After steadily losing his milk money for a long time, Denker discovered former world chess champion Emanuel Lasker's book Common Sense in Chess in the school library, studied the book, and soon "the nickels came pouring back with interest".

He first gained attention in chess by winning the New York City individual interscholastic championship in 1929 at age 15.

In the next decade he established himself as a leading rival to Samuel Reshevsky, Reuben Fine, and Isaac Kashdan as the strongest U.S. chess player.

His first really strong international event was Syracuse, New York 1934, where Reshevsky won convincingly, with Denker placing just behind him.

Denker successfully defended his U.S. title in a 1946 challenge match against Herman Steiner, winning 6–4 at Los Angeles.

During World War II Denker played exhibitions at army bases and aboard aircraft carriers.

[1] Also in 1946, he played at the very strong Groningen tournament, the first major event following World War II, scoring 9.5 out of 19 and securing draws against Botvinnik and Smyslov, and losing after achieving a winning position against Max Euwe.

His peak results were scored from 1940 to 1947, in U.S. Championships and on his trips to Europe for tournaments at London, Hastings and Groningen.

Chess Trust – the driving force behind the prestigious Denker Tournament of High School Champions (named in his honor).

He wrote many chess articles and in 1995 the book: The Bobby Fischer I Knew and Other Stories (co-authored by Larry Parr; Hypermodern Press).

[1] A graduate of New York University, he married the former Nina Simmons in 1936, a marriage lasting 57 years until her death in 1993.