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I’d say White has a winning advantage (+-)
1. Bc4+
Black has only 2 legal moves: 1. … Kf8 or Kg7. Whichever Black chooses is answered by the deadly 2. exf6
1.Bc4+ Kf8 2.exf6 looks very strong. If 2…Bxf6 then 3.Bc5+ and 4.Rf1+ is good whereas if 2…hxg2 3.fxe7+ Qxe7 4.Bc5! seals black’s fate. There may be other lines but I’d play this…
I would play g2xh3.
The position is about even.
I would rather be White.
1. e5xf6 followed by checks by the bishops, pawn rook or queen should make Black very uncomfortable.
Bc4+ wins
The first commenter is correct. Bc4 is overpowering. After 2.ef6, it is over because the rook comes in on the f-file, or the queen’s bishop comes onto c5.
Let us look at the position. White has on his plus side his control of the center and the bishop pair with several open diagonals for them to operate. On the minus side, he is a rook and a couple of pawns down. Black’s positive is his material advantage and two advanced pawns. But he’s stifled by the lack of mobility for his pieces and the exposed king. Overall, my assessment is that white has significant positional advantage in this position (presumably he sacrificed a rook to get this advantage).
How would white convert his positional advantage to an outright victory? A lot of people have pointed out what I think is indeed the correct line – starting with 1. Bc4+, following up with 2. exf6 (with/without a check depending on what blacked played as his first move). I don’t think black can hold the position for much long, for example:
1. Bc4+ Kg7
2. exf6+ Kxf6 (2… Kh7? 3. Qf4 and checkmate cannot be avoided)
3. Bd4+ Kg5
4. Qe5+ and so on. I haven’t done a full analysis, but without any tangible threats black will be checkmated sooner or later in this position.