Surely this doesn't increase intelligence just optimization power. If you are going to introduce definitions stick by them. :)

This jumped out at me as well, though I forgot about it when writing my other comment.

I think it's important to distinguish between what I'd call "internal" and "external" resources. If we took the "intelligence = optimization power / resources" thing to literally mean all resources, it would mean that AIs couldn't become more intelligent by simply adding hardware, which is arguably their strongest advantage over humans. It might also mean that bacteria could turn out to be "smarter" than humans - they can accomplish far fewer things, but they also use far less resources.

Intuitively, there's a clear difference between a larger brain making a human more powerful than a dog ("internal resources"), and a larger bank account making a human more powerful than another human ("external resources"). Fortunately, this distinction emerges pretty easily from Legg & Hutter's intelligence formalism. (Luke & Anna didn't actually use the formalism, but the distinction emerging easily from the formalism suggests to me that the distinction actually carves reality at the joints and isn't just an arbitrary one.)

The formalism is fundamentally pretty simple: there's an agent, which receives a stream of observations about the environment, chosen from some set of symbols. In response, it chooses some action, again chosen from some (other) set of symbols, and gets some reward. Then it makes new observations and chooses new actions.

Legg & Hutter's formalism treats the agent itself as a black box: it doesn't care about how the agent reaches its conclusions, or for that matter, whether the agent does anything that could be called "reaching a conclusion" in the first place. It only looks at whether the agent is able to match its actions to the observations so as to produce the highest rewards. So "internal resources" would be things that go into that black box, only affecting the choices that the agent makes.

"External resources", on the other hand, are things that affect the agent's set of actions. Intuitively, a rich person can do things that a poor person can't: for instance, buying a house that costs a million dollars. In Legg & Hutter's formalism, the rich person would have a broader set of actions that they could choose from.

We can then rewrite "intelligence is optimization power divided by resources" as "intelligence is the optimization power of an agent when their set of available actions is held constant". I think this is a pretty good match for our intuitive sense of "intelligence". If you can solve a puzzle in one move by bribing the person who's administering it, that might get you a higher amount of reward, but it doesn't make you more intelligent than the person who doesn't have that option and has to solve it the hard way. (If you wanted to be exact, you'd also need to hold the set of observations constant, so that e.g. a seeing person didn't end up more intelligent than a blind one.)

ETA: Technically, the poor person does have the same set of actions available as the rich person - they too can claim to have a million dollars and try to tell their bank to transfer the money to the seller. It's just that the same actions produce different consequences - if you don't have the million dollars in your bank, the bank will refuse to obey you. But saying that they have different sets of actions gets close enough, I think.