So your existing knowledge about the game is what let’s you use the account’s resources to optimize the world.
This I say explicitly in the post. See conclusions:
besides the observation region O, we also need to know a certain amount of bits detailing the rules of the world. In its uncompressed form, this knowledge is always greater than the amount of optimization (for example, with CCSWAP gates, we would need four addresses for each optimized bit);
The bit about locks and lock-like processes comes from the original question I linked at the top; you should go check that (and the accepted answer) for full context. Essentially I set out in this post to actually disprove that answer, because I didn’t find it satisfying; I ended up finding that the answer itself is not per se wrong, but it applies with constraints to a reversible system. If you consider uncompressed knowledge about the rules of the world (in your example, the source code of the game), put together with the password, you always have more bits of knowledge than of optimization. However, since compression is a thing (for example, you don’t actually know the source code when stealing an account), I doubt that’s a hard theorem. All I can say on that is “there are situations in which n bits of knowledge can be turned into N>n bits of optimization, but only as long as the world is already set up to allow you to do so”. It would be interesting to have a reasonable definition of what a “natural” set of laws would be like and whether lock-like maps could ever spontaneously occur within it.
This I say explicitly in the post. See conclusions:
The bit about locks and lock-like processes comes from the original question I linked at the top; you should go check that (and the accepted answer) for full context. Essentially I set out in this post to actually disprove that answer, because I didn’t find it satisfying; I ended up finding that the answer itself is not per se wrong, but it applies with constraints to a reversible system. If you consider uncompressed knowledge about the rules of the world (in your example, the source code of the game), put together with the password, you always have more bits of knowledge than of optimization. However, since compression is a thing (for example, you don’t actually know the source code when stealing an account), I doubt that’s a hard theorem. All I can say on that is “there are situations in which n bits of knowledge can be turned into N>n bits of optimization, but only as long as the world is already set up to allow you to do so”. It would be interesting to have a reasonable definition of what a “natural” set of laws would be like and whether lock-like maps could ever spontaneously occur within it.