Educational draw against Computer4-Impossible: Finding the right plan when down

Hello all, here is an interesting theoretically drawn position I achieved (and held) against chess.com's Impossible level computer in a 30+30 time control. 

The game itself is very educational, where we played a Carro-Kann, Breyer variation. I will have the full game at the end of the post, though the bulk of this entry is going to be focusing on the endgame, and holding the draw. Holding a worse position is a massively important skill for a chessplayer to have in their arsenal. Everybody loves finding the best way to win a superior position, but the fact of the matter is sometimes you're worse! Finding the right plans when things go awry is critical. This post is going to help broaden (or reinforce) your endgame knowledge, and hopefully get you thinking on how to fight on in tough positions! 

We'll start with a key position that occurs later in the game, work our way to the truely drawn end position, and then go back and see where I think the computer itself failed to understand how to play for a win when it still had chances. 

Take time to look at this position and consider:

-          What plan(s) does black have in motion?

-          How can white put up stiffest resistance to blacks plan(s)?

-          What resources might white have in the position?

- Blacks plan should be fairly straight forward. Advance that passed B-pawn! It should also be noted that black has a 3v2 majority on the Kingside (though this is still drawish).

- If white can trade off the b-pawn for the d-pawn a draw becomes much easier. As such, white should aim to get his rook behind the b-pawn and perhaps use his minority to disrupt any harmony black can achieve with his kingside should his king try to help the b-pawn advance. 

- White has an active rook and a passed d-pawn of it's own. Never underestimate the power of active pieces in the endgame. If you are looking to round out your endgame knowledge I highly recommend literature by Dvoretsky (likely better for players above 1800+ elo). 

We now have a very interesting position. Black has got his b-pawn all the way to b2, but his rook on b1 is anchored down and preventing promotion, where white's rook is active and ideally placed. White's d-pawn lives on, and white's h-pawn looks to stir up trouble. How might this game procede? 

In the next diagram, we will see the game reach the clearly drawn position, in spite of most engines favoring black between -2.67 all the way to -3.98!

White is down two full pawns, but black has no means of making progress! The computer managed to entice me into playing Rxg7+ after it shuffled it's king in position to grab my h-pawn (and avoid the 50-move draw rule), but the game was still a dead draw. We eventually reached this position: 

There are two major blunders white could play in this position. Can you find both of them?

The first one we've already covered. Kxh3 loses on the spot to Rh1+. The second one I've seen players mess up in these types of positions more frequently than you may think. Much of the game has come with white checking the black king around, but getting check happy here is a loss! Why is Rb3+ in the above position so horrific? 

Gonna take a look later - thanks for posting!

One of the best threads I have seen lately.

Thanks guys! Been swamped lately, but I'm going to try to keep all sorts of good stuff coming. Endgames, tactics, perhaps even a series on a specific opening should I find the time. 

@APG817 The computer declined several draw offers during the game. Since the engine reads the position as utterly decisive it played on, only making pawn moves to prevent the 50-move rule. As humans we can understand that there is no way to make progress but Comp4 played it out to the bitter end!  

Since White can draw with correct play, I would think all 12 of White's losing moves should be considered major blunders.

I wondered if someone would want to go into the semantics of that. Technically yes, there are several losing moves for white in the position described. Perhaps it's an oversimplification to describe it as "two major blunders", but the idea is that 

1. Poor Rook move (any rook move on the eighth aside from Rd8+ is ridiculous and losing on the spot). 
2. Poor King move (the King is ideally placed and getting fancy loses on the spot)

So in regards to "major blunder" 1, yes, there are 9 terrible rook moves to go with the two terrible king moves. 11 moves that lose, and 2 major conceptual blunders.

Getting all technical on me!  

Pfren, thanks for the additional analysis, and Capt. Obv, thanks for sharing the game and notes. Was enjoyable study. I figured that with the computer showing you down 3points, there was a win in there still, and you managed to pull out a draw from it! Good on you.

Actually, 10 terrible rook moves. (Did you count Rxb2?)

Guilty! I stand corrected :) 

Drat. I did miss this, thinking I could still achieve my h-pawn advance after tucking my king away on f2, but between g6 and some other move orders I am lost after f5+. Well, the silver lining is at least Comp4 missed it too! 

Turns out this was more educational for myself than I thought. Thanks for catching that pfren!