If they run your function from within theirs they simply tell the computer to start reading those instructions, possibly with a timer for stopping detailed in other parts of the comments. If they implement a VM from scratch they can mess with how the library functions work, for instance giving you a time that moves much faster so that your simulation must stop within 0.1s instead of 10 and they can run your code 100 different times to deal with randomness. Now implementing your own VM is probably not the optimal way to do this, you probably just want to do a transformation of the source code to use your own secret functions instead of the standard time ones.

Unless one of the contestants have time limits on their VM (or on their simulations in general). You can of clearly implement a VM where time goes faster just by pretending they have a slower processor than you really run on.

Unless the other contestant wrote a virtual machine in which they are running you. Something which I think would be quite doable considering the ridiculously large time you've got (10s gives ~10^10 instructions).

Hasn't been very consistent lately. Might try this later.

Not strictly speaking. Warning, what follows is pure speculation about possibilities which may have little to no relation to how a computational multiverse would actually work. It could be possible that there are three computable universes A, B & C, such that the beings in A run a simulation of B appearing as gods to the intelligences therein, the beings in B do the same with C, and finally the beings in C do the same with A. It would probably be very hard to recognize such a structure if you were in it because of the enormous slowdowns in the simulation inside your simulation. Though it might have a comparatively short description as the solution to a an equation relating a number of universes cyclically.

In case that wasn't clear I imagine these universes to have a common quite high-level specification, with minds being primitive objects and so on. I don't think this would work at all if the universes had physics similar to our own; needing planets to form from elementary particles and evolution to run on these planets to get any minds at all, not speaking of computational capabilities of simulating similar universes.

Your question is not well specified. Event though you might think that the proposition "its favorite ball is blue" is something that has a clear meaning, it is highly dependent on to which precision it will be able to see colours, how wide the interval defined as blue is, and how it considers multicoloured objects. If we suppose it would categorise the observed wavelength into one of 27 possible colours (one of those being blue), and further suppose that it knew the ball to be of a single colour and not patterned, and further not have any background information about the relative frequencies of different colours of balls or other useful prior knowledge, the prior probability would be 1/27. If we suppose that it had access to internet and had read this discussion on LW about the colourblind AI, it would increase its probability by doing an update based on the probability of this affecting the colour of its own ball.

You seem to be neglecting the possibility of a cyclical god structure. Something which might very well be possible in Tegmark level IV if all the gods are computable.

Note, according to my 30 seconds google scholar search, it is dipping/oral snuff that causes a higher risk of oral cancer. Nasal snuff seems safer (or perhaps less well researched).

That is true. However according to my experience you don't need to spend much time in the library itself if you know what you're looking for (you can always stay for the atmosphere). What takes time is going to and from the library. The value of this time obviously depends on a lot of parameters: is the library close to your route to/from some other place, are you currently very busy, do you enjoy city walks/bike-rides, etc.

Have you tried snuff? It smells quite nice and can help clear your nose as well as deliver nicotine.