It's incredibly gamey, but William the Bastard starts with over 1,000 gold so he can support the cost of the invasion force that is about to attack England. If you wait until he is committed across the Channel, it becomes a Xanatos Gambit. If you imprison him successfully, you can confiscate his lands and cash, prevent him from taking the throne of England (which makes Normandy leave France), and gain some demesne. If you fail, he goes to war with you, but he is already committed to a war in England, so you have more or less free reign to siege his holdings. He can't white peace with Harold unless Harold is willing (and Harold is probably not willing until he pins and destroys/loses to William's army). So, either way, you can grab his stuff. The catch is that he might squander the cash before you force him into prison if you fail to catch him at first.
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Excelent let's play anyways