34...Rxc3 bxc3 Bxf2 Kxf2 Rd3 is sure way to win, as we play a rook and 3 pawns against a single horse. There is no way they can win that. The final might be long thou...

34...Bg4 is a good move too. They can't go anywhere, the only thing they can do is to push a pawn or move the bishop a little. In fact, they may need to push h5 to make a place to put the queen, hehe, which is anyhow bad, after Red3, we get the queen for a single rook (and save the bishop).

Ok, I had a look to the last two, and also to Rc1, Red3 (like I didn't want to give the rook in c3, hehe) and Bd3.

I would definitively like Bg4 better than others. In the [U]worst[/U] case, we get the queen for a single rook (and save our bishop). In the best case, we mate them very fast.

[B]34...Bg4[/B] is my choice. As SM88 already "voted" for it (he suggested it), if WMH has no serious objection to it, I will post it tomorrow morning (24 hours from now).

BTW, @SM88, they can't move the knight, that would be the best version for us...

[QUOTE=LaurV;345129]BTW, @SM88, they can't move the knight, that would be the best version for us...[/QUOTE]

h2 is open and able to receive a knight without complete harm except it would allow Bh3#, but the rest are all blocked or under attack I agree.

[QUOTE=science_man_88;345152]h2 is open and able to receive a knight without complete harm except it would allow Bh3#, but the rest are all blocked or under attack I agree.[/QUOTE]
They can not move that knight, all knight's moves are fast mate, except Nd4, which is also mate, but longer.
Nh2 is mate in 1 move with Bh3. Nd2, Ng1, Ne5 is mate in few moves after Rg3, nothing can avoid the mate. With Ne1 they give it for free and this is also mate after Re3xe1, Qxe1, Rxe1, we transform the pawn or take the bishop for it in f3, after Rg1. It follows mate in few moves.
Nd4 is a bit more complicate, after the exchange Bxd4, cxd4, we go Re2, Qxe2, Bxe2, and that's it, we have a rook and few pawns advantage (much better then in version with 34..Rxc3, there we had the same, but against a knight, now the knight is gone).

It took some time for me to go thru all the lines for Bg4 and found that all the lines that favored us, so Bg4 it is.

it looks like they replied Nd4

[QUOTE=science_man_88;345358]it looks like they replied Nd4[/QUOTE]
Perfect, like this we get the queen for a single rook, as said: Bxd4, cxd4, Re2. Any other play is mate. Here they are forced to take the rook, any other move we may take the queen for less, or even for free, or mate them faster. If for example they play Bf3, we exchange all and escape with a clean rook. They can check us with the bishop, but this is helping us to advance the king. So, the only reasonable continuation after Re2 is: Qxe2, Bxe2. We now play a rook and a couple of pawns in advantage, which is sure win for us in about 15-20 moves. I believe I can mate them in less moves, as the white king can't leave the corner anymore after the exchange (but I did not find a sure mate yet, honestly I did not look too hard, this game is played anyhow, it is not so palpitant anymore). If I would be them, I would give up now.

A quick reply is in order, maybe even a conditional reply.

[QUOTE=LaurV;345409]Perfect, like this we get the queen for a single rook, as said: Bxd4, cxd4, Re2. Any other play is mate. Here they are forced to take the rook, any other move we may take the queen for less, or even for free, or mate them faster. If for example they play Bf3, we exchange all and escape with a clean rook. They can check us with the bishop, but this is helping us to advance the king. So, the only reasonable continuation after Re2 is: Qxe2, Bxe2. We now play a rook and a couple of pawns in advantage, which is sure win for us in about 15-20 moves. I believe I can mate them in less moves, as the white king can't leave the corner anymore after the exchange (but I did not find a sure mate yet, honestly I did not look too hard, this game is played anyhow, it is not so palpitant anymore). If I would be them, I would give up now.[/QUOTE]

I was originally thinking Rg3+ forcing Kh2 but then I lost how to win.