Evaluating thinning cards

When trying to evaluate a card like King of Beggars, numbers 13 for 10, 13 for 6 and 20 for 10 all get mentioned. One of those doesn't mean much, while the other two are reasonable estimates but mean completely different things, and there's a lot of uncertainty about which is which and why. Shinmiri has often talked about it since the last patch, and this post is, unsurprisingly, basically saying the same things, but I hope writing it down systematically and in one place could help with understanding it. And it's not like I'm using my degree for anything better atm anyway.

tl;dr: As a starting point most thinning cards can be compared to a normal card with the same provisions that's worth ~7 extra points, adjusted for the consistency they give you, or the consistency they cost you. For cards like Mage Assassin that are part of a specific combo just use the usual trick of Blightmaker + Mage Assassin = 7 + 4 points for 6 + 4 – 4 provisions instead.

10 for 9 Roach

Say you're building a deck and it's going great. The deck is extremely consistent and thins very well, and at the end of the game you'll usually expect to play everything except for say, 4 4p bronzes each worth 7 points. This is hardly the norm (NR lol), but some decks come close (obviously so with Calveit), and it will make the math easy. Everything written for a while will assume this ideal deck with 7 point bronzes which almost always draws its cards etc., and we'll try to compare it to other realistic scenarios later.

Anyway, your deck is 24 cards with a single 9p spot left, and through some bad oversight on your part you've narrowed it down to two choices: Roach, and a proactive 10 for 9.
We've already assumed that the deck is consistent, so adding or removing Roach doesn't affect that; the only question is how many points will your deck play with Roach compared to the deck with the 10/9 instead.

The answer, as spoiled by the title, is that they're exactly the same.
At the end of the game, the non-Roach deck has played its 10/9 and has 4 bronzes left, the Roach deck had Roach summon for 3 points, and has 3 bronzes left, which means there was an extra 7 point bronze played.

In this case, Roach was exactly the same points as playing a 10/9 gold from hand, which makes it very much comparable to such a card (but note that even in this simplified scenario the point distribution, in particular points per round, probably differs).

The same math applies to cards like Fercart* which play and draw you a card, except it's even more obvious, since you can literally watch them draw you one of those remaining 4p bronzes. This makes Fercart comparable to a 10/7 from hand, even without extra synergies, which is why people play him.

(* In fact, it applies to many, many different cards. This is actually bad, but we'll discuss it later.)

3 for 5? Roach

Since your Roach and non-Roach deck have the same number of points, you upload and write guides for both. On Turn 1 you always open with a specific 11/8. T2, the Roach deck plays a 7/4 bronze, while the non-Roach deck plays that nifty 10/9 it replaces Roach with, which as expected amounts to exactly the same 21 points by T2.

But you realize there's a third option. Instead of replacing Roach with a gold, you could replace it with one of those forgettable 7/4 bronzes. This frees up 5 provisions and you use them to upgrade that 11/8 opener into a 14/13 one.

Well 14 is exactly the same points T1 as the Roach deck, and the rest of the game is same too. The new deck has an extra bronze that never gets played, but that doesn't change anything. All three of your netdecks have the same points already by T2; Gwent is finally balanced.

Here we see that an 11/8 gold with Roach in deck is point equivalent to a 14/13 gold without it. In this case, you might as well say that your opening 11/8 gold is actually a 14/13. In a more likely scenario you don't have that rigid of a game plan, and Roach comes out of your deck whenever you play your first gold, whatever it might be. You could say that 3 points are simply added to the entire deck (as if by a leader ability), and you spent 5 provisions to buy them. Since you expect 5 extra provisions to be worth more than 3 points, that doesn't sound particularly convincing. Fercart on the other hand costs 3 extra provisions and ads 3+ extra points to a card, which makes it considerable.

Both of these perspectives on Roach are reasonable, usable, and equivalent, but the numbers in 10 for 9 mean different thing than those in 3 for 5. The first compares it to a card from hand, the second is more like switching to a leader with 3 more points but 5 provisions less. The first is probably more intuitive and only compares cards with the same provision cost, but it requires you to pick a particular fixed value for those 4p cards which would otherwise remain unplayed. The second requires you to believe that extra provisions convert to extra points easily and 1:1, which isn't realistic either.

tl;dr: You can either add whatever points your worst cards play for to compare a thinning card to a standalone one, or subtract 4 provisions to see how much it costs you to add its nominal points to the deck. That is, in this model scenario you can, otherwise the values need to be adjusted.

I'll mostly stick to the first method for the rest of the post to avoid confusion, but everything else remains the same.

Combos and ?? for 4 Mage Assassin

We've seen that having an 11/8 gold with Roach plays for the same total points as a 14/13 one without it, and this is the principle people use when they call Blightmaker+Assassin an 11/6 (instead of 11 for 10) or Simlas into rebukes as a whatever for 12+5-4+5-4 = 14 etc. (If you're not familiar with the concept, just think of two toy decks like above, with cards sorted by Calveit and all 4p's having the same value, and one deck plays the unbuffed witcher trio, while the other replaces it with a 9 for 13 gold and two 4p bronzes; you'll see that both have exactly the same, underwhelming points.)

Since Assassin itself thins from the deck for (often) 4 points, if you applied the Roach math from before you'd call it an 11/4 standalone or 4 free points for 0 extra provisions. Well obviously that's not a good idea: if you replaced the Assassin with an 11/4 standalone, then you'd be left with a 7/6 Blightmaker in your deck. If you really want to compare Assassin to a 4p bronze from hand, you need to do something like "11 – (the opportunity cost of a 7 for 6) points". Or just stick to 11 for 6 for the combo, it works fine.

King of Beggars is actually similar. Most current meta decks don't play KOB, they play KOB+Savolla, and playing Savolla is far from free. If Savolla is the only thing that pulls it, it's probably better to just call the entire combo an X/15 instead of guessing what Y = 13 + 7? – (opportunity cost of Savolla) in a Y/10 is supposed to be. (Of course, knowing that Y is absurdly too large is important from the balancing perspective. Otherwise you end up nerfing Blightmaker instead of Mage Assassin.)

Everything wrong with the math above (aka why Decree isn't 7 for 9)

The assumptions we started with (nothing bricks, everything except 4p's played) is basically what every deck aims for, but most don't achieve it commonly, let alone regularly. In the simplified scenario the thinning done by Roach, Fercart, Milva, Decree, Amphibious Assault and Ciri Dash all evaluate to a total of 7 extra points added to their base value throughout the game, but obviously those effects are vastly different, and the confounding effects for real world decks are countless.

Most importantly by far, what was meant by thinning here here has nothing to do with consistency.
There's a big difference between Maddoc, which usually thins itself seamlessly in Round 1, and KOB or Milva, which probably actively clog and hurt your draws for the entire game. Even better, there's cards like Riders which still see play at their meager 8/6, but they never force you to mulligan a high provision card. Finally you have tutors, with some of the worst baselines (except for AA). Yes, Decree is actually 7 for 9 if you just draw your golds, but Naglfar into an undrawn Regis can easily be 10 more points than what a non-tutor 9 prov card would have gotten you there.

The effects of this – whether positive or negative – get more amplified the less consistent the rest of the deck is, and the obvious question is how to evaluate them. Certainly for tutors it might not make sense to even try with a numerical value. You either need them to make the deck work or you don't. Otherwise, X+7 does serve as a starting point. KOB definitely hurts your draws, so it's worse than 20 for 10 spender. How much worse? I can't offer a good way to gauge that, unfortunately, but clearly not nearly enough in this case. It's not like you can easily say how much Alzur's Thunder plays for, but you do start at 5 for 5 and extrapolate from there, and you need a sensible number to start with cards like KOB too.

Addendum: Echo cards and 12 for 8.5?! Amphibious Assault

Putting a 13 prov AA into your deck and drawing it early gives you up to 2×5 baseline points + it thins by one, at worst letting you play an extra 7/4 bronze. Effectively, it's the same total points as playing a 17/13 instead, but realistically it's even better than that. Of course, AA plays from hand twice, so instead of comparing it to a single card from hand, you might want to compare it to two. Here's a way to do that.

17/13 gold (which is comparable to AA) and a bronze can be replaced with with two 8.5 prov golds. 17/13 and a 7/4 are 24 points (i.e. same as playing two "12 for 4" with AA), so those two 8.5 prov golds would need to be 12 points to be the same. 17/13 or 2 x 12/8.5 from hand are the same thing, and both significantly underestimate the true potential of AA in NR. Card's good. (Of course it's possible to only draw AA late, which loses you 5 points/a tutoring opportunity, or to "waste" points on tutoring provisions that you would have drawn anyway, but still.)