Which one sounds like nausea? I've never had that strong a reaction to a bad argument.

It sounds like nausea; like you get when you're intoxicated and the room starts swimming--your faculties try to make sense of what's happening, and fail.

I think that while a sleek decoding algorithm and a massive look-up table might be mathematically equivalent, they differ markedly in what sort of process actually carries them out, at least from the POV of an observer on the same 'metaphysical level' as the process. In this case, the look-up table is essentially the program-that-lists-the-results, and the algorithm is the shortest description of how to get them. The equivalence is because, in some kind of sense, process and results imply each other. In my mind, this a bit like some kind of space-like-information and time-like-information equivalence, or as that between a hologram and the surface it's projected from.

In the end, how are we to ever prefer one kind of description over the other? I can only think that it either comes down to some arbitrary aesthetic appreciation of elegance, or maybe some kind of match between the form of description and how it fits in with our POV; our minds can be described in many ways, but only one corresponds directly with how we observe ourselves and reality, and we want any model to describe our minds with as minimal re-framing as possible.

Now, could someone please tell me if what I have just said makes any kind of sense?!

You worked that out that yourself? (upvoted) Working out the best strategy is unfortunately a bit more complicated than just summing up each column, since by that logic everyone would go Green/Blue, and you'd then beat them with Red/Green or something else that beats Green/Blue. But I'm still impressed with your matricial mastery.

This is the correct equation for any attack pair. Now just need to do a 16-16 table to see what wins over what. I'll do it during lecture tomorrow.

The red sword is strictly worse than the blue sword. Beyond that I'm too lazy to figure it out.

 D S D*S a1 a2 a3 a4 s1 100 80 8000 6336 6256 6400 6080 6268
s2 80 100 8000 6120 6120 6000 6080 6080
s3 150 50 7500 6210 6035 6500 5700 6111.25
s4 50 180 9000 6156 6426 5400 6840 6205.5
6205.5 6209.25 6075 6175 Da -12 -8 -20 0 Do 0.1 0.15 0 0.24

My first instinct was to make the table above, which may or may not be readable here (EDIT: mostly readable, some tab glitches). I first calculated each sword's damage per minute (obviously, in general you want the highest value here), and then worked it out as applied to each armour type.

Here's where it gets... tricky, as you want the sword that maximises damage to all armour types, and the armour that minimises damage from all sword types. Do we look at average values? That could leave you open to being gamed by someone whose choices are poor except against your specific choices.

The best average choice here, by the way, is clearly Sword 1 (Blue) and Armour 3 (Yellow). But Sword 1 is not the best choice against Armours 2 and 4, and Armour 3 is not the best choice against Swords 1 and 3.

Nevertheless, the difference is small enough that I would still go with them; in the end, I think, being optimal like that is still the best strategy, as players with worse choices will be outcompeted. I am niggled by the thought that the optimal armour is not actually optimal against the optimal sword, but I don't think you can really do anything about that

I wish this were written in a way that would be more accessible to non-Less Wrong readers!

I like the use of the quotient set here. In fact, I would go on to use it more comprehensively: not only does our observer-moment define an equivalence class, but any particular context implementing it does, too. It could be a simulation, or a simulation in a simulation in a (...), a small corner of a more general mathematical system, anything. The point is that for any and every defined part, it too will always be part of a quotient; there will always be an indistinguishability of what's happening below.

As a result of this: does it mean anything to be 'a simulation'?

My own current thinking is that the Born rule - the everydayness of everyday life - is a reflection of how consciousness must function. I am just not entirely sure how yet...

No, as described, you have probability (1/2)^n of becoming copy #n, and #99 and the original share (1/2)^99.

The original is copied once -- giving 50% #0 and 50% #1. Then #0 is copied again, giving 25% #0, and 25% #2. Then #0 is copied again, giving 12.5% #0, and 12.5% #3, and so forth.

This seems like a useful reductio ad absurdum of this means of calculating subjective expectation.