Let A be the event that the kibitzer makes a mistake at (as soon as) the fifth ply, B the event that the kibitzer is influenced by CG's rating and C its complementary event, that is to say, the kibitzer is not influenced by CG's rating.

Then, if we can estimate the probability of B, C, A/B, that is, the event of making that mistake under the influence of the assigned rating, and A/C, the event of making that mistake due to other causes, it is possible to work out the probability of B/A, the event of being under the influence of CG's rating knowing that the mistake was made by applying Bayes' theorem:

P(B/A) = P(A/B)*P(B) / [P(A/B)*P(B) + P(A/C)*P(C)]

<xrt999> 33...Ra5+, 34. Qa4 Rxa4+, 35. Kxa4 Rxc2 (much better than 35...Rd4+) -- that gives Black a big advantage with one queen up.

<xrt999> It is because 35...Rd4+ 36. Ka3 (that helps White escape the checkmate).

So, 35...Rxc2 is a lot better than 35...Rd4+.

So let's rewind a few moves and put ourselves in white's shoes. It is white to play ... and lose.

click for larger view

Black's e4 pawn is a potential game winner ... for either player! As a passed pawn, black dreams of ramming it up the board to promotion. But as an isolated passed pawn, white looks forward to overpowering it, winning it and then converting his pawn plus into an endgame win.

Black's previous move 29...Rfd8 probably gave white a clue that something was not quite right. Instead of protecting his e4 pawn, black doubles rooks on the d file. Then white spots the trick: 30.Qxe4 loses to 30...Rd2+.

So white needs to prepare Qxe4. After all, the pawn isn't going anywhere. So he possibly imagines a reorganisation of his troops ... 30. Rc1 to protect the c3 pawn, 31. Kb1 to unpin the c3 pawn, 32. c4 to protect the c4 pawn. Then we can think about Qxe4 or perhaps we first want to trade off the rooks. Easy peasy.

Or maybe he dreams of playing Rc2 either before or after the Rd2+ trick.

30. Rc1 Rxc5

click for larger view

Now white miscalculates. Black has undoubled rooks on the d file, apparently releasing some of the tension. White thinks he can defend against 31...Rd2+ by playing 32. Rc2.

click for larger view

This was the position that white expected after playing 31. Qxe4. The rook check will not have come as a surprise to him ... he has been guarding against it for the past couple of moves. What he has missed is that the Rc2 is pinned and that Black wins with the killer 32...Qxc3+.

You've overlooked 33. Kc1 Qxa1+ (not mate) 34. Kxd2 (that costs Black a rook). Can't you see that the Black Rook on d2 is unprotected????

After 33. Kc1, the correct move is 33...Qxc2+!, 34. Qxc2 Rcxc2+, 35. Kb1 Rxe2 (Black wins two rooks and mates soon)

<YouRang> You should take a look at the Black Rook on d2 that is unprotected.

do you mean Ra5+? >

Yes, of course I can that the rook on d2 in unprotected! (...now that you've mentioned it).

Haste makes waste. :-(

We mistaken posters might be recalling that the d-file was covered by a "safe" R at the combination's beginning, so then we saw a semi-epaulette mate with the Q at a1. It is significant that the posters making the mistake are all experienced and probably abbreviate their analysis with pattern recognition.

Fully agree, and nicely put. I have a theory that as we get older and more experienced, we tend to simplify more. So we stop truly looking at things and instead we classify them into easy to manage categories. Where a child would look at something with open eyes of wonder, we greybeards hardly notice things.

I find it incredibly illuminating to follow the thought patterns of my 8 year old son. He sees things that I don't give a second glance to.

The Rd2 has been protected successively by the Rd8, the threat of QxQ and the Qc3. So the more experienced amongst us classify it as "protected" and don't notice that each of the protections has disappeared.

I don't want to beat this poor horse into glue, but I partly agree with each of the three previous posts on the subject. I (along with 3 others) made this error and I can recall the general sequence of my thoughts. Originally, I was going to post the solution as 31.... Rd2+! 32.Rc2 Rxe2(?) 33.Rxe2(?) Qxc3+. In the course of writing this up, I realized that 33.Qxe2 cooked it, so I quickly worked out the correct 2nd move 32...Qxc3+! and the correct follow-ups, including 33.Kc1 Qxc2+. It was when I actually wrote out the final piece of the post that I "saw" and wrote up the Qa1# hallucination.

I think there were a few things going on here:

1. I'd found the two key moves Rd2+ and Qxc3+, so there was a tendency to relax and treat the rest of the solution as an afterthought. This is close to what fellow hallucinator <Johnlspouge> said in his last post.

2. Trying to present the completion of the solution in a neat little package, it was desirable to find a one move answer to meet each legal white response to Qxc3+. Qa1# is an aesthetically pleasing finish, so in a way, the wish was father to the thought.

After 32...Qxc3+! White's another try is 33. Ka3 Ra5+, 34. Qa4 (forced) Rxa4+, 35. Kxa4 Rxc2! -- It's much stronger than 35...Rd4+ because if White declines the rook trade, he will face the inevitable checkmate. Otherwise, White reluctantly has to trade the rook to avoid being mated.

Black actually forces simplicity and the rook trade with 35...Rxc2! because White has no major and minor pieces left on the board when Black has a one-queen advantage.

<xrt999> 35...Rxc2! 36. Rxc2 (forced) Qxc2 , so that's why 35...Rxc2! is much stronger than 35...Rd4+. Did you get it, <xrt999>?

I mean that 35...Rxc2! 36. Re8+?? Kf7 with double attack - forcing White to give up another rook to avoid getting mated. 0-1