Josh Waitzkin chessmaster mastery quiz - order of check vs trade in bishop and knight endgame [closed]

Question

Update: The computer aspect of this can be answered with showing more lines such as in the lichess engine where Bxh3 is strongly preferable to a5+.

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Note: See this meta post. In re the answer of Brian Towers♦, not sure if the following is relevant, but: I'm not a n00b. I'm just a bad player. Haven't played in awhile, so I'm just reviewing/revising the stuff. In fact, I think it's my non-n00bish ness that enables me to question Josh Waitzkin's claims. As it turns out, some of my answers are better or equal to Josh's. See here and here. I'm not saying I deserve praise for the effort of thinking, looking it up and even typing up the results of the engine here. I just really don't think I should've gotten unsolicited advice about using an engine. Again, see this meta post.

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Taken from: Josh Waitzkin Chessmaster Strategy Section 7 - the mastery quiz.

Position: Black to move. (See here on chess.com)

[Event ""]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White " "]
[Black " "]
[Result "*"]
[SetUp "1"]
[FEN "2b5/p5n1/1pBk3p/1P6/1K3p2/5P1N/6P1/8 b - - 0 1"]

Here's what happened:

1. Josh says trade bishop for knight and then do a5 check.

2. My answer is to do a5 check, but Josh says it is 'not quite right' to do a5 check 1st.

3. I checked this on the chess.com engine, which says both my answer and Josh's are 'best' moves (but technically the evaluation is slightly higher for Josh's answer).

Question 1: Is there a difference if I do check before the trade?

Question 2: Josh says a5 check is wrong ('not quite right' or something). So, Josh is wrong to say a5 check is wrong?

Answer 1

OK, here the long version by request.

Blacks options are 1...a5+ 2.Kc4 Bxh3 3.gxh3 Ne6 or 1...Bxh3 2.gxh3 a5+ 3.Kc4 Ne6 (both followed by Ke5 to restrict the wK), which is a simple transposion.

Let us assess the position first: Near hopeless for White. He has the bad bishop and nothing to attack. Trading it off is immediately lost since Black has a protected passer, the whole point of a5+. The position is not completely hopeless yet, as Black must demonstrate some technique (see below), but enough that I resign against myself.

Thus maybe it's time for desperate options. And they exist: 1...a5+ 2.bxa6?!? Kxc6 3.Nxf4, followed by the attempt to distract Black with the f and g pawn, give the Knight either against the h or b and win or trade the other, and let Black demonstrate he can mate with B and N. (Even GMs have failed this, a certain one comes to mind who got the much deserved schadenfreude.)

Of course this attempt would be hopeless against me either, but it simply is nonexistent if you first play Bxh3. A mathematician would tell you that you should always force - an additional option by the opponent per definition can't improve the result of a variant. (A pragmatist says it's OK if the variant is even more lost than the alternatives.)

But in this case I'd prefer Bxh3 because I have to think less. A convincing plan: Ng5. The wB must go to g4. Or White pushes the Ph3 to h5, in which case Ng7 forces him to g4 or g6 anyway. In both cases Nf5 followed by Nd6+. Poor Pb5. The wK must retract to a4 or d3, in the latter case K-d5-c5, Ng5 again, and now the a-pawn can run.

As you see, White can do zilch to attack the bP even with the king. Contrast it with all the details necessary for the other variant. Thus Bxh3 first saves you much energy, even if objectively it makes no difference.

Answer 2

Josh says trade bishop for knight and then do a5 check. Is there a difference if I do check before the trade?

I think you answer your own question:

chess.com engine says both check and trade are 'best' moves

And in this case the engine is right. To understand why you need to understand the concept of a forcing move.

A check isn't just a forcing move it is absolutely forcing. If your queen is threatened or captured that is also forcing but you can ignore it if you have a check or a mate elsewhere on the board.

If you have a choice of two forcing moves, as here, then in choosing between them you just have to check whether any possible responses to one also negate the other.

Here, in reply to a5+ white can either take the pawn and lose the bishop or move the king. Moving the king doesn't stop BxN so playing a5+ first still allows playing BxN second.

If black plays BxN first then white has no useful zwischenzug. If white doesn't retake then white is just a piece down.

It's probably worth adding a couple of words on using the engine. If your main goal in playing and studying chess is entertainment then use the engine whenever you want, whenever you feel it will enhance your entertainment and enjoyment.

If, however, your main goal is to improve your chess then switching on the engine should always be the last thing you do, never the first. The point being that you will experience very little improvement unless you exercise your brain and if you rely exclusively on the engine and other people's brains then your brain is not going to get any exercise and your improvement is going to be held back.

You should always engage your brain first and struggle and try and solve the problem on your own. Once you've done that then, particularly with complex variations where you might have missed something, it can be a good idea to switch on the engine and double check. For trivial exercise, though, you should resist the temptation else the engine may become a crutch instead of a useful tool.