Regarding deck taxonomy, I think maybe a key distinction is this: if you were to replace each card in your deck with n copies of itself (for n=2 the starting deck becomes 14xCopper, 6xEstate), would you typically be drawing the same number of cards each turn, or the same proportion of your deck?

I haven't done the math, but I would assume that Smithy/BM draws the same 5-sometimes-8 cards if you double/triple/etc. the deck, and most conventional (village+smithy) engines continue drawing 100% of the deck when you double it, since drawing deck is a function of total +cards, having enough +actions to support that, and drawing those in the right order, all of which stay the same when you add more of everything while preserving proportions (I gut-sense). [hand-wavy justification-ish: sampling with and without replacement converge to the same limit when the thing sampled from grows to infinity. Variance decreases as n increases—the sum of more dice looks more bell-shaped and less flat.]

So my distinguishing criterion seems to do the right thing for typical BM and typical engine decks. Probably it also works for engines that draw 70-90% of the deck, e.g. 10xCity plus starting deck plus some Bridges—though I definitely would want to do the math here and verify that nothing weird happens when you double all the things.

The impact of drawing O(1) cards vs. Ω(n) cards is of course that your output on a typical turn is proportional to the average/total per-card output, respectively, and that changes how you build your deck. So even though I'm not running the deck-doubling thought experiment when analyzing a board, I probably am thinking through the *implications* of that math.

One open question: are there in-betweens? Are there decks where you draw something like Θ(sqrt n) or Θ(log n) as you double/triple/n-plicate your deck? What do they look like?

MQ raises both the trivial point that decks are not static over time (duh) and the non-trivial point that this makes "draws the deck" undefined unless we're talking about one or more points in time. For my O(1)-vs.-Ω(n)-criterion, "when you start greening" sounds like a good point in time, or else "at the maximum" (and please don't tell anyone that O(...) is a partial ordering)—these seem roughly to be what we mean when we try to distinguish between engines and non-engines. (I also read MQ's post as saying "there's quite a bit of gray area". I'm not addressing that here.)