It's a rough concept if you think about it. I mean... someone who is always acting chaotically with total randomness is going to be unpredictable. But that's one type of unpredictablilty. Given enough time and information and roughly infinite computing space, you could render even that individual predictable. Besides, what's the point of acting with complete randomness, since if every action is random, there's never any intent- any goal.
If you take a file and encrypt it using something like PGP, that, to you, is unpredictable. You know the public key, and use it to send a message. You can't predict what the encrypted version is (although your computer can!, and you could if you really wanted to take the time to do it). You can't predict what the private key to render the information intelligible again is. But the message still has meaning to those that can read it.
So really, valuable unpredictablility won't be unpredictable to you. It'll be part of your plan. In the anime "Kenshin", Kenshin wins his fights because his opponent is incapable of predicting his actions- but Kenshin always knows what he's going to do next. But Kenshin is also flexible in changing his plans.
Like I always say, be like water. Given an incline, you can't predict the path water will take down it. In places, it gets redirected by the properties of the incline, rocks, trees, etc. can determine the shape of a river. But the river also will shape the ground. It will cut a channel. In India, they have countless "migrating" rivers, which baffle geoligists. The rivers will change course by hundreds of meters in a single year.