I think you must mean 48 ... R2a6 since 48 ... R7a6 loses.

After 48 h6 R2a6 49 Rxa6 Rxa6, the position is

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Rybka has the score as -0.18 at depth of 28 plies. I've played it out a little. It looks like black will not promote the d pawn.

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Analysis by Fritz 11: Depth 22/45 1176kN/s time 27min19

1. (-0.88): 28...e3-e2 29.Re1xe2 Ne5-f3+ 30.Kg1-f1 Nf3xd4 31.Rg2xg7+ Kg8xg7 32.Re2xe8 Qb7-h1+ 33.Nh3-g1 Rc8xe8 34.Qd1-g4+ Kg7-f7 35.Qg4xd4 Qh1xh2 36.Qd4-d5+ Kf7-f6 37.Ng1-f3 Qh2-f4 38.Kf1-f2 Re8-e7 39.Qd5-d8 2. (0.75): 28...Qb7-d7 29.Bd4xe5 Re8xe5 30.Nh3-f4 Rc8-e8 31.Nf4-d5 Kg8-h8 32.Kg1-h1 Qd7-f7 33.Qd1-g4 e3-e2 34.Nd5-f4 Bg7-h6 35.Nf4xe2 Bh6-d2 36.Re1-b1 Bd2xb4 37.Ne2-f4 Bb4-c3 38.Qg4-h4

(, 01.02.2008) for those that don't know :
Depth = search progress in i/2 moves or ply
22 = general depth 45 = critical lines depth
The speed at which it generated and evaluated positions was 1,176,000 per second.
By moving e3-e2 black has a winning advantage of 88/1oo of a pawn.

Spassky vs Korchnoi, 1977

after 48 h6 R2a6 49 Rxa6 Rxa6. There were some impressive swings in Toga's evaluation, presumably reflecting its event horizon. I list the extremes of evaluation's swings:

plies 9/24 time 00:00 value +2.86

plies 18/53 time 01:42 value -1.01

plies 25/75 time 1:59:54 value -0.04

At each extreme, the value remained at the extreme 0.06 for three plies. There is no real news here, I suppose: machine evaluation is undependable in endgames, and stability of the evaluation does not guarantee accuracy.

With respect to <CRWynn>'s statement about R vs. N endgames, one would need to know a lot about the depth and stability of the specific evaluation before drawing any conclusion.

Zappa Mexico 64 plays an alternative line than Shredder or Rybka, in which both the d pawn and h pawn promote. It appears to be drawn (+0.2 at depth 16/50). The trouble with some programs and drawn positions is that there can be a huge variety of lines that all end up drawn, so it is hard for the engine to prune the search tree. This does not mean that the machine evaluation is unreliable, it just means you want to go pretty deep. If there really is a draw, this takes a long time.

The position based on Spassky-Korchnoi is clearly drawn, it will just take more cycles for some engines to get there than others.

Agreed. Thanks for taking a look.

I would not bother with analysis at the 28th move. The following line is quite forcing and any deviation makes it much worse for the deviator:

28. Bxd4 e2 29. Rexe2 Nf3+ 30. Kf1 Nxd4 31. Rxg7+ Kxg7 32. Rxe8

Now RV's Rybka likes 32... Rxe8 and 32... Qh1 equally, while Hiarcs gives Rxe8 a bit of an edge (about 0.1 worth). Curiously Hiarcs usually gives more decisive evals than Rybka, but not in this case, it agrees that the black's advantage is about 0.8 or so/

So I would not start analysis any earlier than the end of the above line. You could even continue for a bit longer, e/g:

32 ... Rxe8 33. Qg4+ 33 ... Kf7

and now there are two closce choices, 34. Qf4 or 34. Qxd4. Forward analysis seems to favor the latter, but backslide moves the former to the frontrunner position, so the position at the end of the above might be a useful point to start. This gives you 10 plies headstart. I continued 34. Qxd4 another couple of moves and never got it to show anything better for the black than -0.82. Definitely not enough to claim the win based on the engine eval, but this could be one of the position where human insights are superior to silicon.

Overall, <Terry McCracken> and <Jimfromprovidence> might be right -- there is plenty of game left and Larsen might have resigned too early.

Here's the entire line for easy cut/paste, if you find my suggestion useful:

1. c4 c5 2. g3 g6 3. Bg2 Bg7 4. e3 Nf6 5. Nc3 e6 6. Nge2 O-O 7. O-O Nc6 8. Nf4 b6 9. b3 Ba6 10. Bb2 d5 11. Re1 Rc8 12. d3 d4 13. exd4 Nxd4 14. a4 Qd7 15. Nb5 Rfd8 16. Nxd4 cxd4 17. b4 Bb7 18. Bc1 Re8 19. Nh3 e5 20. Bxb7 Qxb7 21. f3 Nd7 22. g4 f5 23. gxf5 gxf5 24. Ra2 e4 25. fxe4 fxe4 26. Rg2 e3 27. Bb2 Ne5 28. Bxd4 e2 29. Rexe2 Nf3+ 30. Kf1 Nxd4 31. Rxg7+ Kxg7 32. Rxe8 Rxe8 33. Qg4+ Kf7

In fact with engines, then the faster your computer, the less often you get incomplete evaluations. It's as simple as that, but we need quite a bit faster machines before we can forget about this issue.

When there is a win, there are normally a lot of ways to blow it, and the engine can prune them to get a small tree. The thing about a draw is that usually once you get past a certain point where the draw has been achieved, then the tree explodes with lots of meaningless variations that the engine can't prune away because many of them have the best (and worst) evaluation of 0.0.

28. Bxd4 e2 29. Rexe2 Nf3+ 30. Kf1 Nxd4 31. Rxg7+ Kxg7 32. Rxe8

Now RV's Rybka likes 32... Rxe8 and 32... Qh1 equally, while Hiarcs gives Rxe8 a bit of an edge (about 0.1 worth). Curiously Hiarcs usually gives more decisive evals than Rybka, but not in this case, it agrees that the black's advantage is about 0.8 or so/

So I would not start analysis any earlier than the end of the above line. You could even continue for a bit longer, e/g:

32 ... Rxe8 33. Qg4+ 33 ... Kf7"

Well I've been running the analysis of the final position for 10 hours now so I'm not about to stop it. I did do some a little further down (starting at move 42 in the then best line for Rybka).

At the moment Rybka is in the 19th ply from 28 Bxd4 and the position is evaluated as -0.98 which is making the draw a little less clear. Here are the lines Rybka is analyzing at the moment:

19 554:46 -0.98 29.Rexe2 Nf3+ 30.Kf1 Nxd4 31.Rxg7+ Kxg7 32.Rxe8 Rxe8 33.Qg4+ Kf7 34.Qf4+ Kg8 35.Qxd4 Qh1+ (10.833.451.791) 333

19 556:01 -3.49 29.Rgxe2 Nf3+ 30.Kf1 Rf8 31.Bf2 Nxh2+ 32.Kg1 Nf3+ 33.Kf1 Nxe1 34.Qxe1 Qh1+ 35.Ng1 Bd4 (10.843.637.481) 332

18 551:16 -4.83 29.Qxe2 Nf3+ 30.Qxf3 Rxe1+ 31.Kf2 Rf1+ 32.Kxf1 Qxf3+ 33.Nf2 Rc7 34.Rg3 Qf4 35.Be3 Qe5 (10.797.771.015) 334

18 552:31 -5.15 29.Qa1 Nf3+ 30.Kh1 Nxd4 31.Qa2 Rf8 32.Rexe2 Nxe2 33.Qxe2 Rce8 34.Qd1 Qf3 35.Qg1 Re2 (10.811.178.301) 333

-0.98 29.Rexe2 ...

-3.49 29.Rgxe2 ...

In the future, note that don't need to go deep to see the big advantage of Rexe2, so just slide forward after, e.g. 16 plies show a huge difference, and restart (make sure to set the engine options to keep the cache intact). This will release lots of memory and accelerate the search substantially (I am assuming you allocated as much cache as possible).

There are some cases when the valuation will change substantially at depth 20 plies or more, but this happens very rarely.

BTW, note also that the lines produced by the engine cannot be trusted much past 1/3rd of the search depth. Rybka might be better in this respect, but in your most promising line, I am pretty sure that 34.Qf4+ is inferior to 34.Qxd4. However, this advantage might show up only after 14 plies or so (which means that your search won't find that improvement until it reaches 24 plies deep. If you look at the times it took your engine to get to 16, 17, 18, 19 plies, you can extrapolate it and figure out how much longer you'll need to run.

What you say about focusing the analysis further down the line is usually a very good idea, and the Shredder interface makes it quite simple (you just make the moves and the analysis continues with cache intact, etc.).

But there is one exception when you should not do that. That is when you have significant drawing chances. The problem with playing down the most promising line is that early on that line is probably being selected by the engine for winning chances; if those evaporate then you may have skipped past a line which was less promising to the engine when it thought it was looking for a win, but which may be easier in which to gain a draw (e.g. a sacrifice to get a draw).

Of course without knowing the time factor in this game – a final verdict is unclear given that Tal (whom I would equate to Fischer, were it not for the health factor) 4 years later won the World Blitz Championship. We know the unfortunate history of Larsen (0-6 vs Bobby). Who said you can’t play the player? ...it is a part of Chess which makes it a ‘game’. I would have bet on Tal regardless.

But let us face it – most top grandmasters have a great respect both for each other and the natural synergy of Chess. If this were a position reached by Kramnik-Anand they likely would be happy to settle for a draw (as they did in a double-edged position in Mexico). Some positions are too beautiful to be compromised by either human error or computer post-mortems: which by the way are beginning to look more like a modern day >ZeNo[s]PaRaDoX<.

Of course Tal was just being ironic, but even in the most ironic remark is still some kind of truth hidden (at least most of the times). And yes, of course Tal's "short glance" at a position is much deeper than my "longer calculating", no doubt about it.

But I doubt that Tal has always calculated his "insane sacrifices" to the bitter end, otherwise all of his sacrifices would've been sound (which was in most of the time not the case) or never played. IMHO Tal realized one thing, sacrifices do not need to be 100% sound, they just need to create a lot of big problems for your opponent, whether he/she can solve them is the question (imo Topalov's sacrifices work similar, even if his sacs. are nowhere close to Tal's masterpieces). The reason for Tal's unique greatness was not his (great) calculating skill, but rather his creativity and imagination. He was the best to foresee a position and had faith in his evaluation of those positions.

There are some other great (semi-)ironic quotes, that somehow point toward the direction of such an interpretation.

Well after 20 hours of analysis from the final position, and now just about 5 hours of analysis from the position after 33 ... Kf7

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The continuation that Rybka prefers is 34 Qf4+ instead of 34 Qxd4:

21 17:15 -1.07 34.Qf4+ Kg8 35.Qxd4 Qh1+ 36.Ng1 Qxh2 37.Qd5+ Kh8 38.Qd4+ Qe5 39.Qxe5+ Rxe5 40.Kf2 Kg7 (158.256.879) 156

21 15:02 -1.16 34.Qxd4 Qh1+ 35.Ng1 Qxh2 36.Qd7+ Re7 37.Qf5+ Kg7 38.Qg4+ Kh6 39.d4 Rf7+ 40.Nf3 Qh5 (141.155.613) 160

20 10:51 -3.31 34.Ng5+ Ke7 35.Qh4 Rf8+ 36.Ke1 Ke8 37.Qxd4 Qh1+ 38.Kd2 Qg2+ 39.Kc3 Qxg5 40.Kb3 Rf7 (98.216.159) 154

20 11:17 -4.70 34.Nf2 Nf3 35.Qh5+ Kf8 36.Qh6+ Qg7 37.Qf4+ Qf7 38.Qxf7+ Kxf7 39.Ne4 Ke6 40.h3 Rf8 (102.463.888) 154

It's starting to look like Larsen's draw might be slipping away.

Larsen overlooked a clever defensive resource pointed out in <RV>'s and other's analysis here, winning back a piece and only remaining an exchange down with a pawn as compensation after 28...e2 29.Rexe2 Nf3+ 30.Kf1 Nxd4 31.Rxg7+ Kxg7 32.Rxe8 Rxe8 33. Qg4+! .

Rather this one:

"Later, I began to succeed in decisive games. Perhaps because I realized a very simple truth: not only was I worried, but also my opponent."

It looked for a long time like white had some sort of drawing chances, but I would have to say now that it's probably lost. In every line white has play but eventually there is a black answer, although some of them are deep and take a long time for engines to find. Larsen might have been right to conclude that this was going to be a nasty struggle, and against Tal, who had just hit him with 28 ... e2, he might have felt that this one not one of Tal's bad days. I think patzer2 may have called it.