Students Demonstrate Subtle Analytical Mistake

• NM danheisman
• | Aug 22, 2012
• | 12346 views

Last week, one of my students showed me a position and asked what I would do. I thought it was fairly instructive (it turned out to be!), so I will ask you the same question. In the following position, assume you are playing a long time control game (say 40 moves in 2 hours) and have plenty of time on the clock. What would you do and why? To get the most out of this instruction, don't read further until you have completed this task.

One key to beginning analysis is to notice that White has a discovered attack on c5 if he can move his knight from d4 with tempo. This should lead to the following three captures as possible candidates: 1.Nxe6, 1.Nxc6, and 1.Rxc5 (to try to lure the queen onto the diagonal of the e3 bishop). In giving this problem to a few students of various levels the weaker students might miss 1.Rxc5 but all the stronger ones considered it right away, often to the detriment of not even considering 1.Nxe6 or 1.Nxc6, but that’s getting ahead of ourselves.

In de Groot’s book Thought and Choice in Chess he calls the next stage of the thought process progressive deepening. What you should do to start is take 20-45 seconds and look briefly at each of the three strong candidates to try to get a feel for which one you think is most likely best. To take longer on any one candidate at this point (which several students did) is to just waste time; if there's another clearly better move, you don't want to spend ten minutes on a lesser one (Purdy: "Look wide before you look deep"). You are trying to find the best move you can in a reasonable time, not necessarily determine exactly how good is the move you wish to play.

Once you have determined which move is the most promising, it is time to examine it in more detail, putting the other moves away as possible improvement for later. Most students chose the move 1.Rxc5. It so happened that I chose 1.Nxc6 as the first move to examine more deeply, but the first choice does not always matter as much so long as your logic is good and you eventually get to the finish line correctly; I had to get to 1.Rxc5 and 1.Nxe6 soon enough. The key point is that you should now get a better feel how good your first candidate is, so you can then compare it to the others.

In the case of 1.Rxc5, all the stronger students pretty quickly realized that 1…Qxc5 was hopeless due to the discovery 2.Nxe6 when the queen is attacked by two pieces and the rook on f8 is also forked. Therefore, when the smoke clears, White is bound to be ahead by at least a piece.

That means 1…Nxd4 is Black’s only other try to save material (he can just ignore 1.Rxc5 but then he is down a piece, so not many players as Black would do that!). One stronger student did the problem too quickly and did not even get this far, assuming that if 1…Qxc5 lost then 1.Rxc5 won, and did not go further. That could have been a monstrous mistake if 1…Nxd4 turned out to be a good defense.

This is where my initial student had a problem. He looked at 1...Nxd4 and saw that 2.Rxc8, 2.Bxd4, 2.Nxd4, and 2.Qxd4 were all candidates and started to despair! He said he felt like he was not that fast at calculating and that it might take him all day. He was surprised when I responded that was not necessarily so - you don't usually have to figure out exactly how good all the lines are, as we shall see!

After 1.Rxc5 Nxd4 most students assumed White should play 2.Rxc8, but I did not approach it that way. I considered that White’s four tries were 2.Rxc8+, 2.Nxd4, 2.Bxd4, and 2.Qxd4. But then I noticed that 2.Qxd4 simply held the rook on c5 twice and there were no more complications – White is ahead a piece.

This is where the most instructive part occurs => At this point, after finding 2.Qxd4, I pretty much don’t need to look at 2.Rxc8 also – it’s not relevant unless either 1.Nxc6 or 1.Nxe6 also wins a piece, when I might wish to know if 1.Rxc5 wins more than a piece (which it can’t, since Black can always just stop after 1.Rxc5 and make some innocuous move remaining down the bishop).

Several students protested, “How can this be? Don’t you wish to find the strongest move?” My answer was logical. Yes, I want to find the strongest move on the move I am considering (the first move), but I don’t always need to find the strongest move on my second move of the sequence to prove that I have found the strongest first move! So if 1.Rxc5 Nxd4 2.Qxd4 leaves me ahead a piece then, unless 1.Nxc6 or 1.Nxe6 also wins a piece, this proves that 1.Rxc5 is best, and I don’t need to know how much better my choice can be if Black tries 1…Nxd4 and I play 2.Rxc8. That’s just a waste of time at this point.

In other words, if I am analyzing three candidate moves A, A’, and A”, and I see the move sequence A,B,C, where if B is the dangerous key reply for my opponent, I only need to find a C such that it proves A is the best move. I don’t need to find the best C at this point if the C I find is sufficient to yield a better position than the other lines A’,B’,C’ and A”,B”,C”, assuming their C is best. In this case that means if 1.Nxe6 and 1.Nxc6 don’t win a piece and if 1.Rxc5 Nxd4 2.Qxd4 does, then I don’t need to find a move better than 2.Qxd4 to prove that 1.Rxc5 is best, even if there is a move better than 2.Qxd4. Looking for one is irrelevant and a waste of time! This is what my initial student (and several others) did not understand. They thought they had to figure out how everything in order to determine the best move. (Note: this logic also works the other way around: If you analyze 1.Rxc5 Nxd4 2.Rxc8 and find it wins a piece or more first, then you don't necessarily have to analyze 2.Qxd4 too at this point).

Well, we do have to consider the other two candidates for White's first move, so let’s next analyze 1.Nxe6. This capture would work great if Black was forced to recapture 1…fxe6?, allowing 2.Bxc5 or even 2.Rxc5. Howver, pretty much everyone found that Black could instead reply 1…Bxe3 hitting White’s queen, which is sufficient to maintain the balance.

However, the same idea does not work for Black after 1.Nxc6, when 1…Bxe3? is bad because of the zwischenzug 2.Ne7+, which some students missed. Therefore, Black needs to recapture on c6 in a way that guards c5, so 1…Rxc6 is forced. But then White’s only attempt to win material would be the pseudo-sacrifice 2.Rxc5 Rxc5 to try to take advantage of the pin on c5. But even if White somehow wins the pinned rook he would only net a piece, which is as much as he can win with 1.Rxc5 anyway. And the prospect that 1.Nxc6 Rxc6 2.Rxc5 works looks superficially doubtful.

A sure win of a piece is better than a possible win of a piece, so I would reject 1.Nxc6 as well. Therefore, I have found that 1.Rxc5 is thus the best move. However, in a slow game if you see a win of a piece (or any move that seemingly wins), that is a red flag that the move is super-critical, so I would check my analysis several times before playing such a seemingly winning line. Playing it quickly is not a sign of intelligence that you figured it out so quickly, but rather a sign that you are not so wise as to be careful.

Finally, let’s assume White does play 1.Rxc5 and the opponent replies 1…Nxd4. What would you do now?

I’ll tell you what I would do. First I would re-analyze my “C”, in this case 2.Qxd4, to make sure it really is as good as I thought it was. If it continues to check out as just as effective as I thought, then I would likely put it in my pocket as the best move (“King of the Hill”) and look for a better one. The leading alternative is 2.Rxc8, and, unlike on the previous move, now I would be very interested to see if I could do even better than 2.Qxd4. It’s tempting to just play 2.Qxd4 since this wins easily, and I would do so in any short time limit game or if short on time. However, with so much time on my clock, I would look to see if I could win even more than a piece, say a rook or even two pieces with 2.Rxc8, making the win all that more secure. Of course, if 2.Qxd4 (or any "C") put me ahead a queen or led to a trivial checkmate, I would not bother to look for a better move.

In practice, many of my students, after analyzing ABC, when they actually do move A and the opponent replies B, they play C right away, even if it does a lot less than win a piece (it did win a piece in the above position). Immediately playing your previously calculated move is a terrible mistake in long time control games for the two reasons: 1) You can visualize C better once A and B have been played, so you should always check your analysis even if you did it thoroughly last move - you might find an error now that you can "see" better, and 2) Just because your analysis was correct does not always mean that C is best (as we showed earlier). Therefore, even if your analysis was correct then, unless you are winning trivially or short of time, it makes sense to follow Lasker’s Rule: If you see a good move, look for a better one.

Consistently practicing this analytical philosophy in cases like this could make the difference between being 1800 and 1900, which is probably a lot more than you would get if you took a pill memorizing an opening book!

• 22 months ago

This article essentially describes Alpha-Beta pruning - see <http://en.wikipedia.org/wiki/Alpha_beta_pruning&gt. The essential idea is that you can discard a possible move as soon as you can see that there is a crushing response to that move. In this case, a "crushing" response is one that makes that move at best worse than another move.

In this example, the possible move (1... Nxd4) is "crushed" by (2. Qxd4) because it must be at best worse than (1... Qxd4). Therefore we can discard (1... Nxd4) in our analysis, and don't need to consider moves like (2. Rxc8).

• 3 years ago

This is such a great, practical lesson that can be applied in every game. I can't wait for the tournament this weekend and to make a concerted effort to put this into practice! Heisman= Best thing to happen to Chess.com since Pruess and Rensch!

• 3 years ago

What about h3?  Seriously coach, very nice article, that is advice anyone up to a fairly high level could benefit from.  I would be interested in what exercises you use, if any, to hone this skill.  The tactics trainer comes to mind, but could you shed some other possible ideas.  Again, thanks for the insight.

• 3 years ago

I saw 1.Rxc5 straight away.  I was also aware before calculating that it was the ' only ' possible tactical solution available.  Both 1.Nxc6 and 1.Nxe6 simply break the tension and activate the black pieces.  I was blind to 1.Nxe6 and I'm happy about it.  Learning tactics and how to calculate is not just about what to look at, but also what ' not '.  Having calculated 1.Rxc5 and had it turned out bad, then 1.Nxc6 would be logical as a strategic solution aiming to trade minor pieces because of blacks IQP and I would check it's soundness - remember black's pieces are becoming more alive as 1.Nxc6 opens the lines.

• 3 years ago

@ Draconis:

Well put, Draconis - until the 'royal game' should be 'solved' [or 'cracked'] one day, then can we place judgement upon ourselves as to who's in fact 'perfect'.  Until 'then', let us [still] continue to enjoy the game for what it is [or stands for], and may the bones continue to roll inside its secret 'code' ...

And that's the way 'I' see it! ...

• 3 years ago

Coach Heisman is too polite to say it apparently, so I will. Both of greg556's points are misguided and wrong (though clearly made in all sincerity and with the desire to learn more).

1. If your opponent plays in such a way as to "exploit" the fact that you will play variations that result in you winning a piece with no compensation for the opponent, any good chess player would be happy to be  "exploited" in this way game after game. Chess is 99% tactics, and 1% strategy. Dan would obviously not recommend choosing a move that wins material but loses the game - which is why he looks at the response of the opponent and then finds a decent follow up move.

2. In fact, the analysis technique Coach Heisman is teaching is much like what a computer program would do if it was limited in time and space (memory) and computing power. But in real life chess games, all humans are similarly limited. Heisman excels at presenting practical advice that is useful for winning games in the real world - not in solving the game of chess generally. If you are searching for the "ultimate truth" it's probably better to apply your talents to philosophy or science. Chess is a contest between two imperfect brains. It is a game. It is not a fine art, and finding the best move possible won't advance the human condition in any significant way.

With all due respect: play, listen to Coach Heisman's advice, and enjoy your increased frequency of victory.

• 3 years ago

Greg556: thanks again -  "Gain of piece > unknown complication" - That's not what I wrote - I wrote that in the complication the most (!) you could gain was a piece. So a line that wins a piece is at least as good (and likely better) than a line which at most wins a piece - and in this case probably doesn't - but since you are going to play 1.Rxc5 in either case there's no sense wasting time debating between the second move.

• 3 years ago

Thank you for responding.  I understand that, and I understand the point: if you find one move that is good, then the only question you have to ask yourself is, are other moves _better_, if not, you needn't proceed further on that branch.

But I think my original post still applies--what you mean by "better" seems limited.  Without considering your strategic plan, for instance, how do you know that the complications of some of the other lines won't be better in the long run?  "Gain of piece > unknown complication" is the equation I am questioning.  (I am certainly not insisting on anything!  Just pushing back a little hopefully to learn more about your thinking on this point.)

(What you described is a search algorithm, even if you don't use those terms.  In a general sense that's what all chess analysis is.  In an even more general sense, that is one way of describing the game of chess in its entirety.  Finding (searching for) the best move among choices.  How do you do it?  That's your algorithm.)

• 3 years ago

Greg556 - Thanks. I don't think I was suggesting an algorithm. Not sure where you read that. I simply pointed out a subtle but important mistake many of my students made when analyzing this position (that wasted time) and how others could learn from that mistake

• 3 years ago

While this search algorithm will work well for a medium player (and I am no where near even that), it seems dramatically limited in two ways:

1.  It is purely tactical and reactionary.  In your whole analysis you never mentioned what the goal of your plan is.  To be happy with the gain of a piece without knowing what I plan on doing with it, well, that is the way I have played since fourth grade, and I think it clearly limited.  More than that, if your opponent knows your only interest is securing a material advantage, it would be easy to exploit this narrow focus.

2.  Your search algorithm is very myopic.  This is the entire difference between computers and humans.  They can easily look three or four (or, obviously, far more) moves ahead.  If you are just looking for the "best" move within the very limited world of the next move, again you are finding locally good moves but you can easily get stuck on a globally losing branch.

Again, while this article is instructive generally in how to approach analysis, and it will lift a bad player (me) up to the heights of mediocrity, I don't think it will serve to reach the best play possible.  (Interestingly, that metaphorically is exactly my point--it will get you local advantage, but global limitation.)

• 3 years ago

i would have played Nxe6 possibly. the knight puts pressure on both the rook and bishop and threatens a gain in material

• 3 years ago

It appears that some readers missed one of the main ideas of the article: There is nothing wrong with looking at 1.Rxc5 Nxd4 2.Rxc8 first (instead of 2.Qxd4). That does not waste (much) time, although 2.Qxd4 is simpler. The point was that if you find that either 1.Rxc5 Nxd4 2.Rxc8 OR 1.Rxc5 Nxd4 2.Qxd4 works, there is little to be gained from looking at White's other second move(s) too. You are only trying to find the best first move so you can play it; that process does not always require finding your best second move at that time (in this example finding the best first move for White does not require you to determine the best White second move, just an adequate one). However, once you play 1.Rxc5, then, if your opponent responds 1...Nxd4, it usually is worth analyzing to see if another move is better.

• 3 years ago

I recently had a private lesson with an IM who reviewed some of my OTB tournament games. He gave me similar advice regarding tactical analysis when the black and white pieces come into contact - maybe I should have read your aricle first and saved \$80 .   Cant wait to try this out - I think it will save brain energy in the long time control games.

• 3 years ago

IM Fins0905: Thanks! In the article I wrote: " (Note: this logic also works the other way around: If you analyze 1.Rxc5 Nxd4 2.Rxc8 and find it wins a piece or more first, then you don't necessarily have to analyze 2.Qxd4 too at this point)" which is what you did, and is equally correct, as you know.

The point was that if someone is analyzing the first move and finds a second move that works (2.Rxc8 or 2.Qxd4 - I did not mean to imply it had to be 2.Qxd4, which is "simpler" but maybe does not pop up as quickly), then they don't need another second move that works, too. They can wait until the second move to decide if there is anything better.

• 3 years ago

"In giving this problem to a few students of various levels the weaker students might miss 1.Rxc5 but all the stronger ones considered it right away, often to the detriment of not even considering 1.Nxe6 or 1.Nxc6, but that’s getting ahead of ourselves."

I have been trying to place myself in this, ummm, strength hierarchy. You see, I've been playing chess for just about 6 months now. When you said "strong players", how strong? I mean, I immediately saw the position and thought, hey, 1.Rxc5 Nxd4!

• 3 years ago
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• 3 years ago

Very interesting. I analyzed 1.Rxc5 Nxd4 2.Rxc8 almost automatically, and I was quickly satisfied that White was winning. Thus, I cut off my analysis right there. 2.Qxd4 didn't occur to me at all until I continued reading.

Objectively, both moves are easily winning, but 2.Qxd4 is the more difficult to spot because 2.Rxc8 is the logical continuation of 1.Rxc5. We've mentally resolved to pitch the rook, and there's no slowing down! A "disruption" like 2.Qxd4 doesn't come so easily (to me, at least).

This is probably for good reason. Experience tells us that a full-stop in-between move like 2.Qxd4 is less likely to be effective in desperado-type situations, so we've conditioned ourselves to prioritize continuation moves like 2.Rxc8 over candidates like 2.Qxd4.

Chess improvement is evolution :)

Great example. Thanks for that!

• 3 years ago

Excellent article Dan... Thank you very much :)

• 3 years ago

Great article Dan, thank you very much!!

• 3 years ago

Nice article.