Osama bin Laden, game theorist
This post is not about bin Laden's decision to hide in plain sight, although that seems to have been a pretty good strategy. We take his decision to reside next to Pakistan's top military training center as a given. The question is, should he have arms in his compound? One's initial reaction is that it is quite odd that he was not armed.
Once the Americans discover where he is, their choices are limited. A small, quick raid is the most likely to minimize the chances word will leak to Osama (and he escapes) or that the Pakistani military becomes involved (bloodshed and embarrassment for the U.S.).
If he is armed and resists, he will be killed. If he is not armed it will be difficult for the Americans to know he is unarmed so he is killed -- in particular, he does not want to be taken alive so he has every incentive to act like he is armed.
In either case he's dead. Which does he prefer? To be killed unarmed. In death he'd get good PR out of it. Killing an unarmed person raises questions about the justice of the killing.
Or does it, now that you know the reason he was not armed?