 4

20 Dec 2003 - by Walter Trice

This match is the Final of the 1987 Monte Carlo World Championship which pitted former World Champion Bill Robertie against Jerry Grandell, who would win the title in 1997. This is the fourth instalment of this series with Games 12 to 15.

Rating:  4.00

Robertie Vs. Grandell - Part 3

20 Nov 2003 - by Walter Trice

This match is the Final of the 1987 Monte Carlo World Championship which pitted former World Champion Bill Robertie against Jerry Grandell, who would win the title in 1997. This is the third instalment of this series with Games 9 to 11.

Rating:  5.00

Robertie Vs. Grandell - Part 2

20 Oct 2003 - by Walter Trice

This match is the Final of the 1987 Monte Carlo World Championship which pitted former World Champion Bill Robertie against Jerry Grandell, who would win the title in 1997. This is the second instalment of this series with Games 4 to 8.

Rating:  4.75

Robertie Vs. Grandell - Part 1

20 Sep 2003 - by Walter Trice

This match is the Final of the 1987 Monte Carlo World Championship which pitted former World Champion Bill Robertie against Jerry Grandell, who would win the title in 1997. Let's see how they played before the bot era.

Rating:  4.33

Horan Vs. Ballard - Part 3

20 Aug 2003 - by Walter Trice

Walter Trice comments on a match played at the U.S. Invitational Championship of 1984 between Backgammon Giants Billy Horan and Nack Ballard. Here is the final part with Games 9 to 13.

Rating:  4.00

Horan Vs. Ballard - 1984 - Part 2

20 Jul 2003 - by Walter Trice

Walter Trice comments on a match played at the U.S. Invitational Championship of 1984 between Backgammon Giants Billy Horan and Nack Ballard. Here is Part 2 with Games 6-8.

Rating:  5.00

Horan Vs. Ballard - 1984

20 Jun 2003 - by Walter Trice

Walter Trice comments on a match played at the U.S. Invitational Championship of 1984 between Backgammon Giants Billy Horan and Nack Ballard. Here is Part 1 with Games 1-5.

Rating:  5.00

Magriel Vs. Low - 1981 - Part 2

20 May 2003 - by Walter Trice

Walter's second match from Bronze Age BG was between Paul Magriel and Roger Low in 1981. Here are Games 5-8. Warning: multiple games mean more board positions to open than in a normal GV article, please be patient as the article downloads.

Rating:  4.57

Magriel Vs. Low - 1981

20 Apr 2003 - by Walter Trice

Walter's second match from Bronze Age BG was between Paul Magriel and Roger Low in 1981. Here are Games 1-4. (Warning: Multiple games mean more board positions to open than in a normal GV article, please be patient as the article downloads.)

Rating:  4.82

Bronze Age Backgammon II

20 Mar 2003 - by Walter Trice

Part Two of Walter's comments on a seven-point match from the 1978 ABC Super-16 event played between Jason Lester and Oswald Jacoby.

Rating:  4.80

Bronze Age Backgammon I

20 Feb 2003 - by Walter Trice

The 1970's are generally believed to have been a time when the backgammon was wild, woolly and barbaric but the truth about the "70's style" is more complex...

Rating:  4.58

Master Vs. Amateur VII

20 Jan 2003 - by Walter Trice

Article 7 of Walter's comments on the 11-point semi-final match played at the 50th Indiana Open between Bill Robertie and Jim Curtis. Here are Games 10 and 11, the last two of this match.

Rating:  4.47

Master Vs. Amateur VI

20 Dec 2002 - by Walter Trice

Article 6 of Walter's comments on the 11-point semi-final match played at the 50th Indiana Open between Bill Robertie and Jim Curtis. Here are Games 8 and 9.

Rating:  5.00

Master Vs. Amateur V

20 Nov 2002 - by Walter Trice

Article 5 with Walter's viewpoint on the 11-point semi-final match played at the 50th Indiana Open between Bill Robertie and Jim Curtis. Here are Games 6 and 7.

Rating:  4.33

Master Vs. Amateur IV

01 Nov 2002 - by Walter Trice

Article 4 of Walter's comments on the 11-point semi-final match played at the 50th Indiana Open between Bill Robertie and Jim Curtis.

Rating:  4.14

Master Vs. Amateur III

25 Oct 2002 - by Walter Trice

Games 3 and 4 with Walter's comments on the 11-point semi-final match played at the 50th Indiana Open between Bill Robertie and Jim Curtis.

Rating:  4.55

Master Vs. Amateur II

18 Oct 2002 - by Walter Trice

Walter continues his comments on the 11-point semi-final match of the 50th Indiana Open between Bill Robertie and Jim Curtis.

Rating:  4.62

Master Vs. Amateur

11 Oct 2002 - by Walter Trice

Walter Trice begins a new series on GammonVillage today sharing his knowledge of the tactics and theory behind the moves in positions from matches that he has collected over the years.

Rating:  4.57
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Celebrating 15 years in backgammon games