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Sample chess game
=== Sample Game ===

 +---+---+---+---+---+---+---+---+
 | '''r''' | '''n''' | '''b''' | '''q''' | '''k''' | '''b''' | '''n''' | '''r''' | 8
 +---+---+---+---+---+---+---+---+
(contracted; show full)
 +---+---+---+---+---+---+---+---+
 | '''R''' | '''N''' | '''B''' |   | '''K''' |   |   | '''R''' | 1
 +---+---+---+---+---+---+---+---+
   a   b   c   d   e   f   g   h 

Black plays the best defense.
The white pawn is blocked from further advances, and the king has a new escape square on h7.

White's position is still overwhelming, but there is no immediate way to checkmate.

Now let us take a step deeper into chess reasoning.
White knows he is winning and wants a quick kill, but can't see how to get it.
He is annoyed that the black bishop on c8 prevents him from playing 9.Qf5+ and administering the coup de grace.
Therefore he asks himself, what if the were no black bishop on f8?

9. Bxb7

 +---+---+---+---+---+---+---+---+
 | '''r''' | '''n''' | '''b''' | '''q''' |   | '''b''' | '''n''' | '''r''' | 8
 +---+---+---+---+---+---+---+---+
 | '''p''' | '''B''' | '''p''' |   |   |   | '''p''' |   | 7
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   | '''k''' |   | 6
 +---+---+---+---+---+---+---+---+
 |   |   |   |   | '''Q''' |   |   | '''p''' | 5
 +---+---+---+---+---+---+---+---+
 |   |   |   |   | '''P''' |   |   | '''P''' | 4
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 3
 +---+---+---+---+---+---+---+---+
 | '''P''' | '''P''' | '''P''' | '''P''' |   | '''P''' | '''P''' |   | 2
 +---+---+---+---+---+---+---+---+
 | '''R''' | '''N''' | '''B''' |   | '''K''' |   |   | '''R''' | 1
 +---+---+---+---+---+---+---+---+
   a   b   c   d   e   f   g   h 
⏎

⏎
Balck's position is still precarious, but there is no immediate way for white to force checkmate.

Now let us take a step deeper into chess reasoning.
White knows black is on the run for the moment, but if he has a chance to regroup, the game is far from over.
Three pawns for the sacrificed knight is roughly material equality.

If white brings additional forces forward with 9.Nc3 or 9.d4, the obvious developing moves, black will harass the white queen with 9... Bd6.  That would force white to lose time protecting the queen.  Black would gain time to get his pieces out and get his king to safety.

White desperately wants a quick kill, but can't see how to get it.
He is annoyed that the black bishop on c8 prevents him from playing 9.Qf5+ and administering the coup de grace.
Therefore he asks himself, what if there were no black bishop on f8?
If only that annoyance were removed, I could do great things.

9. Bxb7

 +---+---+---+---+---+---+---+---+
 | '''r''' | '''n''' | '''b''' | '''q''' |   | '''b''' | '''n''' | '''r''' | 8
 +---+---+---+---+---+---+---+---+
 | '''p''' | '''B''' | '''p''' |   |   |   | '''p''' |   | 7
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   | '''k''' |   | 6
 +---+---+---+---+---+---+---+---+
 |   |   |   |   | '''Q''' |   |   | '''p''' | 5
 +---+---+---+---+---+---+---+---+
 |   |   |   |   | '''P''' |   |   | '''P''' | 4
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 3
 +---+---+---+---+---+---+---+---+
 | '''P''' | '''P''' | '''P''' | '''P''' |   | '''P''' | '''P''' |   | 2
 +---+---+---+---+---+---+---+---+
 | '''R''' | '''N''' | '''B''' |   | '''K''' |   |   | '''R''' | 1
 +---+---+---+---+---+---+---+---+
   a   b   c   d   e   f   g   h 

White finds the only winning move, but having found it, puts black in dire straits.
Black's best bet is to ignore the white bishop and harass the white queen with 9...Bd6, but then white calmly plays 10.Qa5, maintaining the threat on f5 and forcing black to sacrifice material.  One possible continuation is 9...Bd6, 10.Qa5 Nc6, 11.Bxc6 Rb8.  The checkmate has been avoided, but now white has a large material advantage (four extra pawns) and can win slowly and surely with patient developing moves like 12.Nc3.

As it happens, black does not understand the danger.  He grabs the bishop for a material advantage of his own (bishop plus knight versus four pawns) and suffers the consequences.

9... Bxb7

 +---+---+---+---+---+---+---+---+
 | '''r''' | '''n''' |   | '''q''' |   | '''b''' | '''n''' | '''r''' | 8
 +---+---+---+---+---+---+---+---+
 | '''p''' | '''b''' | '''p''' |   |   |   | '''p''' |   | 7
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   | '''k''' |   | 6
 +---+---+---+---+---+---+---+---+
 |   |   |   |   | '''Q''' |   |   | '''p''' | 5
 +---+---+---+---+---+---+---+---+
 |   |   |   |   | '''P''' |   |   | '''P''' | 4
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 3
 +---+---+---+---+---+---+---+---+
 | '''P''' | '''P''' | '''P''' | '''P''' |   | '''P''' | '''P''' |   | 2
 +---+---+---+---+---+---+---+---+
 | '''R''' | '''N''' | '''B''' |   | '''K''' |   |   | '''R''' | 1
 +---+---+---+---+---+---+---+---+
   a   b   c   d   e   f   g   h 

10. Qf5+

 +---+---+---+---+---+---+---+---+
 | '''r''' | '''n''' |   | '''q''' |   | '''b''' | '''n''' | '''r''' | 8
 +---+---+---+---+---+---+---+---+
 | '''p''' | '''b''' | '''p''' |   |   |   | '''p''' |   | 7
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   | '''k''' |   | 6
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   | '''Q''' |   | '''p''' | 5
 +---+---+---+---+---+---+---+---+
 |   |   |   |   | '''P''' |   |   | '''P''' | 4
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 3
 +---+---+---+---+---+---+---+---+
 | '''P''' | '''P''' | '''P''' | '''P''' |   | '''P''' | '''P''' |   | 2
 +---+---+---+---+---+---+---+---+
 | '''R''' | '''N''' | '''B''' |   | '''K''' |   |   | '''R''' | 1
 +---+---+---+---+---+---+---+---+
   a   b   c   d   e   f   g   h 

At last!  Black has only one legal move.

10... Kh6

 +---+---+---+---+---+---+---+---+
 | '''r''' | '''n''' |   | '''q''' |   | '''b''' | '''n''' | '''r''' | 8
 +---+---+---+---+---+---+---+---+
 | '''p''' | '''b''' | '''p''' |   |   |   | '''p''' |   | 7
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   | '''k''' | 6
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   | '''Q''' |   | '''p''' | 5
 +---+---+---+---+---+---+---+---+
 |   |   |   |   | '''P''' |   |   | '''P''' | 4
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 3
 +---+---+---+---+---+---+---+---+
 | '''P''' | '''P''' | '''P''' | '''P''' |   | '''P''' | '''P''' |   | 2
 +---+---+---+---+---+---+---+---+
 | '''R''' | '''N''' | '''B''' |   | '''K''' |   |   | '''R''' | 1
 +---+---+---+---+---+---+---+---+
   a   b   c   d   e   f   g   h 

11. d4+

 +---+---+---+---+---+---+---+---+
 | '''r''' | '''n''' |   | '''q''' |   | '''b''' | '''n''' | '''r''' | 8
 +---+---+---+---+---+---+---+---+
 | '''p''' | '''b''' | '''p''' |   |   |   | '''p''' |   | 7
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   | '''k''' | 6
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   | '''Q''' |   | '''p''' | 5
 +---+---+---+---+---+---+---+---+
 |   |   |   | '''P''' | '''P''' |   |   | '''P''' | 4
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 3
 +---+---+---+---+---+---+---+---+
 | '''P''' | '''P''' | '''P''' |   |   | '''P''' | '''P''' |   | 2
 +---+---+---+---+---+---+---+---+
 | '''R''' | '''N''' | '''B''' |   | '''K''' |   |   | '''R''' | 1
 +---+---+---+---+---+---+---+---+
   a   b   c   d   e   f   g   h 

White continues the attack with a special kind of check, the ''discovered check''.
He moves a pawn, but it isn't the pawn which gives check.
It is the white bishop, attacking from its home square, which delivers the blow.

Note that the black king has no legal moves, and the white bishop is safe from capture, so interposition is the only option.

11... g5

 +---+---+---+---+---+---+---+---+
 | '''r''' | '''n''' |   | '''q''' |   | '''b''' | '''n''' | '''r''' | 8
 +---+---+---+---+---+---+---+---+
 | '''p''' | '''b''' | '''p''' |   |   |   |   |   | 7
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   | '''k''' | 6
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   | '''Q''' | '''p''' | '''p''' | 5
 +---+---+---+---+---+---+---+---+
 |   |   |   | '''P''' | '''P''' |   |   | '''P''' | 4
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 3
 +---+---+---+---+---+---+---+---+
 | '''P''' | '''P''' | '''P''' |   |   | '''P''' | '''P''' |   | 2
 +---+---+---+---+---+---+---+---+
 | '''R''' | '''N''' | '''B''' |   | '''K''' |   |   | '''R''' | 1
 +---+---+---+---+---+---+---+---+
   a   b   c   d   e   f   g   h 

At this point white has an easy win with 12.Bxg5+ Kg7 13.BxQ.
The material advantage of a queen and five pawns for a bishop and a knight is overwhelming.
However, weak players have been known to play on in completely hopeless positions rather than resign.
In order to forestall a long, boring mop-up operation, white looks for a direct kill.

12. Qf7

 +---+---+---+---+---+---+---+---+
 | '''r''' | '''n''' |   | '''q''' |   | '''b''' | '''n''' | '''r''' | 8
 +---+---+---+---+---+---+---+---+
 | '''p''' | '''b''' | '''p''' |   |   | '''Q''' |   |   | 7
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   | '''k''' | 6
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   | '''p''' | '''p''' | 5
 +---+---+---+---+---+---+---+---+
 |   |   |   | '''P''' | '''P''' |   |   | '''P''' | 4
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 3
 +---+---+---+---+---+---+---+---+
 | '''P''' | '''P''' | '''P''' |   |   | '''P''' | '''P''' |   | 2
 +---+---+---+---+---+---+---+---+
 | '''R''' | '''N''' | '''B''' |   | '''K''' |   |   | '''R''' | 1
 +---+---+---+---+---+---+---+---+
   a   b   c   d   e   f   g   h 

Truly a masterful move!
White doesn't even call check, but mate is now inevitable.

12... Qe7

 +---+---+---+---+---+---+---+---+
 | '''r''' | '''n''' |   |   |   | '''b''' | '''n''' | '''r''' | 8
 +---+---+---+---+---+---+---+---+
 | '''p''' | '''b''' | '''p''' |   | '''q''' | '''Q''' |   |   | 7
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   | '''k''' | 6
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   | '''p''' | '''p''' | 5
 +---+---+---+---+---+---+---+---+
 |   |   |   | '''P''' | '''P''' |   |   | '''P''' | 4
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 3
 +---+---+---+---+---+---+---+---+
 | '''P''' | '''P''' | '''P''' |   |   | '''P''' | '''P''' |   | 2
 +---+---+---+---+---+---+---+---+
 | '''R''' | '''N''' | '''B''' |   | '''K''' |   |   | '''R''' | 1
 +---+---+---+---+---+---+---+---+
   a   b   c   d   e   f   g   h 

Nothing can save black short of white forgetting his plan, but there is some logic to the black move.
Where can the white queen go?
Any black piece she could take is protected.
If white trades queens, then the attack is over, and black is winning.
Finally, if the white queen simply retreats, black will strike back with a check of his own: 13...Qxe4+!

But white must have foreseen this possibility, or he would never have played 12.Qf7 instead of 12. Bxg5.

13. hg+

 +---+---+---+---+---+---+---+---+
 | '''r''' | '''n''' |   |   |   | '''b''' | '''n''' | '''r''' | 8
 +---+---+---+---+---+---+---+---+
 | '''p''' | '''b''' | '''p''' |   | '''q''' | '''Q''' |   |   | 7
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   | '''k''' | 6
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   | '''P''' | '''p''' | 5
 +---+---+---+---+---+---+---+---+
 |   |   |   | '''P''' | '''P''' |   |   |   | 4
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 3
 +---+---+---+---+---+---+---+---+
 | '''P''' | '''P''' | '''P''' |   |   | '''P''' | '''P''' |   | 2
 +---+---+---+---+---+---+---+---+
 | '''R''' | '''N''' | '''B''' |   | '''K''' |   |   | '''R''' | 1
 +---+---+---+---+---+---+---+---+
   a   b   c   d   e   f   g   h 

Black can't get out of this check by interpostion or by moving the king away.
All retreat is cut off by the well-placed white queen.
The only option is to capture the checking piece.

13... Qxg5

 +---+---+---+---+---+---+---+---+
 | '''r''' | '''n''' |   |   |   | '''b''' | '''n''' | '''r''' | 8
 +---+---+---+---+---+---+---+---+
 | '''p''' | '''b''' | '''p''' |   |   | '''Q''' |   |   | 7
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   | '''k''' | 6
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   | '''q''' | '''p''' | 5
 +---+---+---+---+---+---+---+---+
 |   |   |   | '''P''' | '''P''' |   |   |   | 4
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 3
 +---+---+---+---+---+---+---+---+
 | '''P''' | '''P''' | '''P''' |   |   | '''P''' | '''P''' |   | 2
 +---+---+---+---+---+---+---+---+
 | '''R''' | '''N''' | '''B''' |   | '''K''' |   |   | '''R''' | 1
 +---+---+---+---+---+---+---+---+
   a   b   c   d   e   f   g   h 

14. Rxh5++

 +---+---+---+---+---+---+---+---+
 | '''r''' | '''n''' |   |   |   | '''b''' | '''n''' | '''r''' | 8
 +---+---+---+---+---+---+---+---+
 | '''p''' | '''b''' | '''p''' |   |   | '''Q''' |   |   | 7
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   | '''k''' | 6
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   | '''q''' | '''R''' | 5
 +---+---+---+---+---+---+---+---+
 |   |   |   | '''P''' | '''P''' |   |   |   | 4
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 3
 +---+---+---+---+---+---+---+---+
 | '''P''' | '''P''' | '''P''' |   |   | '''P''' | '''P''' |   | 2
 +---+---+---+---+---+---+---+---+
 | '''R''' | '''N''' | '''B''' |   | '''K''' |   |   |   | 1
 +---+---+---+---+---+---+---+---+
   a   b   c   d   e   f   g   h 

Checkmate.  Black can't interpose anything, because the rook is giving check from an adjacent square.
The black king can't move away, because the white queen covers all retreat squares.
The black king can't capture the rook, because then he would be in check from the white queen.
Finally, the black queen can't capture the white rook because she is ''pinned''.  If she moved away, the white bishop on c1 would be giving check to the black king.

Notice that, although material considerations are very important in chess thinking, you don't win by having the most pieces.
You win by delivering checkmate!
White was behind in material the entire game, including in the final position, but came away with the victory nonetheless.