Brays Learning Curve: Reference Positions

 

Money Play. Should Red double? If doubled, should Red take?

2019 - Beginners 12

XGID=—CCbD-B—eC—babc—–:0:0:1:00:0:0:3:0:10

 When we start to teach the use of the doubling cube, we begin with endgame problems because they are easy to calculate exactly. However, the vast majority of doubling decisions cannot be calculated precisely and so we have to rely on reference positions.

These are positions that we have committed to memory where we ‘know’ the correct cube action. When a similar position arises, we make use of the reference position by accessing it and then adjusting our decision based opon the actual position we have to consider.

One of the reasons beginners play so slowly is that they have very few reference positions upon which to draw, and they end up trying to solve problems from first principles which does take a lot of time. The more you play the greater your reference library becomes and the easier it is to find a useful position to use as a reference.

This week’s position is a classic reference position for playing against the five-point holding game.

Red is clearly the favourite and should double now because rolling nearly any double will lose his market. He leads the race by 55 pips so unless White rolls a lot of big doubles he is very unlikely to win the race.

White’s route to victory is to build his home board points (in order), hit a Red checker, contain it and win with a redouble. In this position White has plenty of time to keep his mid-point and Red may soon have to leave a shot as he tries to clear-his own mid-point.

If the race were closer White may have to give up his mid-point and rely on hitting a shot from Red’s 5-pt. The beauty of this type of position is that as White’s racing chances diminish his hitting chances increase.

The rule of thumb is that Red should be 20 pips ahead in the race before he doubles and White can take until he is nearly 60 pips behind. That’s quite a range! Once White is more than 60 pips behind he has to pass because he loses too many gammons, a point you may not have considered.

If you want to study these type of positions in more depth try to get hold of a copy Kit Woolsey’s “The Backgammon Encyclopedia: Volume 1”.

 

Rollout Data from Extreme Gammon

Beginners 12 Rollout

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Bray’s Learning Curve: Opening Roll Responses

Money Play. How should Red play 21?

Basic Begiiners 2

XGID=-a–a-E-C—dEa–c-e—-B-:0:0:1:21:0:0:3:0:10

With the opening roll we look to do three things: make new points; unstack the mid-point and 6-pt; advance the rear checkers.

When responding to the opening roll we will have a fourth option, namely hitting an opponent’s blot. Unlike at the end of the game when a hit can be fatal because of your opponent’s strong home board, a hit in the opening is usually anything but fatal.

However, it does something very important and that is to take a tempo away from your opponent. He will have to spend half of his next roll entering from the bar (and sometimes he rolls 66 and stays on the bar, that is known as a boxcar bonus). Therefore, unless he rolls a double, he is unlikely to make a new point. Thus, he spends his time reacting to your play rather than having the freedom to play his whole roll as he chooses. The more you play backgammon the more you realise how important it is to take tempi from your opponent

Having understood the thinking, you should now to be able to play Red’s 21 in response to White’s opening 32 (played, 24/21, 13/11). Red must hit 6/4* with the 2 to take a tempo. After that the logical 1 is 24/23, getting one of the back checkers moving on its way while White is preoccupied on the bar. All non-hitting plays are too passive as you can see from the rollout.

What about if White had rolled 52, played 24/22, 13/8. How would you play 64?

Before the advent of computers most people played 24/14 but the bots have taught us that 13/3*, taking that all-important tempo, is correct.

There are many other opening rolls and possible responses (actually about 600 of them) but as you play more and more those responses will become second nature to you. The more you play the quicker you will learn them!

Rollout Information from Extreme Gammon

Basic Beginners Rollout 2

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Bray’s Learning Curve: Not Good Enough Too Good to Double

  1. Money Play. Should Red double? If doubled, should White take?

  2. Match Play. Red leads 4-0 to 7. Should Red double? If doubled, should White take?

2019 - Experts 11

XGID=-aC—-b-a—a—abcbb—A:0:0:1:00:0:0:3:0:10

I was watching a match between two strong players on GridGammon when this position came up. Red doubled and White snapped up the cube which I must say surprised me. Red easily won a gammon and the match. I was sure that White should have passed but then started doing some detailed analysis.

Let’s quickly deal with the money game question. Red should double (activating gammons) and White should pass very quickly indeed. Taking this double would be worse than a quintuple blunder – see the rollout below. If you even considered taking this cube in a money game, then some swift re-evaluation of your cube handling is required!

The match score question is very different. This is fundamentally a prime-versus-prime position and it is well-known that these positions generate a high percentage of gammons for both sides. That is exactly what White wants, especially if the cube gets to 4 when a gammon will win the match for him. Holding a 2-cube and already down 4-0 White will need very little excuse to redouble to 4. For example, any game-winning single shot will suffice.

What is truly surprising is that technically Red should not double – see the rollout below. This position falls into the category of “not good enough, too good to double”. This means that Red should leave the cube alone and play on for an undoubled gammon which would get him to 6-0 (Crawford). Of course, he can always use the cube later if the position warrants it. Naturally White should accept the cube if doubled (as he did in the actual game).

Having said all that for practical purposes Red should double. A high percentage of players will drop this and play from 0-5 behind. XG gives you a percentage figure on rollouts that would change its decision. In the rollout below you will see the figure is 3.2%. Many more than 3 out of 100 players will drop this double so unless I was certain my opponent was taking the double, I would ship the cube here.

When watching the match, I had let my money play thinking cloud my match play judgement, one of the most common errors in backgammon.   If you got this problem right for the right reasons, then very well done.

Rollout Information from Extreme Gammon

Money

Experts 11 Rollout - Money

Match

Experts 11 Rollout - Match

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Bray’s Learning Curve: Weighing Anchors

Match Play. Red leads 4-2 to 11. How should Red play 55?

2019 - Intermediates 11

XGID=-aaB-bE-B—bCb–b-dBa—A:0:0:1:55:4:2:0:11:10

This position comes from the recent Boston Open. The score is actually irrelevant to the play.

Red played bar/15, 20/15(2) with his double fives but that was not the best play.

Giving up an anchor in a backgammon game is a major decision and the more I play the more I like to hang on to my anchor. Of course, eventually you have to give up your anchor and run for home but if you can do it with a gain of tempo (i.e. hitting your opponent as you do so) so much the better.

When there is a lot of play left in a position, as is the case here, then normally you are better off holding on to the anchor so that you have a safe re-entry point. There is likely to be quite a lot of hitting before this game is finished and so Red should have kept hold of his opponent’s 5-pt.

He should have played bar/20, 6/1(2)* (Barclay Cooke would turn in his grave with making the ace-point so early!) and then thought about the third five. He could play safe with 13/8 but he has gained a tempo by putting White on the bar. Three checkers on the 15-pt is inefficient and so the spare checker should be put to work with 20/15. 13/8 is too safe a play given the demands of the position and as you can see from the rollout such a passive play is actually a blunder.

The result is that after bar/15, 6/1(2)* Red has maintained a flexible game plan. After bar/15, 20/15(2) he has no choice but to try to tip-toe through the minefield to bring his checkers home safely – a blot being hit could be ruinous. Try playing the position out a few times and you will find just how difficult it is to bring those checkers home.

There isn’t a huge equity difference between the two top plays but the important thing is to understand the concepts behind bar/15, 6/1(2)*.

So, remember – keep hold of your anchors!

 

Rollout Information from Extreme Gammon

Intermediates 11 rollout

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Bray’s Learning Curve: The Third Roll

 

Money Play. How should Red play 32?

2018 - Beginners 11

XGID=-b—-EBB—eD—b-db—B-:0:0:1:32:0:0:3:0:10

After the second roll there are about 600 possible positions. When it gets to third roll there are many thousands so you cannot learn them off by heart, instead you have to learn the appropriate principles.

This position arises after Red has opened with 61 (13/7, 8/7) and White has replied with 31 (8/5, 6/5). Red must now play 32. How should he play it?

Once your opponent has made his 5-pt it is normally correct to split the back checkers to stop your opponent quickly building a prime in front of your rear checkers.

That would imply playing 24/22, 13/10 or 24/21, 13/11. Surprisingly enough both these moves are still errors because they don’t go far enough in applying the correct principle. The correct move is 24/22, 24/21, advancing both rear checkers. One of the ideas behind the play is that if one of the checkers is pointed on, you might be able to make an advanced anchor using the other one.

It is interesting to see how big a blunder 13/11, 13/10 is. That play strips the mid-point of its spare builders and does nothing about addressing the strength of White’s home board position. 13/8 is also very weak because it does virtually nothing to improve Red’s position at a time when he should be taking risks.

The key here is to learn the principle of advancing both checkers and then put that principle into use in your own future games.

Rollout Data from Extreme Gammon

beginners 11 Roolout

 

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Brays Learning Curve: The Opening Roll

 

Money Play. How should Red play 64?

Basic Begiiners 1

XGID=-b—-E-C—eE—c-e—-B-:0:0:1:64:0:0:3:0:10

What could be easier than the opening roll? After all, there are only fifteen of them that you have to learn. Not too much work for anybody.

Five opening rolls are always played the same way: 31 (8/5, 6/5); 42 (8/4, 6/4); 53 (8/3, 6/3): 61 (13/7, 8/7) and 65 (24/13). These moves have stood the test of time although as late as the mid-1970s 53 was often played 13/10, 13/8! The game is old (5,000 years) but some of the theory is quite young.

With the other ten opening rolls you have choices as to how you play them. I have chosen to discuss 64. For years this was played 24/14, simply running a back checker in an attempt to get it to safety. Then people started moving 6x by moving 24/18, 13/x. This applied to 62, 63 and 64. The idea behind this play is to either make the opponent’s bar-point next turn or promote an exchange of hits on that bar-point. Normally that exchange of hits is favourable to the player who opens with the 6x.

For years, players laughed at the third choice, 8/2, 6/2, making the 2-pt. It was felt that this play made a point too deep in the home board so near the start of the game. Then along came computers and lo and behold, they think that making the 2-pt is a very reasonable move.

As you can see from the rollout below there is virtually nothing to choose between the three plays and so it becomes a matter of personal choice (except in match play but that is a lesson for another day). The three moves lead to very different types of game so if you want a simple game choose 24/14. Pick 24/18, 13/9 for complexity and 8/2, 6/2 lies somewhere between the other two.

The opening roll is likely to be the last time you have a choice so enjoy it while you can.

Rollout Information from Extreme Gammon

Basic Beginners Rollout 1

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Brays Learning Curve: Complex Ending

  1. Money Play. Should Red double? If doubled, should White take?

  2. Match Play. Red leads 2-1 to 5. Should Red double? If doubled, should White take?

2018 - Experts 10

XGID=-aC—-b-a—a—abcbb—A:0:0:1:00:0:0:3:0:10

Without an extensive knowledge of reference positions this is a difficult problem. If you have seen something like this before it makes life a lot easier!

I know that if those three checkers on the 2-pt were safely on the ace-point this would be a double and a huge pass but the possibility of White picking up a second (and even a third) checker make things much more complex. Of course, White has to know the right technique to maximise his chances of picking up that additional checker. He must build a prime, then Red has to roll an inconvenient ace and play 2/1* and then White must hit that exposed checker.

White must be patient and the game may well go on for a long time. However, the threat of picking up that additional checker makes this a very easy take for White and in fact, Red only just has a double.  Unless, of course, he thinks that White will drop and believe me a fair few people will drop this.

At the match score, doubling this position would be a gargantuan blunder. White will need little excuse to to redouble to four and put the match on the line as his winning chances from 1-4 down (Crawford) are only 17%. Red must leave the cube where it is at this match score and hope to win a gammon to take him to 4-1 ahead. He will actually win a gammon about 17% of the time from the start position.

Because of the match score Red may not even be able to double if he ends up with a single checker closed out. It will depend upon if he has any other checkers exposed in his home board and White’s exact bear-off structure.

You can learn a lot from this position by adjusting it slightly. For example, change the match score to 1-1, and see what impact that has. As I have remarked before backgammon is a very complex game and you can learn a lot by an in-depth study of any single position. This one is worthy of your attention! 

Rollout Information from Extreme Gammon

Money

Experts 10 Rollout - Money

Match

Experts 10 Rollout - Match

 

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Brays Learning Curve: Gammons Count Double

Money Play. How should Red play 31?

2018 - Intermediates 10

 

XGID=-BBCBBBb—–B—–ababdc-:1:-1:1:31:0:0:3:0:10

Over the board Red played 5/4, 5/2 but that was a mistake.

Red must take advantage of the weakness in White’s home board while it exists. He should note that the race is close, although White has some home board wastage. By next turn White may have tidied up his home board and Red may have to break from his midpoint as he has no safe sixes to play elsewhere. He should not be breaking up his perfect home board, rather he should be using it as a weapon.

The correct play is 13/12, 13/10. Now Red has not wasted any pips in the race and if White hits he risks losing a gammon to any return hit. In fact, most of the plays that break the home board win the same or slightly more single games than 13/12, 13/10 but that play wins 10% more gammons – a huge difference.

Players tend to look at the downsides of any potentially risky play and lose sight of the upsides. Remember that gammons do count double!

Rollout Information from Extreme Gammon

 

Intermediates 10 rollout

 

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Brays Learning Curve: Count the Ways

 

Money Play. Should Red double? If doubled, should White take?

2018 - Beginners 10

XGID=–DF-aCB———–bdbbbb-:0:0:1:00:0:0:3:0:10

This type of position is fairly common so it is best to know how to deal with it.

First, it should be clear that Red should double. With a 15-pip lead in the race and multiple market-losing sequences not doubling here would be a double blunder.

The interesting question is whether or not can White can take. His thinking should go along these lines:

Red will leave me a shot with 62, 26, 44, 55 and 66. I will hit that 30% of the time so that is 1.5 wins out of 36.

What about the race? Red is nominally 15 pips ahead but that is not a true count. He has six checkers on his 3-pt and four checkers on his 2-pt. that will add approximately 6 pips to his adjusted pip count. In addition, he will have empty 4- and 5-pts in the bear-off so that will create further inefficiencies for him. On the down side he has only two crossovers and two pips to get his checkers home while I have 4 crossovers and 15 pips to roll before I can begin to bear-off.

In the 31 games where he doesn’t leave me a shot, can I win 7.5 of them to bring me up to the nine games I need to win to accept the double? To answer that question requires both experience and judgment but it can be made a lot easier if you have a reference document. Luckily, you will find “Backgammon Races” in the download section of my website: www.chrisbraybackgammon.com

The answer in this particular case is that White can take with relative comfort. The key to learning is then to adjust the position to find out what happens when things change. Move the spare on White’s 4-pt to his 5-pt and he can still take the double but move it to his 6-pt and the position becomes a drop.

In the initial position if we move one of the spare checkers on Red’s 3-pt to his 6-pt the position becomes double/drop because 44,55 and 66 now play safely. So small differences in the position can make a big difference to the cube action – tricky game backgammon.

 

Rollout Data from Extreme Gammon

Beginners 10 Rollout

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Brays Learning Curve: Match Play Problem

Match Play. Score 4-4 to 7. Should Red redouble? If redoubled, should White take?

 

2018 - Experts 9

XGID=—B-aDBBB—B–aAbbbc-bb-:0:0:1:63:4:6:1:7:10

Once again, the match score dominates the doubling decision.

For money this would be a very premature redouble as White has all his checkers in play and,  owning the cube, he would be in a powerful position to redouble Red if the game turned around.

However, at this match score the cube is valueless to White and so it is merely a question of whether Red is a sufficient enough favourite to redouble now.

White’s point of last take is 25% (the match-winning chances he would have if he dropped the redouble). Is Red close enough to 75% winning chances to redouble? As ever that is a matter of using experience to make the judgement and an exact percentage estimate is impossible.

However, Red has a five-point prime, a five-point home board and White is on the bar. He is certainly a strong favourite. Over the board I redoubled this position and my opponent dropped.

White should have taken as you can see from the rollout below. Red is near the top of his doubling window but not above it. Therefore, the answer is that Red should redouble and White should take.

Rollout Information from Extreme Gammon

Experts 9 Rollout

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Brays Learning Curve: Good Numbers and Bad Numbers

Money Play. How should Red play 43?

2018 - Intermediates 9

XGID=-BbC-BB-D——–bbcd–bB-:0:0:1:43:0:0:3:0:10

This is not a very difficult problem but Red went astray over the board by playing 24/21, 8/4, which is an unnecessary overplay. White replied with 64, played 7/1*, 5/1 and after Red fanned, White won with cube.

Red should observe that White has 13 checkers in the attack zone and that should flag up an immediate warning. Those extra checkers on the 6- and 5-pts are just itching to join the battle. At the moment White’s sixes and some of his fours play badly but not after 24/21, 8/4.

Equally well Red cannot afford the luxury of the ‘safe’ play which puts a third useless checker on his ace-point and does nothing to help his position.

The correct play is 8/5, 8/4 which puts the checkers where Red wants and just as importantly does not allow White an attack. There is also some duplication of twos.

White is a strong favourite irrespective of which play Red chooses but anything other than 8/5, 8/4 is a bad blunder.

They key is that Red must stop all those checkers in White’s home board coming into play.

Rollout Information from Extreme Gammon

Intermediates 9 rollout

 

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Brays Learning Curve: Blitz

Money Play. How should Red play 31?

2018 - Beginners 9

XGID=aBBAa-B-BA–cCA–e-e—-A-:1:-1:1:31:0:0:3:0:10

This position is used to highlight a very common error amongst beginners, intermediates and sometimes even experts.

Red has doubled and embarked on a blitz. Sadly, he has thrown a poor number. Many players now think that they must give up on the blitz and tighten things up.

I would expect to see 13/9 played quite often and the even weaker 14/13, 9/6 will have quite a few supporters.

The basic strategy for such positions is to keep blitzing until it is no longer possible. This means that in this position the correct play is 8/4*. There is a huge difference between having two rather than one opposing checker on the bar. One bad roll from White, particularly staying on the bar, could see him quickly lose a gammon.

The game-winning percentage for all three of the plays discussed is very similar but 8/4* wins 10% more gammons and that is the big difference.

8/4* leaves five Red blots and that puts many players off making the correct play. Yes, Red will lose some games, and even gammons, when things go badly, but there are very few certainties in backgammon and Red can only play what the dice give him.

Any play other than 8/4* is bad blunder. So remember, have the courage of your convictions, and blitz aggressively until that plan is no longer viable.

Rollout Data from Extreme Gammon

Beginners 9 Rollout

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Brays Learning Curve: Complexity

Match Play. Red trails 4-6 to 7 (Crawford). How should Red play 63?

2018 - Experts 8

XGID=—B-aDBBB—B–aAbbbc-bb-:0:0:1:63:4:6:1:7:10

This position was originally posted on Facebook by Phil Simborg. In terms of degree of difficulty this is a very high tariff problem.

If this was a money game with Red holding the cube on 2 then the answer would be the simple 17/8. Every other play loses too many gammons.

However, this is the Crawford Game and Red must win it in order to continue the match. Gammons are irrelevant and so Red just needs to make the play that wins the most often.

I think a lot of players would elect to play 17/14, 13/7, leaving no direct shots but whenever White rolls a 5 or a 6 Red will very likely be in trouble and what does Red plan to do on his next roll even if White rolls small numbers? That is the key to the problem.

The more direct approach is 17/11, 8/5*, employing the standard backgammon theory of attacking a lone blot. Red may be able to execute a blitz or possibly create a prime.

The one move nobody looks at 17/11, 13/10!! A passive move exposing two blots to direct shots!

Whenever White rolls a 5 or a 6 Red will be in big trouble, although he will have a small amount of residual equity. The big gains come on the 16 rolls when White doesn’t roll a 5 or a 6. Now Red is ideally placed to attack/prime White’s rear checker.

The difference between 17/11, 8/5* and 17/11, 13/10 is small but small differences count for a lot in backgammon. Not one in a hundred players would find and, more importantly, play 17/11, 13/10 over the board demonstrating just how difficult the game can be. Even analysing in the calm of one’s study it is hard to find the right play.

The key is that having once seen the solution you can now take this type of thinking and apply it to future problems even though such a problem may not occur again for quite some time.

Rollout Information from Extreme Gammon

Experts 8 Rollout

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Brays Learning Curve: Run or Prime?

Money Play. How should Red play 63?

2018 - Intermediates 8

XGID=-a-BBCCBA———ccbbcBa-:1:1:1:63:0:0:3:0:10

 The age-old question: should you build the full prime with 8/2, 5/2 and perhaps crack it as soon as next turn, or use that precious 6 to run with either 23/14 or 22/17, 8/5?

When I had this position as White, I knew what I wanted my opponent to do and that was to run. He very kindly obliged and after a couple of good rolls I was actually able to play on for, and win, a gammon.

The correct play by quite some way 8/2, 5/2 – see the rollout below. The keys to the position are:

  • A full prime is much stronger than a five-point prime and even if Red cannot escape a checker next turn, he will still probably have a five-point prime, so he will be no worse off and, if he rolls a six, he is nearly home free.
  • Crucially, White must play before Red rolls again and facing a full prime he will have to move on his side of the board. Big numbers like 64, 65, 55, 54 etc now severely damage his position, giving Red gammon opportunities.

My rule of thumb in such positions is to take the full prime if it is on offer and that rule has stood me in good stead throughout my playing career. If Red had a 65 to play then 23/27, 8/3 would be correct.

Note that 23/17, 8/5 is much better than 23/14 because it halves the gammon losses. The former is an error, the latter is a blunder. Players often forget to take gammons into account properly when deciding upon a move. 23/14 exposes three blots and that is too many when there is a sensible alternative.

So, remember, hardly ever turn down a full prime!

Rollout Information from Extreme Gammon

Intermediates 8 rollout

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Brays Learning Curve: Hit or Point?

Money Play. How should Red play 42?

2018 - Beginners 8

XGID=aa—BD-C—eDa–c-dA—A-:1:-1:1:42:0:0:3:0:10

This is a type of position that I constantly see misplayed by beginners and intermediates.

They nearly always play 20/14*, putting a second checker on the bar. Hopefully not many players would select the craven 24/20, 13/11! Such a passive move is not the way to winning backgammon.

As the great Paul Magriel used to say, “put ‘em where you want ‘em”. This should give you a clue!

The correct play is 8/4, 6/4. This gives Red an excellent long-term asset and considerably reduces White’s chances of counter-play. A quarter of the time he will still be shooting at the White blot on Red’s 14-pt next turn.

8/4, 6/4 wins more games and more gammons than 20/14*. That may surprise many, but that extra home-board point, which is also part of a potential prime, really stifles White’s play.

If you don’t believe this try playing the position a few times. You will soon see that making the 4-pt is much stronger than hitting the extra blot.

Rollout Data from Extreme Gammon

Beginners 8 Rollout

 

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Brays Learning Curve: Flexible Game Plans

Match Play. Red trails 4-5 to 17. How should Red play 54?

2018 - Experts 7

XGID=baaaBBBbBB-aABA–b-c-Ab—:0:0:1:11:4:4:0:5:10

This position occurred in the first match of the final of the recent Cyprus tournament. Red was Aurelien Bonnet and White was Frank Stepler.

Bonnet played the ‘obvious’ 13/9, 7/2 but that move is a blunder. Why is that the case?

It basically resigns Red playing a 3-pt holding game except in a few cases.

Red needs to take advantage of his stronger home board, the fact that White has no anchor and also that White has another exposed blot on his 11-pt.

Red should try to win by going forward. If he can’t do that then he can steer for a well-timed back game and if all else fails, he still has the option of playing a 3-pt game. This gives him multiple possible game plans rather than just one, nearly always a good idea.

The four must be played 7/3*. After that Red needs to release the spare checker on the 21-pt to attack the White blot in the outfield. Thus the 5 is played 21/16. That is much more flexible than 13/8, which in turn is much better than Bonnet’s actual 13/9, 7/2.

As you can see from the rollout 13/9, 7/2 is a blunder. In backgammon it pays to keep your options option and that is precisely what 21/16, 7/3* does.

Rollout Information from Extreme Gammon

 Experts 7 Rollout

 

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Brays Learning Curve: Multiplicity

Money Play. Should Red double? If doubled, should White take?

2018 - Intermediates 7

XGID=aB-BBCBA——-c–bccCc—:0:0:1:00:0:0:3:0:10

This position is deceptive, and I have included it because it is a type of position that many players consistently get wrong. At first glance you might question White’s ability to take but despite the fact that Red is a big favourite to cover the blot on his 4-pt that is only part of what he needs to do.

Red has 28 numbers that cover the blot on the 4-pt and the numbers that don’t cover (4’s and 5’s) escape his rear checkers. That looks powerful but some of those covering numbers are not ideal – look at 33 and 66.

Not only must Red cover the blot, he must also escape three checkers from behind a broken prime (a non-trivial exercise), all the time hoping that White stays on the bar. As soon as White enters that checker he is only one good roll away from escaping.

For Red to win this position all the steps outlined above must be completed. The odds against all those events happening is the product of the individual events occurring. So, for example, if three events all have a 50% chance of happening then the odds against all of them happening is 50% x 50% x 50% = 12.5%. This concept is known as multiplicity.

Now you can get some idea of just how much work Red has to do to win this position so in fact, doubling in this position is a 2.5 times blunder and White’s take is trivial! Even if Red covers the blot and White fans, he probably won’t have a double next turn!

Despite all that I would still expect some players to drop from the White side because they would take an overly pessimistic view of the situation – a perennial problem for less experienced players!

Rollout Information from Extreme Gammon

 Intermediates 7 rollout

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Brays Learning Curve: Risk and Reward

Money Play. How should Red play 61?

2018 - Beginners 7

XGID=-aB-CCC-B—bB—–cbcb-b-:1:-1:1:61:0:0:3:0:10

Red stands well in this position but has not yet won the game. The question is whether he should play this 61 relatively safely with something like 8/2, 5/4 or whether he should play boldly with 13/7, 8/7.

With the cube in the middle you can win the game either by making a well-timed double or by utilising your checkers efficiently. Once you have doubled only the latter option is available to you, so you need to optimise the placement of your checkers.

Beginners have a hatred of leaving unnecessary shots when they think they have already won the game, but the harsh reality is that your opponent will nearly always have winning chances – you must do your best to limit those chances. Everything in backgammon is risk and reward so it is a question of weighing one against the other.

In this position the race is close so White can win by rolling a couple of big numbers. If Red makes the bar that option is largely denied to White but 13/7, 8/7 leaves 13 hitting numbers for White (all 1’s plus 52). Is the risk worth the reward. The answer is yes, Red does better to make the bar than play relatively safely (the safe plays leaves 4 shots).

One key point is that if White hits the blot on Red’s mid-point he won’t be strong enough to redouble unless he has rolled precisely 12 or 21. That is because Red’s broken prime is a still a fearsome barrier that White has to leap with a 2 and then a 5 or a 6.

Learning when to take a calculated risk is key to winning at backgammon. Too often I see beginners shy away from risk because they only look at the negative aspects of a play. They improve when they learn to see the positives, but I admit that it does take time to learn how to think

Rollout Data from Extreme Gammon

Beginners 7 Rollout

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Brays Learning Curve: DMP Problem

Match Play. Double Match point. How should Red play 11?

 

2018 - Experts 6

XGID=baaaBBBbBB-aABA–b-c-Ab—:0:0:1:11:4:4:0:5:10

Firstly, this is DMP so Red wants to make the move that wins the most games. Gammons are irrelevant. Secondly, double aces normally give you a very wide range of choices and this position is no exception. I rolled out ten moves in depth, but it could have been double that number.

The key is that Red must have a plan and not just shuffle the checkers. At the moment White looks as if he is going to get some sort of playable back game and that is precisely what Red must stop from happening. For that reason, moving the checkers in the outer boards is not the right idea. Red should also not worry too much about safety, White’s home board is largely irrelevant at this point.

When I first evaluated this position XG came up with the somewhat exotic 12/11*, 4/3*/2*/1*. That certainly stops White anchoring any time soon! When I performed a rollout sampling 2592 games that play came second! I venture that no human player would find it over the board and even if he/she found it they wouldn’t play it and yet it is entirely thematic with Red’s objectives.

The somewhat more prosaic 4/3(2)*, 3/2(2)* is actually the best play. For the moment that tries to restrict White to an ace-point game at best and Red may do better than that.

Once you have a plan the play is easy to find and extremely logical but without a plan Red may not find the move. So, remember, plan first, play later!

Rollout Information from Extreme Gammon

Experts 6 Rollout

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Bray’s Learning Curve: Bray’s Law

Match Play. Double Match Point. How should Red play 43?

 

2018 - Intermediates 6

XGID=-BCBBBB—–b——–gBcc-:0:0:1:43:4:4:0:5:10

This position occurred in a London League match this week and provides a classic demonstration of Bray’s Law.

That law states that when hoping to hit a late shot to win a game you should only break up your home board  upon pain of death or because there is no other legal play.

The reason for the law is that after hitting a late shot you need to contain the hit blot and you cannot do that easily if your home board is compromised.

That means that in this position 6/3, 6/2 and 5/2, 5/1 should be discounted as candidate plays. Red must advance one or both of his rear checkers while maintaining his perfect home board. Having solved half the problem (maintaining the home board) we are left with two choices; (a) 22/15 and (b) 22/19, 22/18.

Logic says that you want to keep one checker on the 22-pt for later shots if the initial shots are missed. Logic also says that White is very likely to have to separate his two checkers on his mid-point and ideally Red will want to put pressure on both blots. So far this points to 22/15 as the right play. Is there any merit in play (a)? Not really. It makes most of White’s sixes good for him and allows the possibility of one checker reaching the sanctuary of White’s home board.

This simple analysis shows that 22/15 is clearly correct and the rollouts agree with it. Play (b) is an error and any move that breaks the home board is a blunder.

Bray’s Law has helped me to make the correct decision time after time, so I suggest you commit it to memory and use it whenever appropriate.

Rollout Information from Extreme Gammon

Intermediates 6 rollout

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Bray’s Learning Curve: Basic Blitz

 

Money Play. Should Red double? If doubled, should White take?

2018 - Beginners 6

XGID=aB-Ba-C-A—dEa–c-e—-B-:0:0:1:00:0:0:3:0:10

White opened with 32 which was played, 24/21, 13/11. Red rolled 55 which he played 8/3(2), 6/1(2)*. White then fanned and Red has to decide whether to double.

Before the bots came along everybody knew that if you opened 6x which was played 24/18, 13/x and your opponent rolled 55, played 8/3(2), 6/1(2)*, and you fanned you had to drop your opponent’s double because you lose too many gammons.

But there are lots of other early 55 blitzes and ideally you need to know what to do as either side in such situations. With the bots came knowledge and Kit Woolsey was kind enough to document much of that knowledge in his “The Backgammon Encyclopedia – Volume 1”. If you look in there then you will find this position is a double (just) and an easy take. If the White blot were on Red’s 2-pt then Red would not even have a double because White’s blot is further removed from Red’s attacking force.

Kit documented many other early blitz positions in his book. The only problem is that the book is currently out of print because the proofs were lost. Hopefully he will recreate it in the not too distant future. The second volume “The Backgammon Encyclopedia- Volume 2” is in print. Meanwhile if you come across a second-hand copy of Volume 1 my advice is to snap it up quickly.

It is easy to learn these basic reference blitz positions and then use them effectively in live play. Knowing the correct action in such situations saves both time and mental energy and, given how difficult backgammon can be, you need to make use of reference positions as often as you can.

Rollout Data from Extreme Gammon

Beginners 6 Rollout

 

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Complex Endgame


Match Play. Red trails 2-5 to 7. How should Red play 21?

2018 - Experts 5

XGID=-aCC-A——a——-a-ddd-:1:-1:1:12:2:5:0:7:10

This position occurred at the recent Cyprus tournament. Red played the rather dull and prosaic 5/2.

After playing his 21, Red will have either six or seven crossovers left to bear off his remaining checkers. White will have to make six crossovers (don’t forget the one to bear off a checker) to save the gammon. White will also need to roll a minimum of 26 pips to save the gammon. All this implies the race to save the gammon will be close and so Red must play aggressively. There is a huge difference between leading 6-5 (Crawford) and trailing 4-5. Note also that Red will hardly ever lose from this position (see rollout details).

Therefore, Red must take the extra crossover this roll if he can, despite any risks. Having six crossovers left rather than seven may save him a whole roll.

3/1*, 2/1 puts White on the bar but doesn’t get that vital extra crossover. 3/1*/off is the correct play by some way. Red gets a bonus if White rolls 22, 33 or 32 but the key point is the extra crossover. 5/4, 2/off is the same idea but in this variation White is not on the bar and that may be crucial. Despite the few extra shots Red should put White on the bar. Note also, that if White does hit from the bar, he may not be able to safety the blot on his own 5-pt. That will add to Red’s gammon percentage.

This is not the time for timidity (it rarely is in backgammon). 3/1*/off is the play.

 

Rollout Information from Extreme Gammon

Experts 5 Rollout

 

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Brays Learning Curve: Offence or Defence

Money Play. How should Red play 32?

 

2018 - Intermediates 5

XGID=-b—-EBB—eD—b-db—B-:0:0:1:32:0:0:3:0:10

Red has opened with 61 (13/7, 8/7) and White has replied with 31, making his 5-pt. How should Red now play his 32?

The most common plays that I see are 24/21, 13/11 and 24/22, 13/10 but they are both incorrect.

Worse than these two plays is 13/11, 13/10. That play strips the mid-point of spares too early and gives White two tempting targets at a time when he has the better board. 13/8 is the dreadful ‘do nothing’ play. The two hybrid plays mentioned above are better but still wrong.

White has made his best offensive point and the standard tactic against that is to make an advanced anchor somewhere. Red gives himself the best chance to do that with 24/22, 24/21. The idea behind the play is that if White does point on one of the checkers then he will probably have to give up his 8-pt to do so and also Red will have good chances to make the other point that he has started with 24/22, 24/21.

I must reiterate that the time to take risks is in the opening when both players have relatively weak boards.

If Red gets wiped out by White by rolling a double next turn then Red can just drop the subsequent double and move on to the next game. He will still have played correctly and learning to lose is one of the key skills that any backgammon player has to acquire – it happens a lot!

As you can see from the rollout any play other than 24/22, 24/21 is at least an error and some of the plays mentioned above are blunders.

Rollout Information from Extreme Gammon

Intermediates 5 rollout

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Bray’s Learning Curve: Late Hit

Money Play. Should Red redouble? If redoubled, should White take?

 

2018 - Beginners 5

XGID=aBBBBBE—————-de-:1:1:1:00:0:0:3:0:10

This type of position occurs frequently – White was happily bearing off and looking forward to two points (or even a freak gammon) when he left a shot and got hit. Therefore, it is best to know how to handle the cube in such situations.

The rule of thumb is that you should redouble when you have borne off five fewer checkers (or ten fewer checkers if your opponent has two checkers on the bar) than your opponent. Your opponent can take in such situations if he cannot miss when his straggler has once again reached his home board. Typically, that happens when Red has hit a shot from the ace-point anchor rather than from the bar. In that case White will have an empty ace-point and will miss with all aces in the bear-off. That turns the take into a drop.

Once you know the basic reference position you can make adjustments for your particular position. In this week’s position Red will leave an immediate shot with 66 and his sixes and big doubles play awkwardly putting him in jeopardy of a later shot. That is enough to make this position a no double.  Red should take a roll to tidy up his position.

To really learn about this position you should move the checkers around and see what difference that makes. Take one spare checker from the 6-pt and put it on the 5-pt and the position is still not quite a double. Take another checker from the 6-pt and put it on the 4-pt so that the spares are on the 4-, 5- and 6-pts (the perfect bear-off position) and White has a take but by the tiniest of margins.

1-pip differences can make a huge difference in backgammon.

Rollout Data from Extreme Gammon

Beginners 5 Rollout

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Brays Learning Curve: Three on the Bar

 

Money Play. Should Red double? If doubled, should White take?

 

Experts 4

XGID=cA–BbC-B–BbB—–dAb-Bb-:0:0:1:00:0:0:3:0:10

 

Three checkers on the bar is normally a recipe for a swift drop, a resetting of the board and the starting of a new the game. This week’s position is relatively unusual and if you have seen nothing like it before you are going to have trouble evaluating it.

White has three checkers on the bar and a disjointed home board. He also trails in the race by 18 pips with his opponent on roll. However, he holds a 5-pt anchor and his opponent only has two and a half home board points. Furthermore, Red has only ten checkers in the attack zone and three of his checkers still in White’s home board. These latter factors should give White hope especially if Red cannot cover the blot on his ace-point next time.

This position occurred in the Battersea chouette where there are more takes than in “normal” backgammon. The box (Red) did double and of course all four opponents took. What do you think of the cube decisions?

White’s 5-pt anchor is the key point on the board. That will keep him in the game forever and because Red has a shortage of checkers in the attack zone, he doesn’t really have many immediate market losing rolls, unless of course, you think he has already lost his market. However, only the big doubles really threaten White immediately.

In fact, the take is trivial for White, he just has too much play and too many ways to win to give this one up. As for the double it is right on the borderline. You can double or not double and you will be correct. Despite appearances, the position is not very volatile, I would only double this position if I thought my opponent would pass and that wouldn’t happen in the Battersea chouette!

In this instance, the takers were rewarded by being able to redouble Red out later on but of course a one game rollout proves nothing!

The key is to file this position in your memory bank and reuse it. The other way to learn is to play around with the position to see how that changes things. For example, if you take the spare checker on Red’s 6-pt and put it on his 1-pt giving him a three-point home board then the borderline decision is the take and not the double!

Rollout Information from Extreme Gammon

Experts 4 rollout

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Bray’s Learning Curve: Priorities

Money Play.   How should Red play 22?

2018 - Intermediates 4

XGID=—–bE-CAA-cC–bc-e—-B-:0:0:1:22:0:0:3:0:10

Over the board Red chose 24/22(2), 13/9. Was he correct?  Sadly for him, he was a long way from the best move.

Not moving the back checkers at all is a huge error so they must at least advance 24/22(2). After that, if they remain there, then the best move for the other two twos is 10/8, 6/4, followed by 6/4(2) but both of these moves are blunders as is any move other than the correct one.

One the basic principles of backgammon in the early game is that if your opponent has made an advanced an anchor you should strive to do the same. Here Red has as a glorious opportunity to do just that with 24/20(2)!!

The blots left on the 9- and 10-pt are irrelevant. If hit, they can easily be recycled precisely because Red has his advanced anchor. The advanced anchor also cuts down Red’s gammon losses when thing go badly.

After 24/20(2) White is about a 60/40 favourite but Red is in the game for ever. If Red elects to anchor on the 22-pt his sixes are blocked and he can quickly get into trouble.

The key is to understand that the advanced anchor is far more important than the blots. There are many positions in backgammon where having two exposed blots spells extreme danger – this is not one of them!

Rollout Information from Extreme Gammon

intermediates 4 rollout

Bray’s Learning Curve — A Great Member Benefit
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Bray’s Learning Curve: Third Move Thoughts

Money Play. How should Red play 62?

2018 - Beginners 4

XGID=-a—-E-D—fD—c-e–A-A-:0:0:1:62:0:0:3:0:10

There are 15 possible opening rolls. Many of these can be played in different ways. In response each of the possible 21 numbers can also be played in a number of different ways. There are approximately 600 opening rolls and responses. Most players will get the majority of these plays correct over the board.

The same is not true of the third move because by now there are too many possibilities for us to remember and we must rely on general principles to guide us most of the time. Those guiding principles are:

  • Make new points
  • Unstack the heavy points
  • Hit an opposing checker
  • Start the rear checkers moving

Over and above these principles I also like to try to maintain flexibility so that I have the ability to adopt different game plans as the game evolves.

This week’s position occurred in a teaching session with two of my students. Red opened with 52 played 24/22, 13/8 and White responded with 65, played 24/13. How should Red now play this 62?As usual we must consider the candidate plays and then make a choice:

  • 24/18, 13/11 too many double hits.
  • 22/14 minimises shots but it will be difficult to improve the position next time.
  • 24/16 leaves the rear checkers connected, but gives White many more hits, some of them double hits.
  • 24/22, 13/7 gives Red a solid anchor and slots a good point and would be the choice of many.
  • 22/16, 13/11 unstacks the mid-point while reducing White’s hitting numbers and keeps some connectivity between the rear checkers.

My students both selected 24/22, 13/7 and I wouldn’t argue with anybody who wanted to make that move in a chouette. However, settling for the 22-pt anchor so early is a little negative and the blot on the bar-point is exposed to 17 shots.

Long experience had me leaning towards the more flexible 22/16, 13/11 but I wasn’t certain by any means. A long rollout proved me to be correct. It turns out that 24/22, 13/7 is too committal so early in the game and technically it is an error. Remember that flexibility is a key element of backgammon and 22/16, 13/11 provides Red with exactly that.

The key here is to remember the solution to this problem and then apply the technique in similar future positions of your own.

Rollout Data from Extreme Gammon

Beginners 4 Rollout

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Bray’s Learning Curve: Deep Thought

Money Play. How should Red play 42?

2018 - Experts 3

XGID=–bBbbCBCB-Ba—–abbab–A:0:0:1:42:0:0:3:0:10

Before the advent of the bots this roll would have been played bar/21*, 8/6 and nobody would have known that they were making a big error. The early bots such as TD-Gammon and JellyFish were not trusted to play back games correctly and so their recommendations would have largely been ignored in positions such as this.

However, by the time that gnubg and Snowie arrived players had begun to accept that their ideas were fundamentally sound, although there was still some doubt about complex positions. By the time Extreme Gammon took to the stage the bots were viewed as very strong players and everybody paid heed to their suggestions.

I misplayed this position over the board, making the pre-bot era move. As soon as I analysed the position with XG I realised I had forgotten to take its teachings into account. The correct move, by a long way, is bar/21*, 3/1, a move that would have been laughed at in the 1970s. Anyone wanting to make that move in a chouette of that era would have had their mental stability questioned.

However, when you look at the move and analyse it, it makes perfect sense. White has a very well-timed back game and his checkers are all working. In contrast thirteen of Red’s checkers are reasonably well positioned but the two checkers on his 2-pt are out of play. In military terms those two soldiers are off the field of battle and need to re-join their colleagues if possible.

The best way to correct Red’s timing is to force White to hit those checkers so that they can be recirculated. This is the key piece of logic behind bar/21*, 3/1. Having studied bot play in some depth I knew all about this particular recirculation tactic and I was annoyed with myself for missing the opportunity in live play.

Bar/21*, 8/6 is very nearly a blunder and any other move is a blunder or worse. So, please remember the idea and make use of it in your own games, the opportunity occurs more frequently than you might expect.

Rollout Information from Extreme Gammon

Experts Rollout 3

Bray’s Learning Curve — A Great Member Benefit
Bray’s Learning Curve is a USBGF online series by author Chris Bray. Each week Chris lends his sharp insight and easy to understand analysis to help you improve your game. Visit the USBGF Facebook page every Monday to view an interesting backgammon position and join in the lively discussion, return on Tuesday to view the answer. In addition, as a USBGF member, you get access to this companion blog article that includes an expanded explanation.  More about Chris Bray

 

Bray’s Learning Curve – Volatility

Money Play. Should Red double? If doubled, should White take?

2018 - Intermediate 3

XGID=-B-BBaCCB-A———-bbcg-:0:0:1:00:0:0:3:0:10

This is a type of position that I often see misjudged. What normally happens is that Red rolls something like 63 which is played 10/4, 8/5*, White fans and then Red wins a point by doubling White out.

Red has committed the cardinal sin of losing his market because he feared the sequence where he hits loose and then White return hits from the bar and then Red fans. Beware, considering unlikely nightmare scenarios is not the way to make decisions in backgammon.

Red’s thinking should go along these lines:

  • If I point on White’s blot (15 rolls), unless he rolls 26 from the bar I will have lost my market.
  • I will pick and pass with 14, 24, 34, 54 (8 rolls) and if White fans, again I will have lost my market.
  • With all remaining numbers except 64, 44 and 66 I will hit loose and if White doesn’t hit back yet again I will have lost my market. I note that 44 and 66 are both very good for the race.
  • Yes, I will lose some games where I do get hit and stay on the bar but overall, I will gain many more points by doubling now than I will lose in the odd case where thing go wrong.
  • The position is incredibly volatile and so I must double now or I risk losing my market.
  • Therefore, I double.

On the other side of the coin White has an easy take based upon his hitting and racing chances. Like many middle game positions this is both a correct double and a correct take.

Note that if White had a five-point board or even a closed board the doubling decisions for both players remain the same.

Success in backgammon is largely determined by one’s cube handling and here not doubling would be a blunder. If you didn’t double because you were afraid of being hit from the bar then hopefully after reading this article you will have learnt to think more positively.

Rollout Information from Extreme Gammon

Intermediates 3 Rollout

Bray’s Learning Curve — A Great Member Benefit
Bray’s Learning Curve is a USBGF online series by author Chris Bray. Each week Chris lends his sharp insight and easy to understand analysis to help you improve your game. Visit the USBGF Facebook page every Monday to view an interesting backgammon position and join in the lively discussion, return on Tuesday to view the answer. In addition, as a USBGF member, you get access to this companion blog article that includes an expanded explanation.  More about Chris Bray

 

 

 

Bray’s Learning Curve: War Games

Money Play. How should Red play 65?

2018 - Experts 2

XGID=–BB-bBCA—bB—c-bcbCa–:0:0:1:65:0:0:3:0:10

Never forget that backgammon is a representation of war, as indeed are most of the older board games. Thinking in terms of war can often help you to arrive at the right decision with difficult plays.

Faced with this 65 to play over the board, Red elected to move 22/16, 8/3. This seems logical, escaping one of the rear checkers and moving the blot on his 8-pt to safety. The problem is that Red now has one soldier away from the field of battle (the third checker on his 3-pt) and another (the blot on his 16-pt) that might struggle to reach safety next turn.

He could have elected to play 13/8, 13/7, playing completely safe but that play cedes a huge part of the field of battle (the outer boards) to his opponent and he will really struggle to escape his three rear checkers. As is often the way in war cowardice is not rewarded.

He could try 22/16, 13/8. This makes the important 8-pt but leaves two checkers exposed to White’s attack and his hitting numbers are not duplicated with the numbers he needs to cover his blot on the 2-pt. Once again, Red will struggle to safety the blots next turn even if they are missed.

By now you will have found the correct move, 22/11. This keeps all his soldiers (checkers) focused on a key area of the battlefield. The move duplicates White’s three and sixes and now, if the blots are missed, they can be usefully employed to make new points or more easily made safe. If White does give up his anchor to hit (in war terms giving up a key strategic point) then Red’s checkers (soldiers) are well-positioned to counter-attack.

You cannot implement a battle plan that do you not even consider. Here many generals (players) would not even see the possibility of 22/11 and even if they did, they might consider the risk to life and limb too high a price to pay.

However, much of war and all of backgammon is about exercising judgement, creating a balance between risk and reward. Here, the risk is worth the reward. Leaving a double direct shot is relatively rare but this position demands precisely that. In backgammon terms, any move other than 22/11 is a blunder.

Rollout Information from Extreme Gammon

Experts 2 rollout

Bray’s Learning Curve — A Great Member Benefit
Bray’s Learning Curve is a USBGF online series by author Chris Bray. Each week Chris lends his sharp insight and easy to understand analysis to help you improve your game. Visit the USBGF Facebook page every Monday to view an interesting backgammon position and join in the lively discussion, return on Tuesday to view the answer. In addition, as a USBGF member, you get access to this companion blog article that includes an expanded explanation.  More about Chris Bray