While reading about Paul Morphy's games I have come across several instances of phrases like "playing his fellow townsmen at odds of Knight or Rook" or "he extended his offer of Pawn and move to any member of the club" or "Morphy extended the challenge at Pawn and move to him also". It sounds like some sort of handicap arrangement. Can you tell me what these phrases mean and if anything like this is done these days?
What is being talked about are called Odds Games, which are indeed handicaps.
Here’s a quote from chesvariants.com that gives the right idea.
“During the 18th & 19th centuries, it was common to give odds in chess games, which means the practice of giving some advantage to the player with lesser skill. Odds giving can also be an interesting way to play with a computer program whose skill level differs from your own. You can also play the games in pairs, with the winner being the player who checkmates in fewer moves.”
It is not a common practice these days.
The phrase "playing his fellow townsmen at odds of Knight or Rook" meant that Morphy gave up a rook or a knight in the starting position. As an example, here is a well known game.
[Title "Paul Morphy-Alonzo Morphy, New Orleans, 1850"] [FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/1NBQKBNR w Kkq - 0 1"] 1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. Ng5 d5 5. exd5 Nxd5 6. Nxf7 Kxf7 7. Qf3+ Ke6 8. Nc3 Nd4 9. Bxd5+ Kd6 10. Qf7 Be6 11. Bxe6 Nxe6 12. Ne4+ Kd5 13. c4+ Kxe4 14.Qxe6 Qd4 15. Qg4+ Kd3 16. Qe2+ Kc2 17. d3+ Kxc1 18. O-O#
The other phrase “or Morphy extended the challenge at Pawn and move to him also" means that the stronger player was Black and had no f7 pawn.
Here’s an example game from this collection of odds games, although it’s “a pawn and two moves” (same is above, but White already has been given a move).
[Title "Charles Maurian-Paul Morphy, New Orleans, 1854"] [FEN "1nbqkbnr/ppppp1pp/8/8/4P3/8/PPPP1PPP/RNBQKBNR w KQk - 0 1"] 1.d4 e6 2.c4 Nc6 3.d5 Ne5 4.f4 Ng6 5.Be3 Bb4+ 6.Nc3 e5 7.Qh5 Nf6 8.Qg5 Be7 9.f5 Nxd5 10.Qh5 Nxe3 11.Kf2 O-O 12.Kxe3 Bg5+ 13.Kf3 Nf4 14.Qg4 h5 15.Qg3 Bh4