The name is a Spanish horse-racing phrase meaning "by a head", which refers to a horse winning a race by the length of one head. The lyrics speak of a compulsive horse-track gambler who compares his addiction for horses with his attraction to women.

Alfredo Le Pera was an Argentine, born in Brazil, son of Italian immigrants. Le Pera and Gardel died in an airplane crash in Medellín, on Monday, June 24, 1935.

The starting phrase in the B section may be inspired by Mozart's Rondo for violin and orchestra in C major, K. 373.

The song was originally composed in A major. It was thereafter adapted to the violin and the piano sometimes in A major, sometimes in G major.

The tango has since been performed by numerous tango orchestras. Scenes featuring this song can be found in the films True Lies, Schindler's list, Scent of a Woman, and Easy Virtue. During a state visit, U.S. President Barack Obama and First Lady Michelle Obama danced to the tune with and José Lugones, respectively, in Buenos Aires, Argentina on March 23, 2016.

John Williams arranged a version of the piece that appears on the album "Cinema Serenade" with the violin solo performed by Itzhak Perlman

Por una cabeza
de un noble potrillo
que justo en la raya
afloja al llegar,
y que al regresar
parece decir:
No olvidés, hermano,
vos sabés, no hay que jugar.
Por una cabeza,
metejón de un día
de aquella coqueta
y risueña mujer,
que al jurar sonriendo
el amor que está mintiendo,
quema en una hoguera
todo mi querer.

...
Wikipedia