Rubuta ci gaba don wannan sakin layi - Farawa daga 1986, tana riƙe da rawar da ta fi taka rawa a cikin zaɓin chess na ƙasa. Ta lashe lambar tagulla ta tawagar a gasar Chess Olympiad a Thessalonica 1988, da kuma lambar tagulla ta mutum a gasar Chess Olympiad a Elista 1998. Ta lashe lambar azurfa a gasar zakarun Turai ta Team Chess a Batumi 1999. A Shanghai 2001, Alisa Marić ta buga wa mambobi shida "Rest of the World team" a wasan baje kolin da China. A Belgrade 2007, an ba ta lambar yabo ta "St. Sava kyauta" don bikin cika shekaru 20 a matsayin memba na ƙungiyar ƙasa. Ta buga wasan farko a gasar Olympics goma ta Chess (Dubai 1986, Thessalonica 1988, Novi Sad 1990, Moscow 1994, Yerevan 1996, Elista 1998, Istanbul 2000, Calvià 2004, Turin 2006 da Dresden 2008).
) da kuma gasar zakarun Turai guda biyar (Batumi 1999, Leon 2001, Plovdiv 2003, Gothenburg 2005 da Novi Sad 2009). Sau uku Alisa Marić ta lashe Kofin Kungiyar Chess ta Turai tare da kungiyar "Agrouniverzal" daga Belgrade.