He was one of the best players in the world during the early part of the 20th century[2] and in 1950 was among the inaugural recipients of the title International Grandmaster from FIDE.

He learned chess around the age of ten and made rapid progress while studying Oriental Trade in Budapest.

In 1910 he moved to Cologne and from there, travelled and toured extensively, mainly in the Americas, playing matches against local champions and simultaneous blindfold chess.

Kostic played more formal matches against Frank Marshall, Jackson Showalter, and Paul Leonhardt, and won them all.

At Bled 1931, he finished in tenth place, but nevertheless outscored fellow chessmasters Maróczy, Colle and Pirc.

From 1923 to 1926, Kostic travelled to Australasia, the Far East, Africa, India, and Siberia - places that were barely represented on the chess map of the time.