What is pain exactly (e.g., in a mathematical or algorithmic sense) and why is it bad? For example can certain simple decision algorithms be said to have pain? Is pain intrinsically bad, or just because people prefer not to be in pain?

Pain isn't reliably bad, or at least some people (possibly a fairly proportion), seek it out in some contexts. I'm including very spicy food, SMBD, deliberately reading things that make one sad and/or angry without it leading to any useful action, horror fiction, pushing one's limits for its own sake, and staying attached to losing sports teams.

I think this leads to the question of what people are trying to maximize.