Born in Vrnjačka Banja to parents Jevrem Simonović and Ilonka Dobai, both of whom worked as hairdressers, young Ljubodrag grew up in Kraljevo with an older brother Vladimir. Their father Jevrem, a Montenegrin Serb born in 1911 whose mother died while giving birth to him and whose father died right after World War I, made a living as a tradesman (in addition to hairdressing he also worked as seamster and tailor) and over time developed a staunchly communist worldview. Simonović's mother Ilonka came from a mixed background, born to German mother Ana Shumetz and Hungarian father János Dobai, a left-leaning officer who participated in the ultimately unsuccessful 1919 Hungarian Revolution before fleeing over the border into the recently established Kingdom of Serbs, Croats and Slovenes to escape the White Terror of Miklós Horthy, initially settling in Subotica and eventually in Kraljevo where he worked as a machinist.
As a kid, Simonović took up chess, which he got taught at age five by his father, an avid player himself. Simonović played the game frequently, later citing it as the first arena in which his competitive nature had been displayed. He also loved playing football. As a freshman at the University of Belgrade, Duci took part in the 1968 protests in Belgrade.
He got the nickname Duci after the Hungarian word böci.
Simonović started out with KK Sloga from Kraljevo. He debuted for the Yugoslav national basketball team at age 17, going on to make 109 appearances in total, scoring 1018 points. His playing career ended, while a player-coach in Stara Pazova, due to a burst capillary in his throat.
In European championships he played 23 times, in World Championships he played 6 times with 4 appearances in the Olympic Games and 15 at the Balkan Games. All together, he has 6 gold and 2 silver medals. For Red Star Belgrade, he wore number 11 while for the national team, he wore number 5.
Simonović moved to Belgrade in 1968 at the age of 19 in order to play for KK Crvena zvezda as the latest addition to a talented squad led by the 27-year-old Vladimir Cvetković with a slew of up-and-coming youngsters such as 20-year-old small forward Dragan Kapičić and 18-year-old mercurial point guard Zoran Slavnić. Simultaneous to his duties at the club, Simonović enrolled at the University of Belgrade's Faculty of Law, attending lectures and studying for exams.
Coached by Milan Bjegojević, Zvezda, somewhat improbably, won the 1968-69 Yugoslav League title in Duci's first season at the club.
Winning the domestic title meant an opportunity to participate in the European Cup for the following 1969-70 season. Starting off well against lesser opposition in the early rounds, Zvezda eventually got into a difficult quarterfinals group, losing all three of its home-and-away ties against Alexander Gomelsky's defending European champion CSKA Moscow, Aca Nikolić's Varese, and even the seeming minnows of the group ASVEL.
On the domestic front, the club surrendered its title, finishing second to Olimpija as Simonović recorded another stellar season that recommended him for national head coach Ranko Žeravica's Yugoslav national squad at the 1970 World Championships.
Coming off the greatest success of his career, being part of the squad that won the 1970 World Championships, Simonović continued developing his game as Zvezda went through a head coaching change with Đorđe Andrijašević being brought in as replacement to the longtime head coach Bjegojević. Andrijašević wouldn't end up sticking around for long, victim of Zvezda's another indifferent season in the Yugoslav League despite winning the Yugoslav Cup.
In 1971, Simonović graduated from the University of Belgrade's Faculty of Law.
Bata Đorđević became the new head coach, infusing new energy into the team by introducing new players Goran Rakočević and Dragiša Vučinić as Zvezda began piling up wins, both in the Yugoslav League and in European Cup Winner's Cup. Simonović, who turned 23 years of age midway through the season, became the team's number one option on offense, putting up tremendous scoring numbers. Among his many stellar displays throughout the season, one stood out — playing away at Hala sportova against the eternal crosstown rivals KK Partizan he scored 59 points. Making this feat even more impressive is the fact that the three-point shot hadn't been implemented yet.
The season ended dramatically, as Zvezda lost the Cup Winners' Cup final in Thessaloniki 70-74 versus Olimpia Milano in late March 1972 before finishing the domestic league with the identical 17-5 record as KK Split (Jugoplastika), which meant playing a single-game playoff decider for the title. Zvezda won 75-50 thus claiming its second title in three years.
By the summer of 1972, the Slavnić-Simonović-Kapičić trio had finally seemingly matured and big things were expected in the upcoming season.
Despite Simonović having an incident-filled summer with the national team at the 1972 Olympics, he was initially able to put it behind him and contribute greatly to Zvezda's European Cup run. However, all was not well inside the Zvezda locker room as a simmering rift between local Belgrade-born-and-raised players who came up through the club's youth system (Slavnić and Kapičić) and those brought in from the outside (Simonović and Vučinić) had been gaining in intensity.
Cliques were being formed within the squad and things eventually boiled over on 10 January 1973 in Tel Aviv during the away contest versus Maccabi, the first game of the quarterfinals group stage. Zvezda had been leading throughout the game with Duci pouring in baskets from all positions, however, he was not satisfied with the frequency and the quality of passes he's being fed by point guard Slavnić. Slavnić in turn didn't like Simonović's attitude so he decided to stop distributing the ball to him entirely. It wasn't long before Simonović threw a fit, cursing out coach Đorđević right on the floor for not reacting to what's going on, as everything fell apart — despite Simonović scoring 38 points, Zvezda still ended up losing 113-102. Upon returning to Belgrade, Simonović got fined YUD300,000 by Zvezda for "excessive individualism" and "inappropriate behaviour". Deeply dissatisfied over what had transpired and extremely stung by the fine, right after playing a Yugoslav League game versus KK Željezničar Karlovac, Simonović announced a decision to stop playing basketball, saying he'd like to devote his time and efforts to science, having already been pursuing a master's degree in law after earning an undergraduate law degree two years earlier. Considering Simonović had just turned 24 years of age, the Yugoslav media went into overdrive, speculating on the real reasons for what it considered to be a shocking decision.
The Yugoslav national team arrived to Munich for the 1972 Summer Olympics as the reigning world champions from Ljubljana 1970 still hoping to win one of the medals though the team was quite changed. The victory over Italy 85–78 at the beginning of the tournament approved the expectations, but in the second round, the Yugoslav team was defeated by Puerto Rico by a score of 79–74.
It was proven that two players from the Puerto Rican side had used illegal doping substances prompting a protest from the Yugoslav players. Simonović however (aged 23) was ejected from the team upon continuing to protest after the Yugoslav players had been silenced. Yugoslavia eventually finished 5th in the tournament.
After his retirement from sport he has written various books, including: "Rebellion of Robots", "Professionalism or Socialism", "Olympic Deception of the ‘divine baron’ – Pierre de Coubertin." His books center around a critique of Olympism and professional sports.
He authored a piece about the mystery behind the 1987 death of German heptathlete Birgit Dressel at the age of 27.Pobuna robota (Rebellion of Robots), 1981
Sport–Kapitalizam–Destrukcija (Sport-Capitalism-Destruction), 1995
Filozofski aspekti modernog olimpizma (Philosophical Aspects of the Modern Olympism), 2001
Olimpijska podvala (Olympic Deception), 2007
Novi svet je moguć (A New World is Possible), 2007
Ustaj radniče! (Rise Up, Worker!), 2011
Poslednja revolucija (The Last Revolution), 2013
Simonović is married and has three children.
He earned his Magister degree in law and a Doctorate in philosophy.