[1] In the 2008 World Mind Sports Games in Beijing, Kravtsiv won the gold medal in the men's individual blitz event.

In 2010, he tied for 1st-6th places with Dmitry Kokarev, Alexey Dreev, Maxim Turov, Baskaran Adhiban and Aleksej Aleksandrov in the 2nd Orissa Open tournament in Bhubaneshwar.

[3] The following year, he tied for 1st–5th with Pentala Harikrishna, Parimarjan Negi, Tornike Sanikidze and Tigran Gharamian in the Cappelle-la-Grande Open.

[4] He tied for first with Andrei Volokitin and Zahar Efimenko in the 2015 Ukrainian Chess Championship, held in his native city of Lviv, finishing second on tiebreak.

[5] In 2016, Kravtsiv won the Riga Technical University Open edging out Hrant Melkumyan, Arturs Neikšāns, Aleksey Goganov and Jiří Štoček on tiebreak score.