They had success at a young age, both qualifying for the World Youth Chess Championships, where Rudolf finished in the top 10 of the under-12 girls' division in 1999.

[2][4][6] At nine years old, she drew media attention for defeating Hungarian Grandmaster (GM) Lajos Portisch as a participant in a simultaneous exhibition.

[11][12] Rudolf finished in equal ninth place out of 66 competitors in the under-12 girls' division at the 1999 World Youth Chess Championship with a score of 7/11, three points behind the winner Nana Dzagnidze.

[2] Rudolf's childhood idol was her compatriot Judit Polgár, who is widely acknowledged as the greatest female chess player of all time.

[15][16] She rose to a rating of 2100 in the middle of 2002 at age 14 mainly from two second-place finishes at the First Saturday FM B tournament in Budapest and the under-20 Hungarian Junior Girls' Championship in Paks.

[22] Several months later, she entered the under-16 girls' division at the World Youth Championship in Kallithea in Greece and finished equal fourth with a score of 7½/11, one point behind the leaders.

[28] Rudolf closed out the year with a good performance at the World Junior Chess Championship in Yerevan in Armenia, scoring 8½/13 in the girls' division to finish in equal fifth, just a ½ point behind the leaders.

[15][30] At the beginning of the year, Rudolf won the under-20 Hungarian Junior Girls' Championship, scoring 1½ points ahead of second place with 8/9 and gaining enough rating to cross 2300, the threshold for the WGM title.

After a loss to the eventual tournament winner Thorsten-Michael Haub, she won a fifth game against Vera Nebolsina and finished in ninth place with 6/9.

[35][36] The tournament became enshrouded in controversy when three Latvian players (Starostīts, Oleg Krivonosov, and Vladimir Lazarev) falsely accused Rudolf of cheating by hiding a computer in her lip balm.

[37] Starostīts in particular asked the arbiter to confiscate her belongings and refused to shake her hand before their game, an action which could have been penalized.

Marie Boyarchenko, another player at the event, believed these actions were key factors in Rudolf losing that last-round game.

[41][44] After the tournament switched to a 10-player round robin, she won the 2010 event easily by 1½ points over Tóth and Melinda Göcző with a score of 7½/9.

[42] The 2011 event was more competitive, ending with three players tied for first with 6/9 and Rudolf winning over Schneider and Ticia Gara on the tiebreak criteria.

She then began her next event, the Open Internacional Hotel Avenida de Canarias in Spain, with two wins against much lower-rated players.

[15][51] Rudolf was unable to match her success in the Hungarian women's national championship the remaining times she participated.

As the two-time defending champion in 2012, she finished in joint fourth with a score of 5/9, 1½ points behind the winner Petra Papp.

[15] At the 2012 Open International de Cappelle, Rudolf won a game against Yaroslav Zherebukh, a GM who with a rating of 2642 was the highest-rated player she ever defeated.

[54][55] In the middle of 2014, Rudolf earned her final IM norm in the Master Open at the Biel Chess Festival in Switzerland.

[15] After only scoring 4/11 at the European Individual Women's Chess Championship, highlighted by losses against lower-rated players in the last three rounds, she lost 54 rating points.

[15] At her penultimate tournament, she scored 5½/7 at the CE Division de Honor in Spain, a team club competition.

Although she and her teammate Yuriy Kuzubov were among three players who tied for the highest individual score among all participants, her team did not perform well.

[58][59] For her last event, Rudolf played the Isle of Man International Masters, one of the world's leading open tournaments.

She made her debut at the 2008 Dresden Olympiad on the fourth board, playing behind Hoang Thanh Trang, Szidonia Vajda, and Ildikó Mádl.

[72] Rudolf had already begun to combine teaching chess with her playing career when she moved to Spain and resided in Madrid in 2010.

Alongside Judit Polgár, she co-hosted the official coverage of the 2018 World Chess Championship match between Magnus Carlsen and Fabiano Caruana.

[82][83] Rudolf later revealed that she had never "officially" left Spain, and was actually visiting O'Reilly in Ireland when COVID-19 lockdowns prevented her from leaving.