Two Plus Two Forums
Sports and Games
Chess and Other Board Games
Backgammon Forum hosted by Bill Robertie.
Problem of the Week #153: Solution
10-30-2012
, 02:00 PM
Problem of the Week #153: Solution
Cash game, Black owns the cube.
Black to play 6-1.
Something a little different. Find 6 candidate plays. Arrange them in order from best to worst. Discuss.
Note: All ‘cash game’ problems assume the Jacoby Rule is in effect. That is, you can’t win a gammon unless the cube has been turned.
Many years ago, when I was an aspiring chess player, publishing houses began translating and printing some of the best of the Russian chess literature. Serious players had been subscribing to Russian chess magazines for some time. They were mostly collections of current games from Soviet tournaments, and it wasn’t too hard to puzzle your way through given a little knowledge of the Cyrillic alphabet and a few phrases. The books, however, required some real knowledge of Russian and were pretty much inaccessible to Westerners until the English translations appeared.
One day during the Fischer-Spassky match I wandered into the Boston Chess Studio and Dan Harrington was there. (Not unusual; he practically lived there in those days.) We got to shooting the breeze and he asked me if I had read Kotov’s book yet. “What book?” I replied. He gave me a stern look, dragged me over to the bookcase, plucked a book off the shelf, and put it in my hands. “Read it, you can thank me later.”
The book was Kotov’s Think Like a Grandmaster, just out in English and soon to be recognized as one of the all-time classics of chess literature. Unlike most books of the time, Kotov’s wasn’t just a collection of lightly-annotated games or the latest opening analysis. His subject was how to analyze a position at the board – how to organize your thinking so you got the most bang for your buck while your time clock was ticking away the seconds.
Kotov pinpointed a serious problem with the thinking process of the typical mid-level tournament player. Given a tough position at the board, he approached it something like this: “Hmm, tough position – what to do? – this play looks good, let’s see what happens – (analyzes play A for a while) – nothing special there, let’s try this other play – (analyzes play B for a while) – maybe that’s better, still not winning, let’s try again – (analyzes play A again) – hmm, don’t really like that – (notices that he’s used up a lot of time on his clock) – geez, need to do something soon – (notices play C) – hey, that looks good – (makes play C after a few seconds thought and hits his clock) – whew – (notices big flaw in play C) – oops!”
This sort of haphazard thinking, moving from one play to another looking for something that yielded a ‘good enough’ result, carried with it a high risk of never seeing the best play at all. Kotov outlined a better system, which he described in terms of candidate moves. Start by looking at the position and just trying to list all the plays that might be best. Then methodically go through the list and spend some time analyzing each play. When you finish, discard the obviously worse choices and make your move.
This method turns out to have a number of surprising strengths:
> You’re much less likely to simply overlook the best play, since you first spend some time looking for all the reasonable candidates.
> Every reasonable play gets some analysis, so you’re more likely to see the merit in a non-obvious play.
> The amount of time you spend on the move is capped to a certain extent, so you’re less likely to run into time trouble. (All tournament chess games are played with clocks, even in low-rated sections.)
Kotov’s ideas were a revelation to many players (myself included) who had focused their attention on analyzing moves but had never really thought of analyzing the thinking process itself. When I switched from chess to backgammon, Kotov’s ideas naturally carried over. In fact, the candidate move idea turned out to be even more useful in backgammon, since only a few backgammon situations require actual calculation. Many serious errors in backgammon are just a result of overlooking the best play, especially when throwing doubles, and starting the analysis by looking for candidates is the best way to avoid those errors.
Having said all that, let’s move to Problem 153 and start by listing the candidates.
The candidates here are pretty easy to find, since Black has to move his six either from the 8-point, the 13-point, or the 21-point, and in each case he’ll have only a couple of reasonable aces. Here we go:
From the 8-point:
(1) 8/2*/1
(2) 8/1 (not hitting)
From the 13-point:
(3) 13/6
(4) 13/7 8/7
(5) 13/7 5/4
(6) 13/7 13/12
From the 21-point:
(7) 21/15*/14
(8) 21/15* 13/12
That’s a total of eight candidates. Now let’s start to prune the list by eliminating obviously bad plays.
We can start with the two plays that make the one-point. The ace-point is a big liability in any sort of backgame. Making it is only sensible in a position where a successful blitz is a real possibility. With four men back combined with White’s good blocking structure, that’s clearly not the case here. The blitz is a fantasy, so we discard plays (1) and (2).
Now let’s look at (7) and (8), breaking the 21-point to hit. This isn’t a crazy idea. The 1-4 and 1-5 games don’t play especially well as backgames; with the back points so far apart, they’re only somewhat better than a pure ace-point game, so breaking off the 21-point to go forward is sometimes a play.
What makes this position unusual is that both inner boards are weak. If we move two White checkers from the 5-point and 7-point to make White’s 3-point, Black wouldn’t consider hitting; he would need both anchors to survive. On the other hand, if we Black’s inner board stronger, by moving checkers from his ace-point and 13-point to make the 4-point, then Black has excellent chances to go forward and hitting is clearly correct. But with weak inner boards on both sides, we’re in a position where Black doesn’t yet need to commit. By refraining from hitting, he keeps his options open. Now we discard (7) and (8).
With (1), (2), (7), and (8) all gone, we’re looking at 13/7 for the six, followed by one of four possible aces: 5/4, 7/6, 8/7, and 13/12. Can we clearly discard any one of these?
Actually, yes. The worst of the bunch is 8/7. Right now, White has a problem with some sixes. Rolls of 6-3, 6-4, or 6-5 next turn force White to break his 8-point, while 6-6 keeps the blot on White’s 10-point while shoving two more checkers down to his 2-point. Switching from the 8-point to the 7-point lets White play his sixes easily, and we don’t want that, so we’ll definitely keep our 8-point.
The next play to discard is 13/7 13/12. Leaving three new blots around isn’t necessary here. If we play 13/7 and White doesn’t get out with a five, our rolls will play very well next turn. True, they’d play a tiny bit better after 13/12, but at the cost of leaving a lot of blots to be swept up when White does roll a five. Poor risk-reward ratio here, so we’ll let 13/12 go.
That brings us to our top two candidates: 13/6 and 13/7 5/4. The best DMP play is 13/7 5/4. By putting the checkers where they belong, it wins a few more games but loses a few more gammons. The prudent play is 13/6, risking nothing and giving White a chance to throw something awkward.
Over the board I would have played 13/6. The double-slot would be my play if I had a better back game, say a 2-3 or 2-4 game with no dead checker on the ace-point. But rollouts indicate the two plays are a tossup for money; Black’s game is strong enough that he can go for the throat if he wishes. Give yourself credit for picking either play.
Solution: Either 13/6 or 13/7 5/4
Cash game, Black owns the cube.
Black to play 6-1.
Something a little different. Find 6 candidate plays. Arrange them in order from best to worst. Discuss.
Note: All ‘cash game’ problems assume the Jacoby Rule is in effect. That is, you can’t win a gammon unless the cube has been turned.
Many years ago, when I was an aspiring chess player, publishing houses began translating and printing some of the best of the Russian chess literature. Serious players had been subscribing to Russian chess magazines for some time. They were mostly collections of current games from Soviet tournaments, and it wasn’t too hard to puzzle your way through given a little knowledge of the Cyrillic alphabet and a few phrases. The books, however, required some real knowledge of Russian and were pretty much inaccessible to Westerners until the English translations appeared.
One day during the Fischer-Spassky match I wandered into the Boston Chess Studio and Dan Harrington was there. (Not unusual; he practically lived there in those days.) We got to shooting the breeze and he asked me if I had read Kotov’s book yet. “What book?” I replied. He gave me a stern look, dragged me over to the bookcase, plucked a book off the shelf, and put it in my hands. “Read it, you can thank me later.”
The book was Kotov’s Think Like a Grandmaster, just out in English and soon to be recognized as one of the all-time classics of chess literature. Unlike most books of the time, Kotov’s wasn’t just a collection of lightly-annotated games or the latest opening analysis. His subject was how to analyze a position at the board – how to organize your thinking so you got the most bang for your buck while your time clock was ticking away the seconds.
Kotov pinpointed a serious problem with the thinking process of the typical mid-level tournament player. Given a tough position at the board, he approached it something like this: “Hmm, tough position – what to do? – this play looks good, let’s see what happens – (analyzes play A for a while) – nothing special there, let’s try this other play – (analyzes play B for a while) – maybe that’s better, still not winning, let’s try again – (analyzes play A again) – hmm, don’t really like that – (notices that he’s used up a lot of time on his clock) – geez, need to do something soon – (notices play C) – hey, that looks good – (makes play C after a few seconds thought and hits his clock) – whew – (notices big flaw in play C) – oops!”
This sort of haphazard thinking, moving from one play to another looking for something that yielded a ‘good enough’ result, carried with it a high risk of never seeing the best play at all. Kotov outlined a better system, which he described in terms of candidate moves. Start by looking at the position and just trying to list all the plays that might be best. Then methodically go through the list and spend some time analyzing each play. When you finish, discard the obviously worse choices and make your move.
This method turns out to have a number of surprising strengths:
> You’re much less likely to simply overlook the best play, since you first spend some time looking for all the reasonable candidates.
> Every reasonable play gets some analysis, so you’re more likely to see the merit in a non-obvious play.
> The amount of time you spend on the move is capped to a certain extent, so you’re less likely to run into time trouble. (All tournament chess games are played with clocks, even in low-rated sections.)
Kotov’s ideas were a revelation to many players (myself included) who had focused their attention on analyzing moves but had never really thought of analyzing the thinking process itself. When I switched from chess to backgammon, Kotov’s ideas naturally carried over. In fact, the candidate move idea turned out to be even more useful in backgammon, since only a few backgammon situations require actual calculation. Many serious errors in backgammon are just a result of overlooking the best play, especially when throwing doubles, and starting the analysis by looking for candidates is the best way to avoid those errors.
Having said all that, let’s move to Problem 153 and start by listing the candidates.
The candidates here are pretty easy to find, since Black has to move his six either from the 8-point, the 13-point, or the 21-point, and in each case he’ll have only a couple of reasonable aces. Here we go:
From the 8-point:
(1) 8/2*/1
(2) 8/1 (not hitting)
From the 13-point:
(3) 13/6
(4) 13/7 8/7
(5) 13/7 5/4
(6) 13/7 13/12
From the 21-point:
(7) 21/15*/14
(8) 21/15* 13/12
That’s a total of eight candidates. Now let’s start to prune the list by eliminating obviously bad plays.
We can start with the two plays that make the one-point. The ace-point is a big liability in any sort of backgame. Making it is only sensible in a position where a successful blitz is a real possibility. With four men back combined with White’s good blocking structure, that’s clearly not the case here. The blitz is a fantasy, so we discard plays (1) and (2).
Now let’s look at (7) and (8), breaking the 21-point to hit. This isn’t a crazy idea. The 1-4 and 1-5 games don’t play especially well as backgames; with the back points so far apart, they’re only somewhat better than a pure ace-point game, so breaking off the 21-point to go forward is sometimes a play.
What makes this position unusual is that both inner boards are weak. If we move two White checkers from the 5-point and 7-point to make White’s 3-point, Black wouldn’t consider hitting; he would need both anchors to survive. On the other hand, if we Black’s inner board stronger, by moving checkers from his ace-point and 13-point to make the 4-point, then Black has excellent chances to go forward and hitting is clearly correct. But with weak inner boards on both sides, we’re in a position where Black doesn’t yet need to commit. By refraining from hitting, he keeps his options open. Now we discard (7) and (8).
With (1), (2), (7), and (8) all gone, we’re looking at 13/7 for the six, followed by one of four possible aces: 5/4, 7/6, 8/7, and 13/12. Can we clearly discard any one of these?
Actually, yes. The worst of the bunch is 8/7. Right now, White has a problem with some sixes. Rolls of 6-3, 6-4, or 6-5 next turn force White to break his 8-point, while 6-6 keeps the blot on White’s 10-point while shoving two more checkers down to his 2-point. Switching from the 8-point to the 7-point lets White play his sixes easily, and we don’t want that, so we’ll definitely keep our 8-point.
The next play to discard is 13/7 13/12. Leaving three new blots around isn’t necessary here. If we play 13/7 and White doesn’t get out with a five, our rolls will play very well next turn. True, they’d play a tiny bit better after 13/12, but at the cost of leaving a lot of blots to be swept up when White does roll a five. Poor risk-reward ratio here, so we’ll let 13/12 go.
That brings us to our top two candidates: 13/6 and 13/7 5/4. The best DMP play is 13/7 5/4. By putting the checkers where they belong, it wins a few more games but loses a few more gammons. The prudent play is 13/6, risking nothing and giving White a chance to throw something awkward.
Over the board I would have played 13/6. The double-slot would be my play if I had a better back game, say a 2-3 or 2-4 game with no dead checker on the ace-point. But rollouts indicate the two plays are a tossup for money; Black’s game is strong enough that he can go for the throat if he wishes. Give yourself credit for picking either play.
Solution: Either 13/6 or 13/7 5/4
11-02-2012
, 08:42 AM
