During the 1950's and 1960s Minev was one of the strongest players in Bulgaria and competed in the National Championship 22 times, winning it in 1953, 1965, and 1966. He played for the Bulgarian Olympiad team six times: 1954, 1956, 1958, 1960, 1962, and 1966. His best international results were: third at Varna in 1960, second at Warsaw in 1961, a tie for first at Sombor in 1966 and second at Albena in 1975. He was awarded the IM title in 1960,
Minev learned to play chess at about the age of eight, but in his youth his interest was soccer and one day as a result of playing in the cold and rain, he fell ill with a fever and was confined to bed for three days. His mother was upset that he gotten sick playing soccer in inclement weather and she refused to let him play any more. Instead, she bought him a chess set and he began playing at the local club.
At the age of sixteen or seventeen a Russian emigre named Kamen Piskov took Minev under his wing and began training him. By 1947 Minev was good enough to qualify for the Bulgarian championship though he finished in last place; Piskov won the championship.
In an interview Minev was asked what chess books he read during his development. There weren't any chess books available to him except Tarrasch's Three Hundred Games in the library which he borrowed and copied about half of the games from the book. That was right after the War and no literature was available, but he eventually got a hold of Tartakower's Five Hundred Games which he found useful.
While many strong Bulgarian players were professional players sponsored by the government, Minev turned down an offer to become a professional, choosing instead to pursue a medical career. After obtaining his medical degree Minev founded the Bulgarian national toxicology laboratory in Sofia in 1965. In 1972 he was working as the chief of the lab when he was offered the position of deputy editor of the Bulgarian chess magazine. The salary was even better than he was making in the lab, plus he would have time for chess, so he took the job. After five years he was not promoted to chief editor as expected because he was not a member of the Communist party. At about that time Minev began contributing to GM Alexander Matanovic's Chess Informant. Through Matanovic he learned that the Greek chess team was looking for a coach and in 1979 he accepted to coach's position.
In 1982 Minev and his wife, a chemical engineer, were living in Athens when their apartment in Sofia was confiscated by Communist officials so they made the decision to leave Bulgaria permanently. They considered moving to either Austria, Australia or the United States. They chose the US because his wife had friends living in Seattle, Washington.
After arriving in Seattle, Minev edited Northwest Chess and began his association with GM Yasser Seirawan, contributing a column on tactics to Seirawan's Inside Chess magazine. For an interesting story about Minev's impact on the life of Washington State Attorney General Bob Ferguson see this article at Washington State University. Ferguson is a national master whose peak rating was 2227.
In the following game from the chess Olympiad played at Amsterdam in 1954 Minev outplays the great Hungarian master Laszlo Sazbo in a tactical melee.
The Bulgarian team (Minev, Neikirch, Milev, Tsvetkov, Bobotsov, Bobekov) made it to the finals, but only managed to finish in tenth place (out of 12). The Hungarian team (Szabó, Kluger, Barcza, Sándor, Gereben) finished sixth. The event was won by the Soviet Union. Paul Keres, playing fourth board, scored an amazing 96.4 percent. He drew his first game and won the rest. Argentina and Yugoslavia finished second and third. The United States did not send a team; the USCF didn't have the money.