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Author Topic: What does it mean for a card to be "powerful"?  (Read 2005 times)

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Awaclus

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What does it mean for a card to be "powerful"?
« on: April 26, 2018, 10:00:28 am »
+5

I think everyone has an intuitive understanding of what makes a card strong, but it's much more difficult to put it in a formula. Here are some ways to determine card strength and reasons why they don't work:

1. How often (top?) players gain the card
This doesn't take into account a scenario in which nobody gains the card, but it makes an impact by merely being present in the kingdom (e.g. Salt the Earth). It also doesn't take into account a scenario in which a card is only very slightly weaker than many other similar cards (e.g. Walled Village), in which case the card in question is not gained in many kingdoms because a slightly stronger card is gained instead. It also can't tell the difference between a low-impact card that you buy almost every time because it has a low opportunity cost (e.g. Pearl Diver) and a card that you buy almost every time because it has a huge impact (e.g. Goons).

2. How often do (top?) players win with the card vs. without the card
When a card is very strong, top players might have a very high win rate without the card because the weaker opponent will buy the card every time, whereas the top player is better able to consider the rare situation in which the card is not worth buying. The reverse is true for very weak cards. On the other hand, if we consider the entire player base instead of just top players, strong cards that don't have a high skill requirement (e.g. Rebuild) will appear higher while strong cards that do have a high skill requirement (e.g. Bridge) will appear lower. Much like 1), this does not take into account cards that can make an impact by being present even if nobody buys them.

3. If two top players of similar strength play a match where they are and aren't allowed to gain a card, respectively, how big of an advantage will the former have
This addresses all of the previous problems, but introduces a new one: the player who is allowed to buy the card has access to the knowledge that the other player will surely not buy it, which gives them an inherent advantage, partially independently of the card's strength. This also makes self-synergistic cards seem stronger than they really are. In the case of a real match between two real players, as opposed to a thought experiment, it also has the problems that six games is a very low sample size which can result in kingdoms or shuffles favoring one player over the other, and the players might not be giving their best performance at the time of the match even if they are very closely ranked.

Personally, I think that given how difficult it is to objectively measure a card's strength, it might be more important to talk about when to buy the card, and when to consider the card for your kingdom analysis as separate things. How big of an impact it makes in both cases is not so important. For example, Pearl Diver isn't really a very "strong" card, but you can buy it whenever there's nothing better to do, and due to its low cost and spammability, it can make pileout endings easier which is something that you should consider during kingdom analysis. It doesn't make a very big impact in either case, but you're not going to have the thought process "oh Pearl Diver only helps me a tiny little bit here, I guess I'm not going to buy it".

What do you think? Are there any other ways of measuring card strength that actually work?
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JW

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Re: What does it mean for a card to be "powerful"?
« Reply #1 on: April 26, 2018, 10:27:55 am »
+5

3. If two top players of similar strength play a match where they are and aren't allowed to gain a card, respectively, how big of an advantage will the former have
This addresses all of the previous problems, but introduces a new one: the player who is allowed to buy the card has access to the knowledge that the other player will surely not buy it, which gives them an inherent advantage, partially independently of the card's strength. This also makes self-synergistic cards seem stronger than they really are. In the case of a real match between two real players, as opposed to a thought experiment, it also has the problems that six games is a very low sample size which can result in kingdoms or shuffles favoring one player over the other, and the players might not be giving their best performance at the time of the match even if they are very closely ranked.

This definition, but assume that the players play an infinite number of games (varying who is and isn't allowed to gain the card), play equally well on average regardless of whether they're allowed to gain the card or not gain the card, and that the player doesn't know that their opponent isn't allowed to gain the card. Also, gaining the card is probably always allowed for the purpose of ending the game on piles, and the card can't be the Obelisk Museum or Young Witch bane piles for obvious reasons. An actual cage match will be an approximation to that ideal.

Alternately, a strong card is one that Awaclus says is superior to Loan.
« Last Edit: April 26, 2018, 02:11:11 pm by JW »
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samath

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Re: What does it mean for a card to be "powerful"?
« Reply #2 on: April 26, 2018, 10:33:37 am »
+1

In the case of a real match between two real players, as opposed to a thought experiment, it also has the problems that six games is a very low sample size which can result in kingdoms or shuffles favoring one player over the other, and the players might not be giving their best performance at the time of the match even if they are very closely ranked.

Two potential ways to resolve this:
1) Use Judgment Matches to compare two cards. One player is only allowed to gain one of them, and the other player is only allowed to gain the other one. At the beginning of each game, both players simultaneously reveal which card they want access to. If they pick the same card, count that as a win for that card and immediately move on to the next game. Only if they disagree do you actually play the game. This way you could get through a much larger number of games (albeit relying on the players' estimation for most).
2) If you're evaluating a single card, use a bidding for VP mechanism to restrict access to that card. This way, even if you only play the six games, you still get more information from the VP that different players bid. We did something similar with the Bidding for Position Crew Battle on the Discord a few weeks ago.
« Last Edit: April 26, 2018, 03:24:10 pm by samath »
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Re: What does it mean for a card to be "powerful"?
« Reply #3 on: April 26, 2018, 10:47:05 am »
+2

... a scenario in which nobody gains the card, but it makes an impact by merely being present in the kingdom (e.g. Salt the Earth).

That's my experience with Salt the Earth too. Nobody ever gains it, and if one tries to, I slap his hand.
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Re: What does it mean for a card to be "powerful"?
« Reply #4 on: April 26, 2018, 11:11:55 am »
+3

Quote
1. How often (top?) players gain the card

Some cards are powerful, like chapel, but you get full benefit out of a single copy.
It would be silly to say village is more powerful than chapel just because people buy more villages over a game.

---

Also, "power" and "strong" are not really interchangeable, for the purposes of a nitpicky f.ds thread.

Imagine two baseball players. 
1) .350 batting, few home runs
2) .200 batting, lots of home runs

I'd call the second player more powerful, but I'd rather have the first player on my team.

---

That said, raw power of a dominion card could be determined by it's peak use.  What is the most absurd thing that it can do? 
Page thus ranks very highly for me, because complete immunity plus infinite actions is quite absurd compared to many other cards. 
The fact that it takes a lot of time to get rolling doesn't factor into my definition.

Granted, this isn't a useful definition of "power"
« Last Edit: April 26, 2018, 11:27:22 am by weesh »
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trivialknot

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Re: What does it mean for a card to be "powerful"?
« Reply #5 on: April 26, 2018, 12:11:19 pm »
0

My intuitive definition of "powerful" is something that makes you change a lot of decisions.  Pearl Diver is not very powerful because even if you gain one in almost every game, it only really changes a few decisions--the choice to get Pearl Diver over nothing.

If we wanted to make this definition into something that can be objectively and practically measured, I propose the following procedure:
1. Take a large number of games between top players.  Calculate the average number of copies of each card gained.
2. Now look at just the games where X is in the kingdom.  Again, calculate average gains for each card.
3. Calculate the "distance" between the percentages calculated in #1 and #2.  The larger the distance, the stronger the card.

A few problems with this procedure:
a) We're trusting top players to make good decisions.
b) You'd need a really large data set.  Possibly impractically large.
c) This ignores decisions that don't involve gaining cards, or gaining the same cards at different times.  Special mention to events.
d) Many cards (e.g. junkers, Cache) force you to gain cards without it necessarily being a "decision", and this might cause their power to be inflated.
e) This would still underestimate the power of e.g. walled village, but I'm okay with this.
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Re: What does it mean for a card to be "powerful"?
« Reply #6 on: April 26, 2018, 12:51:04 pm »
0

Not that card cost equals card strength but .. I wonder how playtesters come up with the costs of cards. Do they just use intuition? Do they use some formula(s)? As far as I know, the only "formula" they follow is don't price card X less than or equal to card Y if card X is strictly better than card Y (using your favorite definition of strictly better).
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Re: What does it mean for a card to be "powerful"?
« Reply #7 on: April 26, 2018, 04:38:09 pm »
+1

Also, gaining the card is probably always allowed for the purpose of ending the game on piles
This is problematic as for some cards (Messenger, Stonemason), the ability to quickly end the game is part of what makes up their strength.
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Re: What does it mean for a card to be "powerful"?
« Reply #8 on: April 26, 2018, 05:30:04 pm »
+2

Geez, there are actually a bunch of factors to consider here.

The way I would define card strength "Council Room stat" style would be to consider the change in win percentage per extra copy of the card you gain over your opponent(s), but giving more weight when closer to the average number of gains for that card across all games. So for Chapel, you care most about the win % per gain over your opponent when you have ~1 Chapel in deck. For Village, you might care most about the win % per extra gain over your opponent(s) when you have 5 Villages. This way you can better get a sense of how good a card like Peddler, Governor, or Magpie is when you win the split. By centering around the average number of gains for the card in question, you can kind of take into account how easy it tends to be to gain the card, as well as how often the card is gained in general, and to put more weight on win percentage changes occurring when say Village is split 6/4 than when it's split 9/1. In weird cases like Stonemason pileouts, this method still considers cards to be stronger as the likelihood of the card being used as part of a pileout increases.

I don't know, what I described above is not exact or anything. I'm just trying to spitball ideas here.
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markusin

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Re: What does it mean for a card to be "powerful"?
« Reply #9 on: April 26, 2018, 05:59:43 pm »
0

Geez, there are actually a bunch of factors to consider here.

The way I would define card strength "Council Room stat" style would be to consider the change in win percentage per extra copy of the card you gain over your opponent(s), but giving more weight when closer to the average number of gains for that card across all games. So for Chapel, you care most about the win % per gain over your opponent when you have ~1 Chapel in deck. For Village, you might care most about the win % per extra gain over your opponent(s) when you have 5 Villages. This way you can better get a sense of how good a card like Peddler, Governor, or Magpie is when you win the split. By centering around the average number of gains for the card in question, you can kind of take into account how easy it tends to be to gain the card, as well as how often the card is gained in general, and to put more weight on win percentage changes occurring when say Village is split 6/4 than when it's split 9/1. In weird cases like Stonemason pileouts, this method still considers cards to be stronger as the likelihood of the card being used as part of a pileout increases.

I don't know, what I described above is not exact or anything. I'm just trying to spitball ideas here.

Okay, actually this needs to consider the average on the largest number of copies of the card in question a player in the game gains. So if a card is usually split 6/4, you give the most weight on the win % per extra gain for the player with 6 copies of the card, I guess accommodating for the fact that having +2 copies over another player is the minimum in that case. When the card is commonly split 7/3, you take into account that +4 copies over another player is the minimum when you have 7 copies of the card.
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Titandrake

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Re: What does it mean for a card to be "powerful"?
« Reply #10 on: April 27, 2018, 02:33:14 am »
+8

My intuition is that a card is powerful if strategy discussion tends to warp around that card. It's hard to not think about Wharf / Cursers / multi-card trashers / non-terminal trashing when thinking about how to approach a board. It's pretty easy to pretend Raider doesn't exist. You usually have to think about Village because it's not only a source of +Actions, it's one of the best sources of +Actions in the game (the +1 Card on Village is actually ridiculously important and getting it for $3 is a bargain.)

Mandarin is usually ignorable. Sure, it becomes very important to consider if Capital in the kingdom, but otherwise it's not a big deal. In contrast, if you drop Capital into a random board, it's usually worth thinking about. So I'd say Capital is stronger than Mandarin.

If neither player buys Familiar, it doesn't mean it's a bad card, it probably means they have an idea for how to counter it in a way that justifies not spending the buys on Potion / Familiar. There was a game I played against Sicomatic a while back, where I considered a HT/Duke slog against an Ambassador deck. Given my shuffles, I would have gone for it if Familiar wasn't on the board. But Familiar was on the board, and the threat of -10 VP from Curses was too big, so I decided to mirror Ambassador, and then neither of us ended up buying a Familiar because it didn't make sense to.

Metrics based on number of gains, win rate with and without, etc. have the issues that Awaclus mentioned. I feel the right approach is to compute those metrics and then treat them as an interesting source of data. If you try to treat them as some ground truth number indicating power level, you're going to run into issues.

I think the funniest one from the CouncilRoom days was that buying Curse was one of the most winning plays you could make, because people only buy Curses when they're winning and have the 3-pile. I suspect most metrics have a failure case like that somewhere.
« Last Edit: April 27, 2018, 04:03:22 am by Titandrake »
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Re: What does it mean for a card to be "powerful"?
« Reply #11 on: April 27, 2018, 09:18:38 am »
+5

Even funnier, I think according to Council Room Curse/Curse was not the worst opening.
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Re: What does it mean for a card to be "powerful"?
« Reply #12 on: April 27, 2018, 09:47:28 am »
0

After thinking about it, I think my proposal above might be statistically feasible.

In ben_king's analysis of councilroom data, there were about 8000 games with each card (just looking at 2P pro rated games with the top 100 players).  The cards only go up to Guilds, so there are 200 kingdom cards.  And that means there are about 400 games with any given pair of cards.  So you could calculate, e.g., gain percentages with a 5% margin of error.  Now you have two vectors: gain percentages in the average game, vs gain percentages in the average game that has card X.  When you calculate the distance between these two vectors, the margin of error is about 0.05*sqrt(200), or about 0.7.  I think this is small enough that you could detect differences between cards.

Another interesting thing you could do is take all the vectors, and perform principal component analysis.  I'd expect the first component to be engine/BM favorability, but the second component, who knows?

If I had the data in the appropriate format, I'd just try the analysis and see what happens.  Probably there are some pathologies in this method, but you never know until you try it.  As it is, I don't know how to access the data, and I imagine there'd be a lot of data prep work.
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Re: What does it mean for a card to be "powerful"?
« Reply #13 on: April 27, 2018, 10:26:48 am »
+1

If I had the data in the appropriate format, I'd just try the analysis and see what happens.  Probably there are some pathologies in this method, but you never know until you try it.  As it is, I don't know how to access the data, and I imagine there'd be a lot of data prep work.

If you'd like, I could send you the data that I have.  It's all just plain text logs though.
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Re: What does it mean for a card to be "powerful"?
« Reply #14 on: April 28, 2018, 11:37:06 am »
0

Even funnier, I think according to Council Room Curse/Curse was not the worst opening.


That literally does not make any sense. Maybe if I knew the kingdom it might make more sense.
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Re: What does it mean for a card to be "powerful"?
« Reply #15 on: April 28, 2018, 01:50:24 pm »
+2

Even funnier, I think according to Council Room Curse/Curse was not the worst opening.


That literally does not make any sense. Maybe if I knew the kingdom it might make more sense.

Probably an artifact of low statistics.
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Re: What does it mean for a card to be "powerful"?
« Reply #16 on: April 28, 2018, 08:40:42 pm »
+3

Even funnier, I think according to Council Room Curse/Curse was not the worst opening.


That literally does not make any sense. Maybe if I knew the kingdom it might make more sense.

Someone who opens Curse/Curse is probably a skilled player doing so as a joke. On the other hand, someone who opens, for example, Festival/Estate is probably a player who hasn't learned that villages aren't great to open with, or that sometimes it's best to buy nothing.

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Re: What does it mean for a card to be "powerful"?
« Reply #17 on: April 28, 2018, 11:51:31 pm »
+1

Someone who opens Curse/Curse is probably a skilled player doing so as a joke.
There's certainly something unusual going on! Maybe they're deliberately handicapping themself in a game with a much weaker player?

I'm struggling to think of even an edge case in which a Curse/Curse opening could be the strongest play, though. Um. Defiled Shrine in a six-player game?
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Re: What does it mean for a card to be "powerful"?
« Reply #18 on: April 29, 2018, 12:01:12 am »
0

Someone who opens Curse/Curse is probably a skilled player doing so as a joke.
There's certainly something unusual going on! Maybe they're deliberately handicapping themself in a game with a much weaker player?

I'm struggling to think of even an edge case in which a Curse/Curse opening could be the strongest play, though. Um. Defiled Shrine in a six-player game?

I'd be satisfied if there were legitimate cases where it's not the absolute worst opening, assuming the player proceeds to play competently after the opening.
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Re: What does it mean for a card to be "powerful"?
« Reply #19 on: April 29, 2018, 01:56:21 am »
0

Someone who opens Curse/Curse is probably a skilled player doing so as a joke.
There's certainly something unusual going on! Maybe they're deliberately handicapping themself in a game with a much weaker player?

I'm struggling to think of even an edge case in which a Curse/Curse opening could be the strongest play, though. Um. Defiled Shrine in a six-player game?

I'd be satisfied if there were legitimate cases where it's not the absolute worst opening, assuming the player proceeds to play competently after the opening.

As a mind game to make the opponent think they're worse?  I once underestimated an opponent because they opened with copper and I didn't think about Duke.
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Re: What does it mean for a card to be "powerful"?
« Reply #20 on: April 29, 2018, 02:54:24 am »
0

Someone who opens Curse/Curse is probably a skilled player doing so as a joke.
There's certainly something unusual going on! Maybe they're deliberately handicapping themself in a game with a much weaker player?

I'm struggling to think of even an edge case in which a Curse/Curse opening could be the strongest play, though. Um. Defiled Shrine in a six-player game?

I'd be satisfied if there were legitimate cases where it's not the absolute worst opening, assuming the player proceeds to play competently after the opening.

In a game with Mountebank, curse/curse will likely be a better opening than estate/estate.
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Re: What does it mean for a card to be "powerful"?
« Reply #21 on: April 29, 2018, 03:35:21 am »
0

Someone who opens Curse/Curse is probably a skilled player doing so as a joke.
There's certainly something unusual going on! Maybe they're deliberately handicapping themself in a game with a much weaker player?

I'm struggling to think of even an edge case in which a Curse/Curse opening could be the strongest play, though. Um. Defiled Shrine in a six-player game?

I'd be satisfied if there were legitimate cases where it's not the absolute worst opening, assuming the player proceeds to play competently after the opening.

In a game with Mountebank, curse/curse will likely be a better opening than estate/estate.

Would Curse/Curse be better than nothing/nothing? Nothing/Curse?
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Re: What does it mean for a card to be "powerful"?
« Reply #22 on: April 29, 2018, 06:45:36 pm »
0

I'd be satisfied if there were legitimate cases where it's not the absolute worst opening, assuming the player proceeds to play competently after the opening.
OK. By that weaker standard, what about buying Curse, Curse, Ambassador, Ambassador on T1-4? There are going to be kingdoms where that will beat people who for some reason ignore Ambassador entirely.
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Re: What does it mean for a card to be "powerful"?
« Reply #23 on: April 29, 2018, 09:18:56 pm »
0

I'd be satisfied if there were legitimate cases where it's not the absolute worst opening, assuming the player proceeds to play competently after the opening.
OK. By that weaker standard, what about buying Curse, Curse, Ambassador, Ambassador on T1-4? There are going to be kingdoms where that will beat people who for some reason ignore Ambassador entirely.

In a discussion about "strong cards", I think we should assume mid to high level play.  Curse is not a strong card; Ambassador is.
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Re: What does it mean for a card to be "powerful"?
« Reply #24 on: April 30, 2018, 02:15:07 pm »
0

1. How often (top?) players gain the card

I suspect if we took the data from the past year of rated games on Shuffle iT and for each card counted the number of games in which a top-100 player gained it on their turn, we'd have a pretty decent estimate of card strength.

Of the concerns raised about this approach, the Pearl Diver one seems the most problematic, but I don't think it's a fatal flaw. You might just have to deal with that amount of noise. You could try adjusting the counts with "opportunity cost weights", but those might be tricky to tune/assign.

In any case, I'd love to be able to try this and I'd be very curious to see, in particular, the difference between Chapel and Pearl Diver.
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Re: What does it mean for a card to be "powerful"?
« Reply #25 on: May 01, 2018, 03:36:19 am »
0

I meant to respond to this...

3. If two top players of similar strength play a match where they are and aren't allowed to gain a card, respectively, how big of an advantage will the former have
This addresses all of the previous problems, but introduces a new one: the player who is allowed to buy the card has access to the knowledge that the other player will surely not buy it, which gives them an inherent advantage, partially independently of the card's strength.
This is certainly not ideal, but I don't think it's a big issue in practice, as the advantage you gain from knowing you get from knowing that will be roughly proportional to the card's strength anyway. At least I cannot think of an example where this would push an otherwise weak card up. Of course there's a 3-pile threat that means that low-cost cards will get rated better, but you can get around that by enforcing that the player who may gain all the cards should play as though their opponent were allowed to gain the card when it comes to pile control.

This also makes self-synergistic cards seem stronger than they really are.
I don't see why. I mean you would first have to define what "how strong they really are" means.

In the case of a real match between two real players, as opposed to a thought experiment, it also has the problems that six games is a very low sample size which can result in kingdoms or shuffles favoring one player over the other, and the players might not be giving their best performance at the time of the match even if they are very closely ranked.
Of course measurements will get more accurate the more data you have. That would be a trait common to all measuring methods.
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Re: What does it mean for a card to be "powerful"?
« Reply #26 on: May 01, 2018, 05:05:36 am »
0

I don't see why. I mean you would first have to define what "how strong they really are" means.

Well, if we take the "impact" metric from trivialknot's thread as an example, Fool's Gold doesn't make a very big impact in many kingdoms because getting 5 Fool's Golds isn't very impressive and you're better off gaining none, and then nobody buys it and it doesn't affect anyone's other buys either (so we would understand that it's a weak card). But also in many kingdoms, if your opponent starts to buy it, you have to buy it too because getting all 10 Fool's Golds is pretty often too good.
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Re: What does it mean for a card to be "powerful"?
« Reply #27 on: May 01, 2018, 10:52:43 am »
+6

To make an observation that's semi-obvious but I've not seen articulated yet in this thread:

The fact it's so hard to pin down exactly what we mean by "good", "powerful", etc. is a big part of why Dominion is such an excellent game.
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Re: What does it mean for a card to be "powerful"?
« Reply #28 on: May 01, 2018, 02:15:26 pm »
0

The fact it's so hard to pin down exactly what we mean by "good", "powerful", etc. is a big part of why Dominion is such an excellent game.

It's true; but it's also what makes such it such a compelling pursuit.
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Re: What does it mean for a card to be "powerful"?
« Reply #29 on: May 01, 2018, 03:16:47 pm »
0

Also, gaining the card is probably always allowed for the purpose of ending the game on piles
This is problematic as for some cards (Messenger, Stonemason), the ability to quickly end the game is part of what makes up their strength.

That's a good point. Let's use Dan Brooks' recent turn 3 victory as an example to show the rationale for and potential pitfalls of this guideline: http://forum.dominionstrategy.com/index.php?topic=11060.msg755449#msg755449

Using Stonemason's on-gain ability is essential to Dan's strategy. But he also needs to buy out the Trade Routes to end the game. So in a "Dan can't buy Trade Route" cage match game, he wouldn't have been able to pull of the same win. Which wouldn't indicate anything about the strength of Trade Route, just that it happened to be a pile that could get bought out to end the game on a win. So presumably the rule for Stonemason would be something like "gaining Stonemason is allowed for the purpose of ending the game on piles, but using the over-pay is not". Or buying Messenger on the first buy of a turn would only be allowed if the game could be won without using the on-gain ability. The idea is not to artificially restrict paths to victory but to avoid having the abilities of the particular card come into play.
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Re: What does it mean for a card to be "powerful"?
« Reply #30 on: May 02, 2018, 12:54:51 am »
0

Also, gaining the card is probably always allowed for the purpose of ending the game on piles
This is problematic as for some cards (Messenger, Stonemason), the ability to quickly end the game is part of what makes up their strength.

That's a good point. Let's use Dan Brooks' recent turn 3 victory as an example to show the rationale for and potential pitfalls of this guideline: http://forum.dominionstrategy.com/index.php?topic=11060.msg755449#msg755449

Using Stonemason's on-gain ability is essential to Dan's strategy. But he also needs to buy out the Trade Routes to end the game. So in a "Dan can't buy Trade Route" cage match game, he wouldn't have been able to pull of the same win. Which wouldn't indicate anything about the strength of Trade Route, just that it happened to be a pile that could get bought out to end the game on a win. So presumably the rule for Stonemason would be something like "gaining Stonemason is allowed for the purpose of ending the game on piles, but using the over-pay is not". Or buying Messenger on the first buy of a turn would only be allowed if the game could be won without using the on-gain ability. The idea is not to artificially restrict paths to victory but to avoid having the abilities of the particular card come into play.
I disagree that it wouldn't indicate anything about the strength of Trade Route. Trade Route is a $3 action, and you need that here to pull off the win. Restricting card "abilities" is super artificial here because cost is also a card ability. It is easier to pile out with Poor House because it only costs $1. It's arbitrary to describe Forum's +buy as a card ability (though it's essentially just "this doesn't cost a buy") and not take Poor House's $1 as a card ability.

It's super rare for that particular ability of Trade Route to be important (partly because so many other cards have it too), but that doesn't mean it's not part of what determines the strength of the card, just that it's a very very minor factor that matters in maybe 0.1% of games.
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Re: What does it mean for a card to be "powerful"?
« Reply #31 on: May 02, 2018, 12:59:40 am »
0

I don't see why. I mean you would first have to define what "how strong they really are" means.

Well, if we take the "impact" metric from trivialknot's thread as an example, Fool's Gold doesn't make a very big impact in many kingdoms because getting 5 Fool's Golds isn't very impressive and you're better off gaining none, and then nobody buys it and it doesn't affect anyone's other buys either (so we would understand that it's a weak card). But also in many kingdoms, if your opponent starts to buy it, you have to buy it too because getting all 10 Fool's Golds is pretty often too good.
I don't think the impact metric says all about card strength though. If getting all Fool's Golds is too good, then you have to build your deck so that it can accomodate some Fool's Golds in case your opponent goes for them and you need to get some. Because if Fool's Gold is better for them and they can force you to get some, then that's an advantage for them. So it impacts the game even if it isn't bought.

That is assuming that your assessment above of Fool's Gold's strength is correct. I think a lot of the time it isn't super important to prevent your opponent from getting all the Fool's Golds.
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Re: What does it mean for a card to be "powerful"?
« Reply #32 on: May 02, 2018, 01:05:22 am »
0

This doesn't take into account a scenario in which nobody gains the card, but it makes an impact by merely being present in the kingdom (e.g. Salt the Earth).

Yeah this basically doesn't come up. Salt is very weak.

But solutions.

It really comes down to usage frequency. Any time Governor is on the board, you basically have to incorporate it. Same with Goons, or Page, or Peasant, etc. And thus those are top tier cards. The less this is true, the less strong the card. There can be cards with a seemingly weak effect (Dungeon for example) that are absolutely critical to win with. Dungeon increases cycling and start of turn consistency, and despite the lack of flashiness that a card like Goons has, Dungeon has somehow managed to be a very strong card in its own right, simply due to the frequency with which I open it with.
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Re: What does it mean for a card to be "powerful"?
« Reply #33 on: May 03, 2018, 02:17:19 pm »
0

It really comes down to usage frequency.

By 'frequency', do you mean 'at least once', or actual frequency? I might only use (i.e. play) Page once in a game, but it's still a very strong card. I might only use Chapel 2 or 3 times in a game, but it's very strong.

And by 'usage' do you mean 'play', or 'gain', or what? I may gain IGGs, without ever really needing to "use" them, or even wanting them in my deck altogether. And there's gaining by choice (Witch) vs. gaining not by choice (Curse) -- do you mean the former?

There are still flaws with this though. I use Silver a lot -- but often just as a stepping stone to get to other things. Oftentimes I wouldn't use it if I didn't have to. I use Potion a lot in Scrying Pool games. I use Gladiator to get to Fortune - even if I don't necessarily want the Gladiator. For that matter, are split piles by definition top half stronger than bottom half, cus (barring edge cases) it's guaranteed that there are more games in which a card from the top half is gained but not the bottom half than there are vice versa?

How would you do non supply cards? Tournament (and Province?) is strong because of Followers and Trusty Steed, but how would you handle the Prizes?

How would you do Knights/Ruins/Castles?

How does this definition handle cards from the Black Market deck? Rats is (arguably) stronger if it came from the BM deck; Magpie is weaker. Why?

If you do mean something like 'percentage of games this card is in in which you gain the card by choice at least once in the game' then, off the top of my head, Butcher comes to mind (Dungeon in your case). There are probably fewer games that I ignore Butcher than there are games where I ignore Cultist and Monty. But I'd still say Cultist and Monty are "stronger" -- air quotes, because as this thread suggests, I don't really know what makes a card strong.
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Re: What does it mean for a card to be "powerful"?
« Reply #34 on: May 03, 2018, 02:55:00 pm »
+1

Nuclear weapons are pretty weak.
The top players don't use them.

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Re: What does it mean for a card to be "powerful"?
« Reply #35 on: May 03, 2018, 03:00:02 pm »
0

Nuclear weapons are pretty weak.
The top players don't use them.

Are you implying that the United States is not a top player?
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Re: What does it mean for a card to be "powerful"?
« Reply #36 on: May 03, 2018, 03:33:40 pm »
0

It really comes down to usage frequency.
There are still flaws with this though. I use Silver a lot -- but often just as a stepping stone to get to other things. Oftentimes I wouldn't use it if I didn't have to. I use Potion a lot in Scrying Pool games. I use Gladiator to get to Fortune - even if I don't necessarily want the Gladiator. For that matter, are split piles by definition top half stronger than bottom half, cus (barring edge cases) it's guaranteed that there are more games in which a card from the top half is gained but not the bottom half than there are vice versa?

This actually sounds like an argument for Silver being a good card.
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Re: What does it mean for a card to be "powerful"?
« Reply #37 on: May 03, 2018, 03:43:32 pm »
0

If you do mean something like 'percentage of games this card is in in which you gain the card by choice at least once in the game' then, off the top of my head, Butcher comes to mind (Dungeon in your case). There are probably fewer games that I ignore Butcher than there are games where I ignore Cultist and Monty. But I'd still say Cultist and Monty are "stronger" -- air quotes, because as this thread suggests, I don't really know what makes a card strong.

This was what I proposed above, and I still suspect it's better -- because it's both feasible and 'good enough' -- than the other proposed metrics.

Maybe it's not powerful or precise enough to distinguish Mountebank/Cultist/Butcher, but maybe it is! And maybe it would lead to some more interesting discussions about what makes a card 'strong'.
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Re: What does it mean for a card to be "powerful"?
« Reply #38 on: May 03, 2018, 03:58:09 pm »
0

If you do mean something like 'percentage of games this card is in in which you gain the card by choice at least once in the game' then, off the top of my head, Butcher comes to mind (Dungeon in your case). There are probably fewer games that I ignore Butcher than there are games where I ignore Cultist and Monty. But I'd still say Cultist and Monty are "stronger" -- air quotes, because as this thread suggests, I don't really know what makes a card strong.

This was what I proposed above, and I still suspect it's better -- because it's both feasible and 'good enough' -- than the other proposed metrics.

Maybe it's not powerful or precise enough to distinguish Mountebank/Cultist/Butcher, but maybe it is! And maybe it would lead to some more interesting discussions about what makes a card 'strong'.

Perhaps it's the best we've got (for now). In which case Border Village looks like a REALLY strong card .. but maybe it just is? ???
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Re: What does it mean for a card to be "powerful"?
« Reply #39 on: May 03, 2018, 04:38:54 pm »
0

If you do mean something like 'percentage of games this card is in in which you gain the card by choice at least once in the game' then, off the top of my head, Butcher comes to mind (Dungeon in your case). There are probably fewer games that I ignore Butcher than there are games where I ignore Cultist and Monty. But I'd still say Cultist and Monty are "stronger" -- air quotes, because as this thread suggests, I don't really know what makes a card strong.

This was what I proposed above, and I still suspect it's better -- because it's both feasible and 'good enough' -- than the other proposed metrics.

Maybe it's not powerful or precise enough to distinguish Mountebank/Cultist/Butcher, but maybe it is! And maybe it would lead to some more interesting discussions about what makes a card 'strong'.

Perhaps it's the best we've got (for now). In which case Border Village looks like a REALLY strong card .. but maybe it just is? ???
I think we can do better. Two things that come to mind are measuring how often one "safely" ignores the card, and how often it makes the difference in a win. We can approximate those respectively by: percentage of games with the card where the loser gains it by choice and the winner doesn't, and percentage of games with the card where the winner gains it by choice and the loser doesn't (the third category to make this add to 100% is games with the card where both players gain it).

More generally, I think we could be looking at which events correlate with winning the game: gaining a card at all, gaining more copies than the opponent, playing the card more often than the opponent, etc. We might end up with a "power" measurement that includes a bunch of metrics, or even finding numbers to back up intuitive statements like: Chapel is most powerful in singles but Scrying Pool is most powerful in stacks.
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Re: What does it mean for a card to be "powerful"?
« Reply #40 on: May 03, 2018, 06:38:29 pm »
+8

For reference, here are some links to card rankings generated by statistical analysis:

1. How often top players gain the card
2. Win rates conditional on gaining the card
3. How much the presence of a card affects gain percentages of all cards
4. How much player skill correlates with gaining the card
5. How hard it is to predict the winner in the presence of a card

Numbers 1 and 2 are the same as ideas that Awaclus proposed in the OP, and they indeed have the problems that Awaclus mentioned.  Awaclus' third proposal is to play games where one player is banned from gaining the card, but as he said you can't really perform statistical analysis because you'd have to play hundreds or thousands of games.  Basically, Awaclus knows what he is talking about.

Number 3 is the analysis that I proposed, and I personally think it works well, although it overrates things like junkers and copper gainers.

Numbers 4 and 5 aren't attempts to measure card strength, but are nonetheless interesting.  Number 4 mostly shows how overrated or underrated cards are by weaker players (at least they were in 2014).  Number 5 shows how effectively a given card separates strong and weak players.
« Last Edit: May 03, 2018, 06:41:14 pm by trivialknot »
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Re: What does it mean for a card to be "powerful"?
« Reply #41 on: May 04, 2018, 03:56:27 pm »
0

For reference, here are some links to card rankings generated by statistical analysis:

1. How often top players gain the card
2. Win rates conditional on gaining the card
3. How much the presence of a card affects gain percentages of all cards
4. How much player skill correlates with gaining the card
5. How hard it is to predict the winner in the presence of a card

Numbers 1 and 2 are the same as ideas that Awaclus proposed in the OP, and they indeed have the problems that Awaclus mentioned.  Awaclus' third proposal is to play games where one player is banned from gaining the card, but as he said you can't really perform statistical analysis because you'd have to play hundreds or thousands of games.  Basically, Awaclus knows what he is talking about.

Number 3 is the analysis that I proposed, and I personally think it works well, although it overrates things like junkers and copper gainers.

Numbers 4 and 5 aren't attempts to measure card strength, but are nonetheless interesting.  Number 4 mostly shows how overrated or underrated cards are by weaker players (at least they were in 2014).  Number 5 shows how effectively a given card separates strong and weak players.

Cool. Thanks for compiling those links.

RankCard% games gained# games gained# games available
1Tournament95.4%74677825
2Governor93.0%24172598
3Border Village89.3%67087512
4Fishing Village89.2%70067854
5Wharf89.0%70927965
6Forager88.7%70947999
7Goons88.4%70537979
8Masquerade87.7%70318015
9Chapel87.6%84089596
10Ironmonger87.2%69477970
11Mountebank86.9%67577779
12Ambassador83.6%67578078
13Squire83.4%64527732
14Hamlet83.2%65647892
15Plaza82.7%59537196
16Warehouse82.6%66748084
17Hunting Party81.1%62467705
18Candlestick Maker80.9%58597242
19King's Court80.8%62767769
20Black Market80.6%27293386
21Minion80.1%62527807
22Wandering Minstrel79.4%62157828
23Crossroads79.2%61127713
24Swindler79.1%64478147
25Cultist79.0%61037730

I think it's reasonable to conclude from this (old) data that King's Court suffers on this ranking based on its high cost; while Crossroads, Squire and Hamlet benefit from their low cost. The weirdest outliers to me here are Forager and Warehouse, but maybe this is an accurate reflection of the time? Or maybe 3-cost cards get a similar boost to 2-cost cards.

It's hard to judge this list while no longer being in the context that generated the data.
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Re: What does it mean for a card to be "powerful"?
« Reply #42 on: May 05, 2018, 01:31:15 pm »
0

It really comes down to usage frequency.

By 'frequency', do you mean 'at least once', or actual frequency? I might only use (i.e. play) Page once in a game, but it's still a very strong card. I might only use Chapel 2 or 3 times in a game, but it's very strong.

And by 'usage' do you mean 'play', or 'gain', or what? I may gain IGGs, without ever really needing to "use" them, or even wanting them in my deck altogether. And there's gaining by choice (Witch) vs. gaining not by choice (Curse) -- do you mean the former?

There are still flaws with this though. I use Silver a lot -- but often just as a stepping stone to get to other things. Oftentimes I wouldn't use it if I didn't have to. I use Potion a lot in Scrying Pool games. I use Gladiator to get to Fortune - even if I don't necessarily want the Gladiator. For that matter, are split piles by definition top half stronger than bottom half, cus (barring edge cases) it's guaranteed that there are more games in which a card from the top half is gained but not the bottom half than there are vice versa?

How would you do non supply cards? Tournament (and Province?) is strong because of Followers and Trusty Steed, but how would you handle the Prizes?

How would you do Knights/Ruins/Castles?

How does this definition handle cards from the Black Market deck? Rats is (arguably) stronger if it came from the BM deck; Magpie is weaker. Why?

If you do mean something like 'percentage of games this card is in in which you gain the card by choice at least once in the game' then, off the top of my head, Butcher comes to mind (Dungeon in your case). There are probably fewer games that I ignore Butcher than there are games where I ignore Cultist and Monty. But I'd still say Cultist and Monty are "stronger" -- air quotes, because as this thread suggests, I don't really know what makes a card strong.

You're worrying too much about the specifics.

When I say usage frequency, I just mean it comes down to how often you pick it up.

Dominion is a squinty game, it's okay to squint. With something like Page, that you pick it up every game nearly speaks to the power of Champion and the other stuff. You're not picking up Page for Page, but that doesn't make Page weak by any means.

You are right that Silver is picked up a lot, merely as a stepping stone, but it is still picked up a decent amount of times, and is thus a decent opener. But there are plenty of games where you don't in fact pick up a Silver. The point is, you do have to get a Silver sometimes to get to other cards, and if you do have to use a Silver, hey Silver is decent sometimes. It's better than people say it is, because it does accelerate your deck. If it doesn't, that means there's a better route, whether that be a Steward, or an Ironmonger, etc. You say you'd never pick up Silver if you didn't have to, and I agree. I also wouldn't use any other trasher besides Donate if I didn't have to. We're arguing all of the boards, not the best case scenarios.

Black Market, who cares. Completely different rule. You're picking up Black Market every time because it can supply something to you that is ordinarily not in the Kingdom, whatever that might be. You don't worry about non-supply cards, those come packaged with whatever card you can in fact purchase. Knights? Yeah, I pick those up a lot. Don't worry about specific Knights, that there are Knights and you often pick them up is good enough!
« Last Edit: May 05, 2018, 01:35:58 pm by Seprix »
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Re: What does it mean for a card to be "powerful"?
« Reply #43 on: May 05, 2018, 01:37:55 pm »
+1

For reference, here are some links to card rankings generated by statistical analysis:

1. How often top players gain the card
2. Win rates conditional on gaining the card
3. How much the presence of a card affects gain percentages of all cards
4. How much player skill correlates with gaining the card
5. How hard it is to predict the winner in the presence of a card

Numbers 1 and 2 are the same as ideas that Awaclus proposed in the OP, and they indeed have the problems that Awaclus mentioned.  Awaclus' third proposal is to play games where one player is banned from gaining the card, but as he said you can't really perform statistical analysis because you'd have to play hundreds or thousands of games.  Basically, Awaclus knows what he is talking about.

Number 3 is the analysis that I proposed, and I personally think it works well, although it overrates things like junkers and copper gainers.

Numbers 4 and 5 aren't attempts to measure card strength, but are nonetheless interesting.  Number 4 mostly shows how overrated or underrated cards are by weaker players (at least they were in 2014).  Number 5 shows how effectively a given card separates strong and weak players.

Thanks for posting all of this, but it's all also pretty much moot information nowadays. New expansions, new ideas, heck, the entire concept of engine building has improved even further. I would love to have this information compiled today, and see what the numbers say.
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Re: What does it mean for a card to be "powerful"?
« Reply #44 on: May 05, 2018, 03:34:06 pm »
0


I think it's reasonable to conclude from this (old) data that King's Court suffers on this ranking based on its high cost; while Crossroads, Squire and Hamlet benefit from their low cost. The weirdest outliers to me here are Forager and Warehouse, but maybe this is an accurate reflection of the time? Or maybe 3-cost cards get a similar boost to 2-cost cards.

It's hard to judge this list while no longer being in the context that generated the data.

Forager is pretty splashable in like every deck. Pre-adventures, it was almost never a question of "do I want Forager?" but "how many extra Foragers do I want?"
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Re: What does it mean for a card to be "powerful"?
« Reply #45 on: May 11, 2018, 06:46:22 am »
+2

Rats is (arguably) stronger if it came from the BM deck; Magpie is weaker. Why?

Rats is stronger because you don't gain a copy of it.
Magpie is weaker because you don't gain a copy of it.

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crj

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Re: What does it mean for a card to be "powerful"?
« Reply #46 on: May 11, 2018, 09:25:07 am »
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Rats is pretty situational, but if you're using it properly then gaining $4 cards is a strength, not a weakness.

What would be the right cost for a straightforward +1 Card, +1 Action, trash a card? Comparing with Ratcatcher, Lookout and Junk Dealer it's pretty clear it couldn't cost more than $4, and maybe even $3 would be OK.
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ipofanes

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Re: What does it mean for a card to be "powerful"?
« Reply #47 on: May 11, 2018, 09:50:53 am »
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I think it's backwards: If you cannot use the aspect it's a $4 card, the gaining copy aspect is a weakness. If there's no trash for benefit nor remodel type cards in the kingdom, it's hard to justify them. Hitting more consistently with Doctor or drawing them with a string of Scrying Pool draws should not be enough reason. There is a crazy combo with Training and Dominate, and I haven't tried Advance with them. Rats from Black Market are purchased very often, I would guess.
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