"You have won..." -> "Właśnie wygrałeś..."
Wygrałeś is fine if the player's a man. Otherwise, for a woman, wygrałeś needs an A instead of the E: wygrałAś
There are lots of pitfalls like this in Slavic languages, and I imagine in many others.
Speaking as an English developer, the first time you implement a proper translation can be a painful - not to mention enlightening - experience.