He was best known as the chief arbiter at several World Chess Championship matches, in particular the 1972 encounter between Bobby Fischer and Boris Spassky at Reykjavík.

In September 1948, he tied for fourth place at the full German Chess Championship (12th GER-ch) in Essen.

In October 1955, he was second behind Klaus Darga in Hoechst (third FRG-ch), having won a qualifying event in Nuremberg the same year.

In 1957, he held the fourth place in Dublin; a zonal qualifier tournament won by Luděk Pachman.

In 1968 in his home town of Bamberg,[3] he tied for second place with Tigran Petrosian who was the world champion at the time, behind Paul Keres, an outcome described by the Oxford Companion to Chess as "Schmid's greatest playing achievement".

In 1980, he won the fifth edition of the BBC's The Master Game series, ahead of Viktor Korchnoi and Vlastimil Hort.

[4] Representing his national team, he also competed for the Clare Benedict Cup on twelve occasions.

Among the many rare books he owned was one of only ten copies that have survived of the first-ever printed chess manual Repetición d'Amores y Arte de Ajedrez, published in Salamanca in 1497.