He was one of the most original of the Berlin Pleiades (the seven stars of German chess).
In 1839, Mayet defeated Jozsef Szen in a match with (+3-2=1). In 1845, he drew a match with Augustus Mongredien with (+3-3). In 1847, he defeated A. von der Goltz in a match (+14-9=1), but then lost a match with Wilhelm Hanstein (+5-12=1). In 1848, he lost a match to Daniel Harrwitz (+2-5=2). In the London 1851 chess tournament, he was knocked out in round 1 when he lost to Hugh Alexander Kennedy with two losses. In 1851, he lost a match to Adolf Anderssen in Berlin with 4 losses. In 1852, he lost a match to Frederic Deacon (2-5).
In 1853, he took 3rd place in the first unofficial Berlin Championship, behind Jean Dufresne and Max Lange. In 1853, he lost a match to Dufresne (+5-7). In 1855, he lost to Anderssen (+6-14=1). In 1856, he lost to T. Wiegelmann (2-4) in the 1856 Berlin Knockout Tournament. In 1859, he lost a match to Anderssen (+1-7). In 1865, he lost a match to Anderssen (+2-5=1). In 1866, he lost a match to Gustav Neumann (-6=1).