Josh Waitzkin chessmaster mastery quiz - spatial advantage, trading bishops Based on: Josh Waitzkin Chessmaster Strategy Section 7 - the mastery quiz.
Position:
[Event &quot;From Josh Waitzkin Chessmaster Strategy Section 7 - the mastery quiz&quot;]
[Site &quot;?&quot;]
[Date &quot;????.??.??&quot;]
[Round &quot;?&quot;]
[White &quot;-&quot;]
[Black &quot;-&quot;]
[Result &quot;*&quot;]
[SetUp &quot;1&quot;]
[FEN &quot;rn1qn1kr/p2bppbp/1p1p2p1/2pP2PP/4PP2/2P1BN1B/PPNQ3K/4RR2 w - - 0 1&quot;]

White to move. I think h6, but Josh says f5. I could swear that when I did this earlier, the chess.com engine said that they were both best moves. Anyway, now it says f5 is an inaccuracy. But at least it says to do f5 after h6, assuming Black plays Bf8. (link to screenshot)

Is Josh wrong about f5? Actually Josh even explains how Black's position is bad after f5-gxh5, but gxh5 is precisely what the chess.com engine considers a best move.

For h6-Bf8-f5, the chess.com engine says that Bf8 is only a good move and that Bxh3 is best. Bxh3 costs Black 2 pawns, but I guess does relieve some of the pressure of White's spatial advantage. Is Bxh3 really the best or at least strictly better than Bf8?

I'd think maybe it would come down to preference/playing style. Or idk. I would consider Bxh3 an option if this was just 1 pawn. (Josh actually has an example earlier about giving up a pawn for the sake of relieving an outpost or spatial advantage.) But this is 2 pawns!

Edit: I actually thought of the idea that the computer is playing for time or something. By playing Bxh3, White is going to have to do some calculations about the order of moves and counting the material. Black gives up 2 pawns - 1 for position and 1 for time. Idk.
Josh says f5 ... Is Josh wrong about f5?

Yes, although black's position is terrible in any case.
If we look at the initial position and try and assess a number of things are immediately obvious:

White has a lot more space
All the pieces and all the pawns are still on the board

We can also say:

White has completed development
Black still has several pieces on the back rank and unless black can open the h file the rook on h8 is doomed to a miserable life in the near future

So, white has a very big advantage, probably close to winning.
The first two points (space advantage plus all 32 pieces still on the board) mean that it is much easier for white to move the pieces around and very difficult for black. Black's pieces get in the way of each other and there just isn't enough space in the black position for black's pieces. For black, knights are also better than bishops at the moment.
So, what can black do? Well piece exchanges would be very nice. They would create more space in black's position and make it less cramped.
Exchanging bishops would be particularly nice because, as luck would have it, the g7 bishop is occupying a square which would be great for the knight stuck on e8 and the d7 bishop is on a square which would be better for the b8 knight.
With all that in mind the pluses of h6 stand out. Bf8, the only move to not immediately lose material, firmly and further entombs the rook on h8, keeps all the pieces on the board, puts yet another piece on the back rank and moves the bishop off what is the best available diagonal for it to a dead-end square with no prospects. It becomes not much more than a &quot;tall pawn&quot;.
What about f5? That allows Be5+, either immediately, or after a zwischenzug like gxh5 or Bc8 (clearing d7 for the knight). Let's look at what would likely happen after an immediate Be5+ and evaluate the resulting position:
[fen &quot;rn1qn1kr/p2bppbp/1p1p2p1/2pP2PP/4PP2/2P1BN1B/PPNQ3K/4RR2 w - - 0 1&quot;]

1.f5 Be5+ 2.Bf4 Bxf4 3. Qxf4 Ng7 4. h6 Nh5 5. Qh4 Bb5 6. Rf2 Nd7

What you have is chalk-and-cheese. Suddenly black's pieces can breathe. Black is still much worse. The rook on h8 still has no prospects but two more pieces are off the back rank and a bishop which was going to be useless has been exchanged off.

Bxh3 costs Black 2 pawns

Nonsense! I think you are making the mistake of confusing the beginner's &quot;point count&quot; system of 1 point for a pawn, 3 points for a bishop with the real world. There is no way the black bishop on f8 is worth anything like 3 points. Similarly the white pawn on h6 is worth a lot more than 1 point.

Is Bxh3 really the best or at least strictly better than Bf8?

Again let's try looking at a line where black follows Bxh3 with the Nxg7 immediately (the line where black plays Bxf1 is also possible although that puts black one rook exchange closer to a lost endgame) to see what is really involved:
[fen &quot;rn1qn1kr/p2bppbp/1p1p2p1/2pP2PP/4PP2/2P1BN1B/PPNQ3K/4RR2 w - - 0 1&quot;]

1. h6 Bxh3 (1...Bf8) 2. hxg7 Nxg7 3. Kxh3

After 1...Bf8 white has a really obvious plan to take advantage of the weak long diagonal and the monster pawn on h6 - c4, b2, line up the bishop and queen on the diagonal, mate. Alternatively, just leave black effectively a rook down (the piece on h8 is useless) and just break through in the center and mate black that way.
Going back to &quot;beginner's point count&quot; that rook is worth a lot closer to 1 point than 5. Once you get past beginner level you have to value your pieces according to what they can do now and in the near future.
After the sequence ending 3. Kxh3 those threats have disappeared. Black has an outpost for the knight on h5. Black might entertain hopes of playing h6 to open the h file and give the rook on h8 a purpose. Granted the position is still lost but at least there are prospects of counterplay and putting up a fight.