In October 2010, he qualified for the 2010 Winmau World Masters, when he won the first round match 3–1 in sets against Chris Scutt.

On the first day of the competition, he defeated Loris Polese, Craig Robertson, Lee Whitworth and Jim Withers.

He reached the final of the Irish Tom Kirby Memorial, a win in the tournament would have earned him a spot in the preliminary round of the PDC World Darts Championship.

In his debut on PDC European Tour stage in April at the 2022 Austrian Darts Open, he lost to Danny Jansen 6–1 in the first round.

In 2023 Szagański won Players Championship 27, winning matches against Dimitri van den Bergh and Jonny Clayton before beating Connor Scutt 8–5 in the final.

[5] In February, on the 2024 PDC Pro Tour, Szagański achieved a surprise 6–5 victory over Luke Littler in the second round of Players Championship 2.

[6][7] In the PDC ET01 Tour Card Holder Qualifier for the 2024 Belgian Darts Open Szagański was whitewashed, 6–0 by Littler.