R&3p vs R&2p

Below is a game I recently played (white to move in diagram).  I think from this position it's a win for white, but I ended up with just one pawn on the h file.  I think that's a draw, but fortunately(?) for me Black resigned.  So, two questions:

1) Is R+P on h-file vs. R a draw?

2) Is this position a forced win for white?

According to Nalimov, the position after 39. ... fxg4+ is a draw no matter what white's next move. However, after 41. ... Rf5??, white has mate in fourteen with 42. h5! Rxh5 (42. ... Kf6? 43. Ra6+ Ke5 44. Ra5+ wins the rook and keeps the pawn.) 43. Rxh5. 42. Ra6+?? unfortunately returns the position to being drawn, and it remains until black resigns.

So you are correct that the endgame is drawn at least after 39. ... fxg4, and that black should not have resigned, but there was a tactic you missed in there.

I cannot comment with certainty on the position after 29. ... Rxc3, but I would guess that it is probably drawn unless you can force black to exchange his f pawn for your g pawn.

I was pretty sure about that, but I'm just now getting back into chess after a long haitus, so my memory of endgames is a bit spotty.  Thanks for confirming that for me.  I'll have to look into tablebases, that seems pretty nifty.  Do you have any other post-game analysis tools you recommend?  Are the tools on this site worth the subscription fee?

I can't believe I missed the win after 41....Rf5?.  I didn't even look at the pawn check.  I had already concluded that I would need to promote to win.  I didn't see that I could drive his king away with Ra6+.

The tablebase I like to use is just the Shredder 6 man Nalimov tablebase online at http://www.shredderchess.com/online-chess/online-databases/endgame-database.html, but you can also download similar tablebases for use by your engine if you have enough disk space (which you probably don't). I also like to analyze games with Rybka 2.2, which you can download for free, although 2.3 is of course better (and expensive). It's a very powerful engine, but the free GUI I have (Arena) is pretty buggy. But most of the time human analysis is probably more useful. As for the tools on this site, I obviously can't tell you, as I don't subscribe, but they definitely look convenient if nothing else, which does make them appealing.

Just for reference, with pawns all on one side/one pawn island each (space and activity relatively equal of course)
1vs2 is a draw
2vs3 is a draw
3vs4 is a draw
4vs5 gives winning chances

As you can see from the tactic it's usually safer for the rooks to influence from the other side of the board.  When positions advance as far as the middle they often like to get behind too.

As a rule of thumb, as white pressing for an advantage in this position, you usually want to kick off your pawn advances with the knight pawn.  Of course you can look at this with namilov all you want, just some general things to know.

That's good to know.  I feel that I really botched my pawn moves in this position.  Maybe I should have brought my rook back to the 1st rank to support the f-pawn from behind.  I think you're right in pushing the knight pawn, especially in this case.  I played 34. h4 because I was afraid of 34...Rg5+.  But I think I should have played Kf3 instead so I could play g4.

@Eebster: Thanks for the link and suggestions, I'll check that out.  I do need to get an external HDD to back up my wife's photos (and I saw a 1.5 TB one for less than $100) so maybe I can download at least some of them for analysis.

You can download all the tablebases for 6 men or fewer at this site: http://kirill-kryukov.com/chess/tablebases-online/. Note that these are Nalimov tablebases, which means they include en passant, but not castling. This will almost never matter. To give you an idea of the space requirements:

3 men: 65 KB
4 men: 30 MB
5 men: 7.04 GB
6 men: 1.146 TB

But of course, you don't have to download all 6 men tablebases, as you can download them for different piece arrangements individually. The 5 man bases at least are probably worthwhile if you want to use an engine to help analyze endgames.

Also, note: Do not download tablebases with more men without those with fewer men. This can lead to engine search problems (it won't capture a piece because the current endgame is a win according to the base, whereas the simplified endgame is not in its tablebase, and so not known to be a win).

Could you tell me what the estimated space requierment for 7 man TB would be? I looked breifly but couldn't find it.  Would it be on the order of 1000x bigger or even more?

Probably more (if they exist).  Given that 5->6 man is about a 160x increase, I'd guess a 7-man tb would be 1k-5k larger (or maybe even more).

Chess has not been fully solved for seven men, and probably won't be any time soon, but I expect the space requirement would at least be several petabytes.

Heh, I wonder at what point it simply becomes impractical for the space it takes, ie will they bother creating 8, 9 man etc TB in the future.

Well, if you believe Raymond Kurzweil, the Singularity (roughly defined as when computer AI surpasses human intelligence) will occur around the middle of the 21st century.  If something like that comes to pass, we will probably also be able to solve 7, 8 and 9 man endgames (and have the storage capacity to store the tables.

 It seems that most people believe these will never be solved. I find that a bit conservative, but admittedly you do start to approach theoretical limits very quickly. Even with a quantum computer the size of a large planet, you will be unable to create table bases much larger than, what, 15 men maybe? I don't know the exact number, but it is lower than you would think.

I'll bet it has to do with how you define "space," "activity," "relatively equal," and "chances." Nalimov would probably show some continuum from very poor winning chances to very good winning chances as the number of pawns increases.

3vs4 as winning chances... actually as I read that I remember an example of Kasparov failing to defend a 3vs4 rook endgame, even if later analysis found the draw I guess that is winning chances.  If the weaker side has time to set up an ideal structure though I think the chances shrink considerably.

On 5 vs 4 are you saying the practical chances give hope for a draw but technically it's supposed to be a win?  I don't know any specifics about this endgame though, so I'll just have to go with what you said :)

I wouldn't be surprised if the final position in the game is still a theoretical draw

Yeah, it's a dead dead dead draw.