Nyora kupfuurira kweiyi ndima - Kravtsiv akadzidziswa kutamba chess pazuva rake rokuberekwa rechitanhatu nababa vake. Gare gare, akadzidzira muLviv Chess Club. Mumitambo yeWorld Mind Sports Games ya2008
muBeijing, Kravtsiv akahwina menduru yegoridhe mumutambo wevarume mumwe nomumwe. Muna 2010, akafananidza nzvimbo dze1st-6th naDmitry Kokarev, Alexey Dreev, Maxim Turov, Baskaran Adhiban naAlekssej Aleksandrov mumutambo wechipiri weOrissa Open muBhubaneshwar. Muna 2011, Kravtsiv akakunda 3rd Chennai Open. Gore rakatevera, akaenzana 1st<unk>5th naPentala Harikrishna, Parimarjan Negi, Tornike Sanikidze naTigran Gharamian muCappelle-la-Grande Open. Akafananidza kutanga naAndrei Volokitin naZahar Efimenko mu2015 Ukrainian Chess Championship, yakaitirwa muguta rake rekuzvarwa reLviv, achipedza wechipiri pakurambana. Muna 2016, Kravtsiv akahwina Riga Technical University Open achipfuura Hrant Melkumyan, Arturs Neiksans, Aleksey Goganov naJiri Stocek pa tiebreak score.