1.P-K4 P-K4 is how an English chess book from 1960 opens a game, and it means 1.e4 e5. P is the pawn, K4 is the fourth square of the king’s file, and the reason both moves are written identically is the whole idea behind the system: each player counts from their own end of the board.
8 
7 
2 
a 
b 
c 
d 
e f g h 1 Every square has two names
Files are named after the piece that starts on them, split into a queen’s half and a king’s half: QR, QN, QB, Q, K, KB, KN, KR, which in algebraic are a, b, c, d, e, f, g and h.
Ranks are counted from the writer’s own back rank. White’s K4 is e4; Black’s K4 is e5. To convert a Black rank, subtract it from nine, so Black’s QB3 sits on the c-file at rank 9 minus 3, which is c6.
A move is the piece, a hyphen and the destination. N-KB3 is Nf3. B-QB4 is Bc4. Q-R5 is Qh5, and it does not need the K in front of the R because a queen on d1 cannot reach QR5 anyway. Names get shortened whenever only one reading is possible, which is exactly why old books are so slow to read at first.
Captures name the victim
In algebraic you write the square: Bxc6. In descriptive you write what you took: BxN. If two knights could be taken, you say which, BxN/QB3 or BxKN. Pawn captures are the worst of it, since PxP can be perfectly clear or hopelessly vague depending on the position.
Check is ch, sometimes +. Mate is written out as the word. Castling is O-O and O-O-O, unchanged to this day. Promotion is P-Q8(Q), and two pieces that could reach the same square are separated by the departure square in brackets, N(B3)-Q2.
Here is Scholar’s mate in both systems, which is the quickest way to feel the difference:
1.P-K4 P-K4 1.e4 e5
2.B-B4 N-QB3 2.Bc4 Nc6
3.Q-R5 N-B3 3.Qh5 Nf6
4.QxBP mate 4.Qxf7#Look at that last move. QxP would not do, because the queen on KR5 attacks three black pawns at once, so you have to say which one, and it is the bishop’s pawn. In algebraic the square does that work by itself, with no thought required.
Why you still run into it
English-language chess publishing ran on descriptive until the late 1970s, so anything second-hand and older than that is written this way, including the first edition of Bobby Fischer’s My 60 Memorable Games. German and Russian books had been algebraic for decades, which is a large part of why the English-speaking world eventually gave in.
If you are working through an old book, do not translate move by move in your head. Set the position up, play the moves in front of you, and after twenty minutes the file names stop needing conversion. It is a reading skill and not a writing one: nobody has needed to write P-K4 in forty years, and everything modern, including every symbol on this site and every puzzle in the app, is algebraic. If you want old material that repays the decoding, the problem and study literature is where most of the buried treasure is.