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but there's still something curious about simply not giving players most of the choices in the game. i.e. it's possible to make a game with relatively high headroom, but low repetition just by having a lot of content that doesn't appear every run.

I think you're getting at what (I believe at least) is missing from the headroom framework. Alex Smith would appear to value player choices only with regards to their relative probability of reaching a final win state, but this disregards how such a probability is actually computed: in general, the chance of victory depends on future choices, such that the value (sometimes referred to as the 'return') of a choice is actually a composite of every future choice in the chain of choices that make up a playthrough.

more plainly, two choices may have an equal likelihood of victory, but differ (e.g. in length, or composition) in how this likelihood is actually computed. despite their apparent similarity, they can actually be quite different, and in fact quite meaningful to the player, i.e. meaning is clearly not fully represented by the 'probability of victory' signal as Alex Smith would seem to claim. to reuse an example from the article: if two characters play very differently--so differently that learning one teaches you nothing about playing the other, say--but otherwise present equal opportunity for success, I would consider character choice to be meaningful: it determines the rest of your game!

there is something orthogonal to the notion of headroom, I think, and being unaware of it can lead to dangerous conflation (particularly 'high headroom' and player creativity). as you point out, the degeneracy of a 'puzzle' experience (there is only one path) is not the same as low headroom. ultimately what seems like poor design, at least in the context of these sorts of games, is making only one path viable. I think that you can give the player plenty of creative choices early on, as long as they have to pay the price for these choices eventually... and that's what I think could be neat about shroom & gloom, at least in the early game.

on the other hand, giving the player too many options probably overwhelms them with choice and/or puts them in a rut, as you say. this would seem to relate to player creativity in general. this post focuses on sandbox games, not roguelikes, but I am surprised to find that it has some relevance here. offering the player three cards and telling them to make a decision feels a lot like giving the player an interesting and functional design constraint.

regarding farming. at some level I believe that farming (and stuff like exhaustive inventory management) is just 'bad', at least in the sense that it's unintentional (i.e. as opposed to a game 'about' farming). regardless of the value of the reward (and sometimes in spite of it), the cost of farming is usually only player time, and player time is a valuable resource. either just give the player what they want, or incorporate some kind of risk/reward tradeoff into farming, right? curious if you agree. I mentioned this already, but one thing I liked about shroom & gloom was that it puts a negative feedback loop on inventory management. if you try to hoard tons of cards in your home deck, you'll just weaken its draw power overall. I would probably enjoy if farming was given a similar treatment.

this segues somewhat neatly into your other comments.

the thing about CCG's in general, is that the random-draw-from-a-deck is naturally great at getting players to improvise . . . I feel like there's got to be a way to disrupt a farming strategy through introducing more randomness, like if the first half of a run involves a lot of farming, but then some event takes place half way that provides an even better approach, that would reduce the overall repetition, and as I see it the repetition itself is the problem.

I would like to push back a little against this, but not much, because it's more important to preserve your take--particularly in a genre game like this.

but I would say that the whole point in building a deck, from the player's perspective, is to make something that consistently delivers exceptional performance. in order to do this, you need to be able to understand your deck in its totality--you need control. deckbuilders feel like a battle against the machine, where the player always wants more control but is (positively) constrained by some aspect of the design. MTG (which I have very little experience in) has a minimum deck size for this reason.

so when a card shows up in my hand, I already know what to do--it's part of the engine. this is because it is common in these sorts of games to have total information when it comes to the composition of your deck. understanding your deck is knowing all the hands you could draw, and this information isn't gated by anything (in particular: time) so investing into this sort of knowledge can be seen as a weakness in the player that is either encouraged or discouraged by the design. a little like farming I guess. so the extent to which players 'should' improvise I think is very low, or at least the game as it currently exists does not encourage this in play. you could however imagine several changes that would (not knowing what's in your deck is the obvious one, but also cards that mutate in the background, or cards that synergize very broadly, etc.). I am sure slay the spire supports large 'grabbag' decks--I am not a serious enough player to know--but there has to be something that makes these viable, otherwise you just draw into a lot of terminal cards.