I would assign a malicious superintelligence a higher probability than would pure entropy over the space of superintelligences due to the chance of something broken coming out of military research. I would assign this a relatively low likelihood. I am not certain whether I would assign it a higher or lower likelihood than "automatically Friendly ones" - it depends on what you mean by that. I would assign it a higher probability than an AI built without any thought to friendliness being friendly, given that it was built with thought to maliciousness, and there are perhaps a broader range of behaviors we might label "malicious".
By an "automatically Friendly AI" I simply meant one that was Friendly without explicit programming for friendliness. I think that would be more likely than a malicious AI because there are good, rational reasons to be "friendly" (benefits from trade and so on) in the absence of reasons not to be. I can see no rational reason to be malicious - humans that are malicious are usually so for reasons (sadism, revenge, and so on) that I can't see someone programming into an AI.
Make beliefs pay rent. How much rent? Is it enough that they have some theoretical use in designing a GPS or predicting the cosmos? How much rent can actually be extracted from a belief?
In a certain fantasy series, there is a special knowledge of a thing, called the name of the thing, that gives one predictive and manipulative power over it. For example, the protagonist, a young
rationalistarcanist named Kvothe, learns the name of the wind and uses it to predict the movements of the leaves of a razor-sharp 'sword tree' well enough to walk through without getting cut.Another character, which we would recognize as a boxed malicious superintelligence, has the ability to predict everything. Simply talking to it allows it to manipulate your future to its twisted ends.
At first these seem like the usual impossible fantasy magic, but why impossible? If a path exists, a good predictive model should find it.
There's nothing that says the map can't match the territory to arbitrary precision. There's nothing that says beliefs have to just sit passively until they are brought up at a dinner party. But how much rent can we extract?
We are not omniscient superintelligences, so the second power is closed to us for now. The first also seems off-limits, but consider that we do know the name of the wind. Our name of the wind and Kvothe's name of the wind are mathematically equivalent (in that the motion of the sword tree could be predicted by simulation of the wind using the NS equation). So why is it that Kvothe can walk through the leaves of the sword tree, but you, even knowing the NS equations as facts in your map, can not?
Optimization. Algorithmization. Kvothe's name of the wind is optimised and algorithmised for practical use. Your name of the wind is sitting in your cache as a dumb fact ready to guess the password for "how does wind work". Kvothe is reeling in rent utilons while you congradulate yourself for having correct beliefs.
So to collect rent from your beliefs, it is not enough to simply know some fact about the world. It has to be implemented by a good algorthim on the intuitive level. You have to be able to act and see through the wind the way a machinist can act through a lathe and a woodsman can see through footprints in the dirt. The way a surfer or skater can act through his board and see through the subtle vibrations and accelerations.
I don't know if we can reach the level of intuitive causal modeling of the wind that Kvothe has. Maybe it's too hard to integrate such abstract models into system 1. Fluid dynamics is notoriously difficult even for computers. I do know that it's not enough to memorise the differential equations. You can get a lot further than that.
So how much rent can you get from your beliefs? A good rent-paying belief should feel like an extension of your body; You should be able to see and act through your belief like it's another eye or arm. When thinking about how much rent can be extracted from a belief about something, think about what Kvothe would be able to do if he knew its true name.