Who wouldn't look at 34.Qxe8+ and the rather obvious follow-up moves?

That's where you deliberately eschew the *quick* kill in favor of one that produces prolonged agony. Specialists in this field of chess know how to make just the right sub-optimal moves to keep their opponent lingering along with some meager dose of false hope.

Here, it might go:

<34.Qd1?!> "oh no, I could have won with 34.Qxe8+!" <34...Rxe1> thinking that they ended that threat (heh) <35.Qxe1> is dejectedly played and <35...Nf4+!> gets the knight out of trouble by taking advantage of the pinned g-pawn.

White gets out of check and unpins with <36.Kh2 Nxd5 37.cxd5>. Black sees that his b-pawn is in take, so <37...b6 38.Nxd7 Qxd7> [diagram]

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Now, <39.Qe6!> threatens the Q, or Qxf6+ or d6. Since black's K can get over in time to stop the pawn, it seems like <39...Qxe6 40.dxe6 Kg8> is called for.

Then <41.d5 Kf8 42.d6 b5> (note the delicious false hope provided by black's queenside pawn majority) <43.h5 a5 44.Kh3 b4 45.Kg4 a4 46.Kf5 b3 47.axb3> (as if we're worried) <47...axb3 48.Kxf6 Ke8> (or else d7 wins quickly -- black plays right into our hands by avoiding the *quick* loss, Bwa-Ha-Ha) <49.e7 b2 50.Ke6 b1=Q> (getting a queen = last morsel of false hope) <51.d7#!>

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Playing against an inferior chess engine yes, playing against Rybka no. Rybka blocks the white Bishop with her pawn. But even playing against Rybka it's an easy but a little tricky win. Be carefull!>

I am struggling to find a line where black can block the white bishop with a pawn to stop the massacre. At the end of the game line, we get to this position:

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Now if 36...f5, white wins all the black pieces with 37. Bxf5+ Qg6 (forced) 38. Re7+ Kh8 (or Kg8) 39. Bxg6. True, the Nh3 ain't dead yet, but it's got nowhere to run to and will be a gonner soon.

Or perhaps we play something like this: 34...Kh7 35. Be4+ (not the best, but I am trying to give f5 every chance). 35...f5, leading to here:

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Any sensible white move wins easily from here. Fritzie reckons that 36. Nxd7 is mate in 11.

I had suggested: "Even after 34.Qxe8+ Kh7 35.Qxd7 every one of Black's piece's disappears."

You wrote: " If White wants to twist the knife, he plays Re7+ before Bxg6. :-P".

Actually, 37. Re7+ is the fastest way to bring the point home. Black is forced back to hist first rank and kept pinned there by the Rook and Bishop. After 37. ... Kg8; 38. Bxg6 Black cannot escape the back rank and is doomed to be mated in very short order. White settles his Knight on e6 and delivers checkmate with the Rook on the Black back rank.

An illustrative line is given by <wals> in the kibitzing above:

Difficult: Medium/Easy

White is 2 pawns up.

Ok. The white queen is under attack. My first thoughts included blocking the rook attack, with moves like 34.Ne6 or 34.Be6. But i got nowhere. Then i left the position, and hours later, i saw almost instantly that, sacrificing the queen is a good idea. Because, after 34.QXe8+ Bxe8 35. Txe8+. I win a R+B and a 8th rank rook, just by sacrifing the queen. And also the king is nearly stuck. By that line of thought, i found:

34. Qxe8+ Bxe8
35. Txe8+ Kh7
36. Be4+ 1-0 (probably resigns now)

After 36 move, the black king has no squares to run, and that leaves no choice, and he has to block the check with the queen, and after the exchange, white has the advantage of one rook, and the other 2 pawns, of course.

34.♕xe8+ ♗xe8 35.♖xe8+ ♔h7 36.♗e4+

And now everything is hopeless.

36...♕g6 37.♖e7+ ♔g8 38.♗xg6