Balinas was considered the strongest Asian player during the 1960s and 1970s, before the emergence of compatriot Eugenio Torre.
Balinas won international chess tournaments in Hong Kong, Singapore, Manila, and Odessa, USSR during the period.
At the 1966 17th Chess Olympiad in Havana, Cuba, Balinas scored 15½ points out of 20 games (.775) and was awarded the individual silver medal award, behind gold medalist, former world champion Mikhail Tal, who scored 11 points out of 13 games (.846).
In the 1967 Meralco "Beat Bobby Fischer" match series in Manila, of the top 10 Filipino players, Balinas was the only then Philippine national master to hold the future world champion to a draw: R. C. Balinas – R. J. Fischer, Manila 1967.
In 1975, then-IM Balinas achieved a 5-5 score at the Manila Marlboro Classic International Chess Tournament, one-half point short of the grandmaster norm, tying with Gligoric for 6th-7th place.
Balinas defeated world championship candidates Lev Polugaevsky of USSR and Bent Larsen of Denmark, as well as the Czech-American grandmaster Lubomir Kavalek.
Balinas achieved his greatest victory at the 1976 Odessa International Tournament, winning with a 10–4 score.
1.d4 Nf6 2.c4 c5 3.d5 e6 4.Nc3 exd5 5.cxd5 d6 6.e4 g6 7.Nf3 Bg7 8.Be2 0-0 9.0-0 Nbd7 10.a4 Qe7 11.Nd2 a6 12.f4 Rb8 13.Kh1 b6 14.Nc4 Nxe4 15.Nxe4 Qxe4 16.Nxd6 Qe7 17.Nxc8 Rbxc8 18.Bxa6 Rcd8 19.Qb3 Nf6 20.Qxb6 Rxd5 21.Qb3 Rd4 22.a5 Ne4 23.Qf3 c4 24.Be3 Rd3 25.Rfe1 Bxb2 26.Bxc4 Rc3 27.Rab1 Rxc4 28.Rxb2 Qa3 29.Rb5 Re8 30.Re5 Rxe5 31.fxe5 Qxa5 32.Rf1 Qd5 33.Bh6 Rc3 34.Qf4 g5 35.Bxg5 Rc6 36.Bf6 Nxf6 37.exf6 h6 38.Qxh6 1-0 http://www.chessgames.com/perl/chessgame?gid=1331492 Two short draws in the final rounds, vs Bronstein and Tringov, and Balinas had accomplished his miracle.
Balinas' remarkable accomplishment brought great honor to his country, the Philippines, a nation that is sorely in need of heroes."
As a result of his victory in Odessa, FIDE awarded Balinas the International Chess Grandmaster title.
Another of Bobby Ang's excellent article and analysis of Balinas' "invigorating upset win" over GM Ludek Pachman a former Czechoslovakian champion who emigrated and played for Germany during the 1976 Haifa Olympiad.
Pachman, Ludek (2520) - Balinas, Rosendo Carreon (2365) [E14] Haifa Olympiad (Men) (5), 30.10.1976 1.d4 Nf6 2.c4 e6 3.Nf3 b6 4.e3 Bb7 5.Bd3 c5 6.0–0 Be7 7.Nc3 cxd4 [It is time for Black to resolve the situation in the center.
On the other hand, whenever the game takes a tactical turn it is always good for Bali, for it is in such positions that he thrives].
1.e4 c6 2.d4 d5 3.Nc3 dxe4 4.Nxe4 Nd7 5.Nf3 Ngf6 6.Ng3 e6 7.Bd3 Be7 8.Qe2 O-O 9.Bg5N c5 10.O-O-O Re8 11.Kb1 cxd4 12.Bc4 Qb6 13.Rxd4 Nc5 14.Rhd1 Bd7 15.Ne5 Bc6 16.Bxf6 Bxf6 17.Nh5 Red8 18.Nxf6+ gxf6 19.Nxf7 Kxf7 20.Rd6 Rxd6 21.Rxd6 Re8 22.Qh5+ Kg7 23.Rd4 Rd8 24.Rg4+ Kh8 25.a3 Ne4 26.Bb3 Qc5 27.Qf7 Qf8 28.Qxe6 Nd2+ 29.Ka2 Re8 30.Qf5 Nxb3 31.cxb3 Qe7 32.Qa5 a6 33.g3 Qe5 34.Qd2 Bd5 35.h3 Qe6 36.Qd3 Be4 37.Qc3 Bf5 38.Rf4 Qe5 39.Qf3 Be6 40.Rxf6 1-0 http://www.chessgames.com/perl/chessgame?gid=1271089 Balinas' fighting win against the celebrated Candidate's Qualifier and former Czech champion GM Lubosh Kavalek, 1975 Marlboro Chess Classic: Balinas, R ELO 2365-Kavalek, L ELO 2555, Manila, Result: 1-0 1.c4 Nf6 2.Nc3 g6 3.g3 Bg7 4.Bg2 0-0 5.Nf3 d5 6.cxd5 Nxd5 7.Qb3 Nb6 8.h4 h6 9.d4 Be6 10.Qc2 Nc6 11.Bf4 Nxd4 12.Nxd4 Qxd4 13.Rd1 Qb4 14.Bd2 c6 15.h5 g5 16.f4 gxf4 17.gxf4 Qc5 18.b4 Qc4 19.f5 Qg4 20.Bh3 Qg3+ 21.Kf1 Nc4 22.Ne4 Ne3+ 23.Bxe3 Qxe3 24.fxe6 fxe6+ 25.
Rh3 Qb6 34.Rf3 Rd8 35.Qc2 Rd5 36.Kf1 Rxh5 37.Qb3 Qd4 38.Qxe6+ Kh7 39.Rd3 Qa1+ 40.Kf2 Re5 1-0 Here is Balinas' exciting win against another Soviet Champion and World Chess Championship candidate Lev Polugayevski: Balinas, Rosendo ELO 2365 - Polugayevski, Lev ELO 2645, 1976 Marlboro Classic, Manila 1.c4 e5 2.Nc3 d6 3.g3 g6 4.Bg2 Bg7 5.d3 f5 6.f4 Nf6 7.Nf3 Nbd7 8.Bd2 0-0 9.Qc2 c6 10.0-0-0 Qe7 11.e3 Nc5!
h4 51.f6+ Kf8 52.Rd8+ Kf7 53.Rh8 1-0 http://www.chessgames.com/perl/chessgame?gid=1112154 And, Balinas' most famous game, a scorching win against the famous Danish grandmaster and World Championship Candidate Bent Larsen, who played his beloved Larsen's Opening (1.b3): Larsen-Balinas, Manila 1975.