The story behind the coin
Most royal portraits on coins are a performance. This one had a genuinely unusual man behind it.
Wilhelm II became King of Württemberg on 6 October 1891, inheriting the crown from his childless uncle Karl I. He kept a court, but he did not much act like one. He walked his dogs in Stuttgart's public parks, unattended, and let his subjects speak to him in the street. In Swabian dialect they called him e gueter Ma — a good man. For a German monarch in the age of Kaiser Wilhelm II of Prussia (a different Wilhelm II entirely, and a far grander one), that was an odd sort of fame.
The coin exists because of a decision made in Berlin, not Stuttgart. The Empire introduced a 3 Mark silver piece across all its states in 1908, filling the space left by the old thaler as it was withdrawn. Every kingdom, duchy and free city that struck silver had to issue the new denomination to the same imperial standard.
Look at the two sides and you can read the constitutional bargain of the 1871 Empire. The obverse — the heads side — is purely Württemberg: the king's bust facing right, ringed by WILHELM II KOENIG VON WUERTTEMBERG, with the mint mark F for Stuttgart, the only mint that ever struck these. The reverse is not Württemberg's at all. It carries the crowned imperial eagle with the Prussian shield on its breast and the words DEUTSCHES REICH · DREI MARK, identical on every other state's 3 Mark. Each crown kept its own face. All of them shared one currency.
Striking ran through 1914, into the summer the First World War began. Four years later, on 30 November 1918, Wilhelm II abdicated — the last of the German monarchs to do so — ending more than eight centuries of the House of Württemberg. He died at Schloss Bebenhausen on 2 October 1921. His money barely outlasted him: records give withdrawal in April 1920 and demonetisation from 1 January 1921.

