This might be a little off topic, but I'd like to share a couple of times I thought I'd captured kings, but they "escaped".

First example - playing Poland vs the HRE - MTW/VI Vanilla

Sniping attacks by the HRE into Silesia etc had annoyed me. Yes, it was personal. I attacked the small stack with the Emporer in Bavaria. (I had taken a rebel Austria, which may be what annoyed him). He retreated to Franconia. Saxony was rebel, and Lorraine and Flanders were French. I attacked him again, and he retreated to Friesland. Good, the Emporer is trapped, with an army too small to jump into any of the surrounding provinces. I attacked him again, and the HRE retreated to the castle.

The Emporer appeared in Swabia.

Second example - playing Hungary vs Sicily.

The Sicilians had been attacking Serbia by convoying armies over from Naples. The Hungarians had no fleets. Croatia and Greece had ports, but Serbia did not have a port.

After repelling a first attack of Town Militia Serbia was invaded by a larger Sicilian army led by the Sicilian king. Hungary had enough men to reinforce Croatia and Greece to prevent escape. The Sicilian king was then attacked in Serbia. On the battlefield he fled as a single remaining man.

The Sicilian king reappeared in Naples.

No ransom, no gratuitous killing of prisoners.

Now, I'd hate to accuse the AI of cheating, but, how can I put it - maybe it bends the rules sometimes. Sometimes with kings, and many of you will have encountered odd scenarios involving particularly Italian and Sicilian fleets where armies are transported through apparently blockaded seas.

There is no such thing as a "for sure" trapped king.

Hmm ... except when playing the Turks in Early, where the Egyptian sultan starts in Antioch. Invasion of Tripoli on the first turn always seems to work in capturing him.