Kammala jumla mai zuwa: Kravtsiv ya koya wa mahaifinsa yadda za a yi wasa a ranar haihuwarsa ta shida. Daga baya, ya horar da shi a cikin Lviv Chess Club. A cikin
Wasannin Wasannin Wasannin Wasannin Duniya na 2008 a Beijing, Kravtsiv ya lashe lambar zinare a wasan mutum-mutumin maza. A cikin 2010, ya yi daidai da na 1-6 tare da Dmitry Kokarev, Alexey Dreev, Maxim Turov, Baskaran Adhiban da Aleksej Aleksandrov a gasar Orissa Open ta 2 a Bhubaneshwar. A cikin 2011, Kravtsiv ya lashe 3rd Chennai Open. A shekara mai zuwa, ya yi daidai da 1st <unk> 5th tare da Pentala Harikrishna, Parimarjan Negi, Tornike Sanikidze da Tigran Gharamian a cikin Cappelle-la-Grande Open. Ya yi daidai da na farko tare da Andrei Volokitin da Zahar Efimenko a Gasar Cin Kofin Chess ta Ukraine ta 2015, wanda aka gudanar a garinsu na Lviv, inda ya zama na biyu a wasan. A shekara ta 2016, Kravtsiv ya lashe gasar Riga Technical University Open wanda ya fitar da Hrant Melkumyan, Arturs Neiksans, Aleksey Goganov da Jiri Stocek a kan wasan kwaikwayo.