Morphy number

The Morphy number is a measure of how closely a chess player is connected to Paul Morphy (1837–1884) by way of playing chess games. 
As of October 2019, there are very few known living players with Morphy number 3. Many ordinary players have a Morphy number of 6 or more.
Description.
People who played a chess game with Morphy have a Morphy number of 1. Players who did not play Morphy but played someone with a Morphy number of 1 have a Morphy number of 2. People who played someone with a Morphy number of 2 have a Morphy number of 3, et cetera.
The idea is similar to the Erdős number for mathematicians, the Bacon number for actors, and the Shusaku number, the equivalent for the board game of Go.
Origin.
Taylor Kingston states that the idea of the Morphy number may have originated in a June 2000 note by Tim Krabbé, who has Morphy number 4. Krabbé wrote "I once played an official game with Euwe, who played Tarrasch, who played Paulsen, who played Morphy."
Morphy number of famous players.
These are players who are important in making links for Morphy numbers.
Morphy number 1.
Morphy is known to have played about 100 people, but all of the known links for players with Morphy number 2 go through the following five players. A few years after the early lists of players were tabulated, it was discovered that Mortimer was Morphy's friend and he played casual games with him, so is MN1, so previous lists needed to be drastically revised to promote many players. This is because Mortimer had a very long, if not particularly successful, career, including the Ostende-B 1907 tournament. This enabled many famous younger players to gain MN2. These include Mieses, Tartakower, Znosko-Borovsky, and Bernstein, who played beyond WW2, enabling still younger players to become MN3. Some Irish players could go through the Rev. Dr George Salmon, who played in one of Morphy's blindfold chess simultaneous exhibitions.
Morphy number 2.
Everyone in this group played someone in the group above. The Australian champion Frederick Esling achieved MN2 by beating Anderssen in an offhand game and another Australian champion, Julius Leigh Jacobsen (1862–1916) achieved MN2 by beating Bird in a casual match +4-2=1, enabling many Australian players of the early 20th century to achieve MN3.
The following are some of the most important players who have achieved MN2. 
Morphy number 3.
Most of the masters in this group played several members of the previous group. This group includes some of the most important players for making connections to later generations. Botvinnik and Reshevsky played older masters such as Lasker and Janowski, had long careers, and played many younger players. Najdorf was Tartakower's pupil and they played a number of published games together, and Najdorf played blitz right into his 80s, allowing many younger players to achieve 4. Smyslov and Keres had very long careers, so much younger players achieved MN4 by playing them. Gligoric also played Tartakover, allowing many Yugoslav players to achieve 4. C.J.S. Purdy played Tartakower, enabling many Australian players to achieve 4. Fairhurst, who played Tartakover, was many times champion of Scotland, and later moved to New Zealand, so a number of players in these countries achieved 4 by playing him. 
As of October 2019, some of the living players with Morphy number 3 are Leonard Barden, Bernard Cafferty, Melvin Chernev, Borislav Ivkov, Franciscus Kuijpers, Christian Langeweg, Aleksandar Matanović, Friðrik Ólafsson, Jonathan Penrose, and Oliver Penrose.
Morphy number 4.
 many of these players are still alive; a few (such as Short) are still active.
Morphy number 5.
 many of the top [[grandmaster (chess)|grandmasters]] were thought to be in this group (along with a large number of lower-rated players). However several players initially thought to be in this group were actually MN4s, for instance based on playing Smyslov, who played Tartakower and Bernstein.
External links.
[[Category:Chess terminology]]
[[Category:Separation numbers]]