On the original topic, I can't find the threads right now but I've seen the discussion come up several times before on whether +coin or +card is worth more. +card is much more valuable on a non-terminal, but it's very close on terminal cards. Nonetheless, official cards consistently show that +coin is worth more in these situations.
on a terminal, without non-terminals, that makes no sense.
So...Smithy is better than Laboratory, then?
what? laboratory is terminal now?
look at it this way: if no way to gain extra actions exists, then the value of a +cards terminal is exactly equal to the amount of $ you can produce with those cards from treasures. the value of a +$ terminal is exactly equal to the $ it gives. so if the average value of a card in your deck is $1 or higher, then drawing is as good or better.
now, as we all know, in order to buy a province with a random hand of 5 you need an average card value of 1.6, which is
much higher than one. if your deck is worth an average of 1.6 outside the smithy, playing smithy will be the same as playing a terminal that gives you +$4.8, much better than +$3. even after the first reshuffle in a Smithy-Silver opening, the average non-smithy card in your deck is worth about $.8, so opening that over a hypothetical terminal gold costs you only $.6 in expected immediate return.
or we can look at the average value of the rest of your deck needed to buy a province. with terminal gold, (Which I'm gonna call Profiteer from now on) you have 4 other cards to pick up that money from, but you only need $5. so you need $5/4 per card, or $1.25. whereas, with Smithy, you have 7 cards to work with, but you need $8. so you need $8/7 per card, or $1.14. hence Smithy can get provinces faster because it doesn't need as strong a deck. or we can look at how much quickly they can enable gold, since that's a pretty huge deal. BM is all about snowballing up, so early gold is important and if Profiteer can get it faster then there's something to be said for it even if Smithy is better later. so for Profiteer we have 4 other cards and need $3. so we need an average of $3/4, or $.75 per card. not hard to do. however, Smithy gets 7 cards to work with and need $6. that's $6/7. that's $.85. so in that case, early in the game, again we find that Profiteer is better than Smithy.
but if we consult the province numbers above, we realize that it doesn't matter that much, since the Smithy deck doesn't
need to get going as fast as the Profiteer does. it can fall a bit behind, picking up a silver while Profiteer gets a gold, because it doesn't need to be nearly as strong to get provinces.
also, the comparisons of +card to +$ terminals like Wharf-Merchant Ship are inherently flawed because the +card ones are usually
way better. Wharf-Ship is a somewhat flawed comparison anyway in that, as has been pointed out, the second half of wharf is actually non-terminal, and as has been discussed, +cards on non-terminals is a lot better. but the Moat-Duchess comparison is also flawed, in that you're completely ignoring duchess's ability to be acquired, for free, with no spent buy. of course it's gonna have a weaker ability than moat, because you can just pick it up for free whenever you buy a duchy. the horse trader comparison is also flawed because it has a) the +buy thing, which is not as irrelevant as you claim,
and b) the reaction, which is pretty useful in its own right. the mandarin also reracks your money (which is at least $5) when you buy it. all of these cards have upsides that you're completely ignoring to make your comparisons. upsides that are often relevant. unfortunately, due to a lack of actual direct comparisons, there is no direct way to test unless someone who knows more about programming than me can, for instance, set up a game with Steward where one bot always chooses +$2 and one always chooses +2 cards.
