Frankly, you overlooked a major detail...Nf6+ in reply is mate. It is important to notice your "opponent's" moves too.
[FEN "r2qk2r/pp1nnp1N/4p1pQ/3pP3/4b1PP/P1B5/1PP1B3/R3KR2 b Qq - 0 1"]
1... Nf8 $4 (1... Ng8! 2. Qg7 (2. Nf6+ Qxf6 $1) 2... Qxh4+ 3. Kd2 Qxh7) 2. Nf6#
This is a familiar tactic I often get to use myself in another opening line. If black plays 1... Rf8, then comes 2. Bc7! Qe8 3. Nd6 Bxd6 4. Bxd6 and black loses the exchange anyway.
[Title "White to move"]
[FEN "r1bqr1k1/pp1nbpp1/4pn1p/2pp4/2PP1B2/P1NBPN2/1P3PPP/R2Q1RK1 w - - 0 1"]
1. Nb5 Rf8 2. Bc7! Qe8 3. Nd6 Bxd6 4. Bxd6
Chess is about patterns. Since ...
The problem is that 5. Qxh5 isn't check, so Black has time for some back rank tricks (instead of capturing the rook on f6):
[FEN "r1r4k/1p5R/3b4/4q3/B3P1Q1/1n1P3P/6P1/5R1K b - - 0 1"]
1... Kxh7 2. Rf7+ Kh6 3. Qh4+ Qh5 4. Rf6+ (4. Rh7+ Kxh7 5. Qxh5+) Kg7 5. Qxh5 Rc1+ 6. Qd1 Rxd1+ 7. Rf1 Rxf1#
If black plays QxR then white plays Qc3+ with mate to follow. Black's Qg7 stops the mate. With the black queen on b2 white cannot play Qc3. The Re2 move is to divert the black queen
[FEN "5r1k/1pQ4p/3nB1p1/3P4/5p2/1P5P/rq5P/4R1RK w - - 0 1"]
1. Re2 Qxe2 2. Qc3+ Qe5 3. Qxe5+ Rf6 4. Qxf6#
Does it make most sense to just start playing with setting up all the
pieces, or are there smaller "games" that one can/should start with?
It doesn't really matter the age of the person learning to play, there is no point in starting with a full set. There is just far too much to take in and make sense of. The first thing to do is to teach them how to win!...
Assume the board is in it's usual position (the bottom row is the first row) then this is the solution:
[FEN "1B6/8/1k6/R7/1n6/2K5/r6p/q1r1n3 - - - 0 1"]
and Black's last move was b2xc1R++.
I could write an explanation here about I came to this result, but it would essentially be copying @Maxwell's answer. I didn't use it, though.
I tend to disagree with the other answers that suggest starting with just a few pieces.
Kids absorb so much, so quickly. When my daughter was 4, she used to just watch me so she got some familiarity with the shapes of the pieces, but there was no teaching at this time. When she was 5, I taught her the names of the pieces, and then how they all moved. I did ...
Your second basic position allows for 4 more variants beyond those you already gave, indicated by the following diagram:
[FEN "1q6/1q6/1q6/1q6/Q7/K7/8/1k6 w - - 0 1"]
That brings the tally for "basic positions" to 25. Whether that addition makes the list exhaustive or not I'm not completely sure (though I think it does).
In any case, whatever the number ...
Material trumps positional factors, unless the positional factors are extremely pronounced.
The advantage of the bishop pair is often estimated at half a pawn - enough to pressure the opponent, but not always force a win. Rook vs. knight is an advantage of roughly two pawns - clearly winning - so you're gaining a lot in terms of material.
You should cash ...
I'm an FM, and my calculation process would be as follows:
1) See that after 2.Rxg4 Qxh6 2.Rg8 Bf8, I'm clearly winning and White has no follow up.
2) Look at White's king moves to get out of check. Immediately Kd1, Kd2, Kd3 can be discarded since they just let me play ...Rd8+ for free. Also, Kf1/Kf2 lead to the same thing after I play 2...Qf3+. So I'd ...
There is a lot more to this, and this is really not a great tactics problem as much as it is a continuing the attack problem. The difference is that with a tactic problem, you can see the result all the way to the end. Other positions, you have just a feel for it, and you know that you are probably winning, but you have to play what you can calculate, you ...
Moving the king once like that is a priming move in order for Black to be properly aligned at a crucial point in a few moves.
Without the priming move this happens which allows White to win
8/7p/1pBP2pk/pP6/K6P/6P1/1rp5/4R3 b - - 1 49
1... Rb1 2. d7 Rxe1 3. d8=Q c1=Q 4. Qf8 Kh5 5. Bf3++
So it is desirable to get a check in when promoting in order to win ...
I'm going to assume you meant ...Qc7 instead of ...Qc6, since the latter move blunders the queen.
After 1...gxf6 2.Qg4+, Black has three moves:
1) 2...Kf8 loses the queen to 3.Nd7+.
2) 2...Kh7 leads to mate after 3.Bd3+ f5 4.Bxf5+ exf5 5.Qxf5+ Kh8 (5...Kg7 6.Qxf7+
Kh8 7.Ng6#) 6.Qf6+ Kg8 7.Qxf7+ Kh8 8.Ng6#.
3) 2...Kh8 is Black's best move. After 3.Nxf7+ ...
It is quite pointless analyzing moves in lost positions.
Here in either line white will lose a bishop for a pawn.
A queen threat is just that, a threat. Why are you so much afraid of it? The game could continue
In the other line you'd have
Both are very lost positions.
Why the computer picks the first over ...
Yes indeed, n corresponds to king, as we need two kings of a different color to have a legal chess position.
Also, as you give, h = pawn, as otherwise we would have a pawn on the first or last rank, which would be illegal.
It cannot be a queen, as both kings would be in check.
It cannot be a knight, as the "i" on a2 would give check. There is ...
Depth 19 refers to 19 plies, not 19 moves (which would be 2 plies each). So it's reasonable that Stockfish would only find the mate shortly after depth 19, since 10.Qh8# is the 19th ply from the starting position you posted.
I've done this puzzle today too! It's Chess.com's puzzle of the day =)
I have analysed it with Houdini 3 Pro. Here is what it says after 1.Bxg7 :
1...Kxg7 : +5.07
1...Rf7 : +5.43
1...Rfe8 : +5.52
After 1... Rfe8 your move 2. Bxc6?? is a blunder and lose a lot of White's advantage (White is still probably winning but not by much). Houdini evaluates it as ...
A Queen cannot be captured when static by an attacking King.
A Queen cannot capture a piece more valuable than itself.
A Queen cannot move to create a discovered check.
A Queen cannot sacrifice itself for a higher valued piece.
A Queen cannot initiate a double check.
A SMALL NOTE ABOUT DESCRIPTIVE NOTATION:
Both players calculate coordinate from their side of the board towards the opponents. In algebraic notation both sides calculate coordinate from White's side toward the Black.
Therefore, in algebraic notation Queen's gambit starts as 1.d4 d5, but in descriptive as 1.P-Q4 P-Q4 ( not as 1.P-Q4 P-Q5 ).
CONSTRUCTION OF ...
It is just anecdotal, and correlation is not the same as causation, but a few years ago I started using the Mnemosyne spaced repetition program to memorize
Opening lines (a few thousand cards here alone)
Yusupov, Build Up Your Chess et al
Hellsten, Mastering Chess Strategy
Ivashchenko, Manual of Chess Combinations
Rosen, Chess Endgame ...
I did some chess training with Anki and it is certainly a viable way to do it. Though I think I prefer to actually play out the solution on a (virtual) board.
After three passes I am usually able to solve the puzzles instantly, so 7 passes seems to be quite excessive.
I'm not so sure you really have to memorise concrete positions. After ...
Black will trap the queen on the next move, either with Bd6 or b6. For example:
[FEN "r3q3/1pb1rbk1/2pn1p1p/p1Qp1Bp1/3P4/4P1NP/PP3PPB/3RR1K1 b - - 0 1"]
1... Nc4 2. b3 Bd6 3. bxc4 Bxc5 4. dxc5 dxc4
and with a queen and a (passed) pawn for two minor pieces, Black will have no problems to win this game.
Because after Nf6, e5 is a double attack on the d6 bishop and the f6 knight.
The puzzle aside, given that black's dropping the piece anyway, may as well go for something practical, like Nxg3, hxg3, Bxg3+... and take 2 pawns for the piece, with some positional compensation as the king will be misplaced, but objectively white should of course be easily ...
After 20 ... gxf6 21 Ne4 black is in serious trouble. The threat is 22 Nxf6+ followed by 23 Qh7 mate, and in avoiding this she will have to make serious concessions. An example and not unreasonable line:
[FEN "r4rk1/2p2pp1/pqp2R1p/8/8/P1N5/1PQ3PP/5R1K b - - 0 1"]
It is the best move because it wins the knight on h4.
Black has only two squares for its queen after 1.Re4:
2....Qf3 3. Rxh4 winst the knight
2....Qg5 3. Rg4 pins and wins the queen
Note that 1. Re4 is not the only move to save the rook. White could also play Nh5 attacking the queen first and if the queen moves save the rook (e.g. via Rg3).