The point is, Rats trashing curses is an AWFUL plan. It has nothing to do with probabilities of how likely it is to come up.
So, you say, you have a game where the only trashing is rats and some treasure trashing, and there's pretty heavy cursing, and there's card-draw pieces. Ok, I will give you that. Yeah, it won't come up often, but I don't really care, that is not my point, and I agree that it being a rare board isn't really relevant. So let's just assume we're on that board. Great.
You're saying there's a point where the correct move would be to buy rats. You're saying that some point after the curses are gone (I'll give you some flexibility to say, just before they're all gone, only most of them are gone). First of all, this is the exact kind of game where, most of the time, you shouldn't be building an engine, because just going for money will be both faster and, because of the high amount of junk (and lack of trashing), more reliable in the long-run.
Granted, hence why I have said repeatedly that you need things to push you toward engines. A non-exhaustive list includes things like: Colonies, gainers (e.g. Iw, Armory, Haggler), anti-money deck attacks (e.g. Noble Brigand, Cutpurse, Rabble), power engine cards (e.g. Kc, Tr, Border village/$5 draw), engine favoring sifting (e.g. Inn, Cellar, Farming Village). I have stated
from the beginning that the criteria of when to go Rats over duchy is when you will see them often enough to trash three curses. Engines, while not common, make this conceptually easy to estimate. Two turns with a perfect deck drawing engine is the obvious case for Rats being equal to Duchy.
But ok, for some strange reason, you actually want to build the engine. But in this case, where you're drawing your deck pretty much every turn (somehow), you should have enough money to be buying provinces every turn. Or if you don't have that much money, you should be getting money to do that, rather than rats. Or if you don't have the reliability, that first of all will hurt rats, and moreover, you should be getting the engine components to give you that reliability. Or if you're to the point where piles would be an issue from doing that for you, you should be getting the points now now now. At best, there is some situation where you have something like 7 curses, but you're somehow overdrawing your deck anyway, reliably (this already isn't super possible, since you have at least 10 junk/stop cards,but ok, it's vaguely reliable say), and you buy a rats right at the end, or better, you gain one midturn, so you can play it, then draw the new one, and set it up to play and draw all of them in the same turn, netting you some points.
I've built for a colony engine off Iw/Smithy/Farming Village. I spent my first (two?) $5 on Counterfeit and have been going Rabble/Bazaar with $5 sinces (or grabbing doubles of Fv/Smithy). We are out of Farming villages and I draw an Iw. I have 4 Smithies, 4 Rabble (net draw +16) against 6 curses, 3 estates, of course I should expect to skip 2 or 3 with the Fv each draw so that leaves me with 11 draw slots, with a single Bazaar in play I need 4 Plats, one Counterfeit for double Colonies. Presumably my opponent is either trying to pile down Smithy/Fv with me (and hence going engine-ish at least) or he is going to have a hellavu time making a dent in the provinces or 3 pile when he gets repetitively Rabbled.
I draw deck with 1 action and Iw/Rabble outstanding. My Iw is otherwise useless, so I get the Rats. I expect to have three turns (buying 4 colonies over the next two turns, then either more Colonies for an easy win or some form of end game dancing).
Oh my a blindingly obvious example where Rats has low opportunity cost (it is actually competing with estate, not duchy) and there is a nice confluence of gaining, sifting, attacks, and extra VP to make it farcical.
But we can look at a lot of other options. I'm setting up the engine exactly as you outline (say I have Familiar/University/Pool with decent $5's, say I'm just playing with Alchemy, Base, Prosperity and Dark Ages). But it is starting to fail and I want the Duchies "now, now, now". I'm down 6:4 on curses. I draw a Green, a Curse, a Market, a Gold, and dead draw (e.g. something like Moat). I play the Market, draw a curse, I elect not to play the dead draw because I've been deck tracking and know I have low odds of hitting more coin, but good odds of kicking off my engine next turn. I have $4, I'm down by 2 VP - what do I buy?
Another component (e.g. something like Oasis)? Well maybe that will let me win the province split. But that has to take into account 3 piles and the fact that I'm going to give my opponent a free shot at VP - a duchy gets him up by $5 so then I can no longer win with a 4:4 province split and a bonus duchy. Highly situational odds if a component works. Okay well what about estate? It is 1 VP now, now, now. But it literally does nothing for me unless I get a second estate later; which is rare without a +buy. Rats? Okay I might be able to play it for 1 VP and then draw the gained Rats with a Pool for another VP. Well that is actually useful. Going Rats may well be a tactical choice that ends up working well just because you get a busted hand with $4. Its another path to victory, so why not think about it when analyzing the board?
it's really more of a one-off tactical play than something to keep in your mind and watch out for.
Funny, I whole heartedly concur. It is a tactical play that can work well. I have never said otherwise.
The times when you need to keep the tactical possibility in mind are about as common as any specific two card combo. E.g. maybe 1 in 500 games. So you approach a board that has cursing. You quickly see that cursing with no curse trushing means this is going to be a cursing game. Now you have to make a decision - what am I going to do when the cursing is done? You should obviously NOT plan around Rats nibbling away the curses. But if you have an engine setup that looks promising - say other attacks to make the game longer still (note, not discarding attacks that are relatively weak against cursed decks), strong engine cards (e.g. Kc, gainers), and perhaps some more VP so the money player has to take more provinces to secure the win (e.g. Colonies, Fairgrounds, Island) then when you do your calculations for how many points you can score via engine you should keep in mind that Rats can be a pretty nice extra 3-4 on the engine side if you are worried about slipping below 50%+1 before your engine works.
Will this be common? No, as I already said the biggest sieve is the need for other trashing to not be there. What typically makes engines viable after cursing is the trashing. But there are a large constellation of things that move you toward engine besides trashing. Sifting. Gainers. Colonies. Shelters. Other attacks. Power engine cards. Some Alt-VP. Some pseudo-trashing. Goons/Bish. Light trashing. The exact point at which any combination of these works out into a pattern that says "go engine" is highly board dependent, and I'm tired of having people nitpick where exactly the marginal line is drawn. Clearly I can make illustrative cases where the thread isn't derailed, but somehow people who I've beaten every single time I've played them (which I grant is a huge amount of luck beyond what little skill I have) will go gonzo that my marginal cases are too weak. Rats killing curses is a tactical thing. It isn't common but then no specific card interactions are either. What is it, only 5% of games will even have Rats at
all?
I don't mind talking about edge cases. I don't even mind talking about fairly unlikely edge cases, because they do come up. What I do mind is talking about an extreme edge case and pretending it's a common scenario. That's my issue. That's it. If you had simply owned it and prefaced it with, "This is a ridiculously uncommon edge case, but...", I would have no problem.
Oh get off it. I have never said it was common. Your back of the envelope is 1 in 1200, mine is around 1 in 400. I laid out my specific criteria in the very first post - you have be in a place where you'd consider gaining Duchy and the game has to last long enough to eat the curses (seeing the original Rats 3 times is pretty decent as Rats is a bit less harsh on an engine than Duchy, but Duchy is assured points now).
You then proceeded to pretend that I somehow said this was common. I put it on par with any specific two card combo (because there is a LOT of degeneracy between cursers and between engine enablers). Further, there are a lot of common play scenarios that totally warp the odds. E.g. When I play IRL it is not uncommon for me to bring just a few expansions, so we might just have Base, Dark Ages, and Prosperity - which massively inflates the numbers when Rats/Curse killing can be a thing.
"Edge case" has become ludicrous on this forum, we may as well close the forum down to any discussion of specific card interactions - they are all edge cases. I mean do you knwo the odds are that you will Young Witch, Tunnel, and scaling TfB are? Or how about Forager, 2 kingdom treasures, no villages, and cantrip +draw, and a gainer? Or perhaps Chancellor/Stash/Pillage/Alt-VP? Those are my
last three games. In the first, the Bane was Tunnel, the TfB was Butcher and it was totally engineless game because Butchering Golds was easy. The second I went Forager/Pot, grabbed 6 Alchemists (bought a second Pot the turn before grabbing #5&6), then I stocked up on Foragers, then grabbed Loan/Contraband/Gold and quickly went to town with $6 Foragers for a triple province turn followed by a double. In the last I completely ignored the Chancellor/Stash because we also had Rogue and I went engine and buried his Chancellor while stocking up on Islands/Duchies. Each of these were "contrived edge cases".
But then
most games are. The average game has: no significant trashing (e.g. excluding Death Cart, Prssn, etc.), has no draw, and has no villages (includes Golem, Tr, etc.), has no +buy, has no cursing, has no discard, has no gainers and has no Alt-VP.
Every game is a statistical fluke. Yet we hit them. Sure, saying I need these 3 specific cards is pretty rare. But saying I need a number of confluences (one of these 7 cards, one of these cards that is in 40% of games, etc.) is not the same as edge casing.
Frankly, unless you want to give me a statistically robust definition for "edge case" you are just pissing around with a No-True-Scotsman fallacy.