Whakaotihia te rerenga e whai ake nei: I whakaakona a Kravtsiv ki te tākaro tēnehi i tōna rā whānau tuaono e tōna pāpā. I muri mai, i whakangungu ia i roto i te Lviv Chess Club. I te
I te 2008 World Mind Sports Games i Beijing, i wikitoria a Kravtsiv i te mētara koura i roto i te kaupapa blitz takitahi a nga taane. I te tau 2010, i taurite ia mo nga waahi 1st-6th me Dmitry Kokarev, Alexey Dreev, Maxim Turov, Baskaran Adhiban me Aleksej Aleksandrov i te whakataetae 2nd Orissa Open i Bhubaneshwar. I te tau 2011, i toa a Kravtsiv i te 3rd Chennai Open. I te tau e whai ake nei, i taurite ia mo te 1st <unk> 5th me Pentala Harikrishna, Parimarjan Negi, Tornike Sanikidze me Tigran Gharamian i te Cappelle-la-Grande Open. I taurite ia mo te tuatahi me Andrei Volokitin me Zahar Efimenko i te 2015 Ukrainian Chess Championship, i tu i tona taone nui o Lviv, i mutu i te tuarua i te tiebreak. I te tau 2016, i wikitoria a Kravtsiv i te Whare Wananga Hangarau o Riga Open i te taha o Hrant Melkumyan, Arturs Neiksans, Aleksey Goganov me Jiri Stocek i runga i te tohu tiebreak.