Can black win

Here is a position I had in a game I played as black, I blundered by playing Bxh2.. with g3 trapping my bishop and eventually lost , but If that move was not played who had the better endgame position? I feel even though my kingside structure is bad I have a bishop vs knight and am a pawn up but is that enough to win?

yes he can because B vs N with pawns on the opposite sides of the board is a win for the person owning the B. 

Hard to tell, but

1. ..., c5  2. Nf5 , Bc7 3. h3   seems to give white a slight a advantage on tempos by making it able to force rook trade and opening the way for white king to step in,

It is totally winning for black. Black is up a pawn, there are pawns on both sides of the board which is better for the side with the bishop, black will be able to create a passed pawn on the queen side. 

i think it is winning after you are up a pawn

one time i saw my friend playing a game with his grandfather using a standard chess set on the table.   my friend was about to checkmate his grandfather.  but then the grandfather knocked over the table and the whole chess set went on the floor.  then the grandfather told my friend that my friend did not beat him because the game could not complete.

so you should be careful about too in determining whether a person is winning a game or not.  because outside circumstances could prevent the game from completing. 

It has to be winning. But I would not bet on my ability to win it against the toughest defense.

Hi,

The POSITION must be evaluated as a "likely drawn game." The three (3) doubled and isolated Black Kingside pawns are probably NOT worth anything like the value of three pawns abreast. Let's value them at 1.5 points only. If that's true, White with the Knight and his six beautiful pawns holds an ultra-slim 14 to 13.5 point positional/material edge. The key word is the capitalized word POSITION above. Materially Black holds the traditional edge when we "count up" the bodies along the side of the chess board . . . but except for his slight lead in development, POSITIONALLY Black's prospects SUCK. IF it were White's move right now he would move Re1 with the idea of swapping Rooks immediately and taking away what little advantage Black holds. What is that Black advantage? Typically in the endgame the Rook works better with a Bishop than it does with a Knight (by comparison, Queens tend to work much better with Knights than they do with Bishops in the ENDGAME). Getting rid of the Rooks puts the position to the ACID TEST in which, I believe White holds a tiny but undeniable advantage. White's plan will be to put his Pawns in some sort of fortress position abetted by the Knight with everyone safely on White Squares so the Bishop will be impotent to harm them and seeking to get the Black Pawns locked on Black Squares limiting the Bishop's potential. AMEN

      On the other hand, Black does have the move and he does have a better placed rook and a naturally active King which Black does not YET have. And, of course, he has that lone Bishop which tends to be more useful in such endgames than a lone Knight will. If and when the rooks are traded off, the game will become more drawish yet. Much play is left and yes, the Bishop is potentially more mobile than the Knight. However, the game will likely be drawn if played by expert, master or Grandmaster hands. It is Black's move and he must unseat the Knight soon, I believe, and place as many Black Pawns as possible on White Squares to give his Bishop maximum mobility. The problem with this approach is that it tends to be static for both sides and since Black's now "winning" in conventional material terms but losing positionally, both sides will gain their biggest threats by hyper-activating their Kings while seeking to prevent the opposing Kings from being effective against their positions.

Obviously, I disagree fundamentally with both the approach and the evaluation of Rowsweep who said, "yes he can because B vs N with pawns on the opposite sides of the board is a win for the person owning theB." Hopefully, I'll be able to explain the situation sufficiently well for him/her to see why this "snap judgment" is not really doing this complicated endgame position justice.

      Some of the main reasons that Bishops and Knights have both been given the material point evaluation of three points each for at least the last three centuries.  That means: Bishop = 3 Pawns = Knight in other words B = N

      The advantages of the Knight are its ability to travel on and threaten or protect squares of both colors. Its comparative disadvantage lies with its slowness in getting to distant parts of the board. The advantages of the Bishop lie in its ability to attack from a distance and to quickly cover ground. The disadvantages of the Bishop lie in its being confined to just one color squares. Thus there are obvious reasons that these two minor pieces have traditionally been considered EVEN as far as their force or value. More specifically, ENDGAME POSITIONS like the one shown above are the main reasons that these two pieces are considered equal. Both sides will naturally seek to mask their own weaknesses (create positions where their weaknesses are relatively unimportant and protected) and make their own advantages the most critical PLUSES on the board while seeking to exploit the other side's weaknesses and make the other side's strengths seemingly of no consequence. In that effort, a lot of little battles are likely to occur which over and over and over again will tend to tie the position up into situations favoring the Knight over the Bishop IF both sides play very actively. IF on the other hand, Black, realizes his slight weaknesses and acts vigorously to mask them with a less active King at first, those sorts of positions will likely make a draw more highly probable. Why? Because Black does best keeping the Rooks on the board, but he can't afford to let the White Rook penetrate to the last two ranks. Thus the Rooks must likely be traded off which favors White more. In the resulting B vs. N positions are drawish since again IF the Knight gets too active he risks being dominated (trapped) by the Bishop. Whoever risks the most will probably lose.  Thus both sides have good reasons to see a draw as a "good" result for them.

In general, in endgames with pawns on both sides of the board the player with the bishop stands better. This doesn't mean of course that this is a winning andvantage. In this particular case I think the result will be a draw after the exchange of rooks with Re1. Your only weakness might be the doubled pawns on the f file. So, maybe after white plays Re1 you might consider Re5 intending RxR fxR fixing your pawn structure. 

I hope I helped you 

Not only are you evaluating three pawns as less than two (f7 and h7 are worth two pawns, right?), but you are dead wrong even at 2.5.

The doubled pawns do create some liabilities, the most important being the f5 square for the knight. But, because White has three pawns on the other side, no pawn is "wasted" because there would be no way to create a passed pawn anyways, and they can prevent the creation of a white passed pawn just as well as undoubled pawns.

Here is a classical example of that. How do you evaluate the following two positions (with any side to move, it does not matter)?

completly winning, a Pawn is a Pawn. Even if its a doubled Pawn...

The most important "positional" factor in this position is black's extra pawn. People always underrate the importance of pawns and overrate the importance of structure.  The whole reason pawn structure is important is that it determines how easy/hard it is to hang on to your pawns.  So black has a better structure because he has more pawns and none is an immediate target.

Since black is is the only one who can make a passed pawn, black will win this with correct play.  The easiest way would be with a rook trade. The more pieces get traded off, the easier it is for black to convert his pawn.

Fie on Gramps for being a bad sport!

       Why can't people read????!  I said that the doubled and isolated three Black pawns would be worth roughly 1.5 points and not three points as when they are side by side in strong formation.  I recommend Pawn Power by Hans Kmoch; or failing to understand that you might try:  The Complete Idiot's Guide to Chess  . . . little joke there . . . but I am serious, Black's pawns are so bad that after the rook swap White has all the edge and could win, but because the pawns are on both sides expect both Kings to activate and the position to become largely static and a draw!!  Read Pawn Power and come to understand how to play endgames . . . .

you say"the 3 pawns are worth 1,5 points" but when you take off the doubled pawn then even those 2 pawns would be worth 2 points. So a pawn more can never be less than the worth of 2 pawns you genius. You should probably learn a bit more about chess to understand the material worth of pieces. Maybe this might help you: 

Queen=9 points,Rook=5 points, Bishop=3 points, Knight=3 points, pawn=1 point.

Simple mathmatics: 1 pawn+1pawn+1pawn=1 point+1point+1point=3 points. When you include the doubled pawns you could maybe say then the 3 pawns are only worth 2,5 points, but even that would be mathmatically completly wrong. A pawn is a pawn!

I think instead of discussing uncertainty principles we should observe the factual playing here.

The fact is i see a forced rook trade, a Nf5 that is hard to stop and blocks black king's fastest ways as well as threathning forks, and a white king right away ready to come into play, which seems to have a good chance to compensate for at least one pawn disadvantage.

As others have said, no way are they only worth 1.5 pawns.

The problem with them comes in creating a passer, not defence. The fact his those doubled pawns are just as good as normal pawns in protecting against the opponent creating a passed pawn.

And black's extra pawn is on the kingside so that's largely irrelevant.