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Messages - trivialknot

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Variants and Fan Cards / Re: Kudasai's Random Dominion Cards
« on: June 26, 2018, 03:20:18 pm »
I definitely don't understand what Hunted does at cleanup.  It says,
1. If you have at least $3 unspent,
2. you may discard any cards on this.
3. Then you may remove a token from this.
4. If you don't, return this and all cards on it to their piles.

It's ambiguous whether 3 is contingent on 1, or if it's not contingent on anything.  I don't know whether the "if you don't" on step 4 is referring to step 3.

And is heavy-Idol really that strong?  I'm so skeptical.  I really want to try it.   :D

I guess I feel like, in terms of testing cards, what's the difference between 2 players and 3+ players? Well, if a card is great in multiples, then you'll want to be sure it's not crazy if you can get 6 copies of it, like you might in a 2-player game. I think the only cards in Nocturne that fit the bill are Idol and Werewolf, though you could make an argument for Vampire. Idol is admittedly way stronger than my group thought it was, though I don't think it's too strong. And we actually discovered that it was strong after Nocturne testing was over when a new player joined our games and went for a heavy-Idol strategy. So we got to see that play out despite it not being a 2-player game.
The blog has a pretty great series on strategy in 2P vs 3P+ games, and I would say that "you can get more copies of cards" is rather oversimplifying the matter.  If Dominion were mostly playtested with 3P+, the thing I'd worry about is if a card leads to degenerate engine strategy that usually isn't feasible in 3P+, and is particularly unfun in 2P.  So, something like Possession.

But I'm not especially worried, given that apparently the only recent set tested without many 2P games was Nocturne, and Nocturne is solid.  In fact, the one card that DXV seemed to agree has problems is Fool, because it plays too slowly--and arguably this is only a problem in 3P+.

Dominion Articles / Re: Settlers/Bustling Village
« on: June 12, 2018, 03:31:42 pm »
You should find and replace "Border Village" with "Bustling Village".

I find that in some games with copper trashing, you still use Settlers to pick up copper early on.  And then later you get Bustling Village and you don't mind that you ran out of coppers, because putting Settlers into hand from discard is already good enough.

Dominion General Discussion / Re: Favorite/least favorite Landmarks?
« on: June 08, 2018, 10:27:54 am »
I like Keep...

Dominion General Discussion / Re: Transmute here?
« on: June 03, 2018, 12:11:23 pm »
Mint creates a problem by leaving you with an estate-dense deck with no good way to trash them.  Aqueduct exacerbates the problem by incentivizing even more early green, especially when players are relying heavily on silver/gold.  Transmute seems like it might help in that situation by offering the only way to trash green.  But it's not very good, because you're adding two *more* junk cards to your deck, and you don't even see the gold until at least 3 shuffles later.

There's a much simpler solution: don't get Mint.

I'd open Royal Seal/Silver, or maybe Merchant Ship comes first.

Dominion General Discussion / Re: Plotting cards with DATA
« on: May 26, 2018, 12:44:59 am »
What proportion of the variance is explained by PCs 1, 2, etc?
For the first ten components: 0.12466628  0.10312049  0.07666992  0.05565225  0.047911  0.04449083  0.03309127  0.02486287  0.02174379  0.02077453

In total, that's 55%, which means it's pretty hard to describe Dominion cards even with 10 dimensions.

Dominion General Discussion / Re: Plotting cards with DATA
« on: May 25, 2018, 09:35:49 pm »
I... don't understand what Component 1/2/3/4 mean here.  Could you give a brief explanation?
Principal Component Analysis (PCA) is a standard data analysis technique, but it's hard to intuitively understand.  Basically, it tries to describe data using a small number of dimensions.  If your data is spread more or less along a straight line, then the location along that line will be the first component.  If your data is spread more or less along a flat plane, then the location within that plane will be the first two components.

To give an example, suppose I had a survey to ask people about politics.  There are 10 questions, and the answer to each question is a number 1-5.  Thus each person can be placed within a 10-dimensional space.  But I could apply PCA to reduce it to just two dimensions.  PCA won't really tell you what the dimensions mean, but you might look at the data and say, "this first component looks like the left/right spectrum and the second component is the libertarian/authoritarian spectrum."

The same applies here.  PCA generates components that seem to be meaningful, but it won't tell you exactly what the meaning is.  When I say component 1 is "villages vs terminals", that's just my subjective judgment based on looking at the graphs.

Dominion General Discussion / Re: Plotting cards with DATA
« on: May 25, 2018, 01:58:24 pm »
I found a package that adjusts the positions of the labels to overlap less often.  The images are updated, although they may not refresh right away on your browser.  Thanks for the feedback!

Dominion General Discussion / Re: Plotting cards with DATA
« on: May 25, 2018, 11:25:23 am »
Could you make the pictures larger so that the labels are not all on top of each other? It's very hard to read the names of the cards now.
I can make the pictures larger relative to the text, but at some point the graphs just won't fit on mobile screens, and the text will be too small, and still overlapping anyways.  I'll look into solutions, and the images may be updated retroactively.

trivialknot suggests "cards that are best in thin decks" but that doesn't match my understanding of Thief and Bureaucrat, which are among the most negative in component 3. I can't think of a card property that is most exhibited by the pair of cards Thief and Outpost. They both often gain you mediocre cards?
Thief is usually terrible, but one of the few effective use cases is when your opponent has trashed down with e.g. Chapel, and is trying to build up with Silver.  Bureaucrat is also usually terrible, but might be good for injecting payoff in a heavily thinned deck.  Outpost is also best in a thin engine, because that increases the chances that the extra turn kicks off.  These three examples make a lot of sense to me, although I admit that some of the cards that are negative in component 3 appear to just be weak terminals, like Duchess or Navigator.

Dominion General Discussion / Re: Plotting cards with DATA
« on: May 24, 2018, 04:54:56 pm »
[reserved for requests]

Dominion General Discussion / Plotting cards with DATA
« on: May 24, 2018, 04:54:43 pm »
Recently I did some analysis of game logs in order to calculate the "impact factor" of each card.  This is based on 140k 2-player pro-rated games on Isotropic, in which at least one player was ranked in the top 100.  The data only includes expansions up to Guilds.

For my next analysis, I wanted not to rank cards by impact, but characterize/classify cards by type.  I applied Principal component Analysis (PCA), which basically uses a small number of dimensions to describe as much variance among the cards as possible.

The details

I'm going to start out by saying, if you don't understand any of this, and/or you think it's all bullshit, that's okay.  Really, it's just fun to look at the plots whether or not you think they reflect any deeper meaning.  Anyways I'm not going to go into every little detail.  You can ask me anything, or else you can pm me and I'll give you a github link.

In order to do this analysis, I defined two relations, which I call "promote" and "love".  Prom(X,Y) is the extent to which the gain percentage of Y increases when X is present.  Love(X,Y) is the extent to which the gain percentage of X increases relative to other cards, when Y is present.  For each card X, I calculated 412 features corresponding to Prom(X,Y) and Love(X,Y) for each card Y.  I also applied some normalization so that my analysis doesn't care so much about how much it promotes/loves other cards, but rather, which cards it promotes/loves.

Additionally, you might notice that each card is assigned a certain color.  These are based on a basic cluster analysis.  I created seeds for 9 clusters (villages, terminal draw, nonterminal draw, trashing, junking, gaining, payoff, victory), and I used some algorithm to infer classifications for the rest of the cards.  The clustering algorithm is not very good, don't ask me why Rats is a village.  Anyways, it's a guide to the eye.


Here I show a few sample plots, but I can generate more upon request.  Just ask for Component X vs Component Y.  You can also ask one or both of the axes to show the set of cards loved/promoted by component X.

If you would like to request I change my analysis completely, I'll consider it but I may not have time for that.


Without further ado, here are a few plots to start out.

Additional notes

By inspection, I believe the first 6 components correspond to:

1. Important terminal cards vs villages
2. 5-cost cards, vs things that help you get 5-costs
3. Thinners vs cards that are best in thin decks
4. Slog cards vs engine cards
5. Trashing vs draw
6. Cheap cards and defense cards vs strong attacks and gainers

After #6, I couldn't tell what the components were getting at.  Most components describe card types that are complementary to each other.  For instance villages tend to love/promote terminals.  Component 4 seems to be a major exception, in that engine cards seem to love/promote other engine cards.  So component 4 describes cards that prefer to be unmixed.

Other Games / Re: Prismata
« on: May 21, 2018, 06:12:15 pm »
It's not weak, but it can be difficult to use efficiently when you're inexperienced at the game. At best, Rhino can absorb for 1 the turn it comes into play, attack for 1 on the following two turns, and absorb for 1 for the rest of the game. That's way better than Tarsier. Even a Rhino that just absorbs 1, attacks for 1 twice, and soaks for 2 is better than par. If you don't absorb on the Rhino or if it dies before you get full value out of it, then it's weak.
I see.  I wasn't counting the absorption value, but if you get the absorption on the turn it comes out, it seems decent.

I think the training content might encourage over-reliance on walls, which makes the absorption value of Rhinos a bit useless.

Other Games / Re: Prismata
« on: May 21, 2018, 04:38:44 pm »
I was looking at Prismata on Steam for a while, and I finally got it while it was free.  So far, I've only played the episode 1 campaign, and some of the other single-player content.  I'm not sure I'm really interested in playing against randos, but I told a couple friends to get it too, so maybe I'll play with them at some point.  Here are some impressions so far.

Compared to Dominion, this seems far more optimized for digital/online play.  It's relatively easy to visually parse.  There aren't any mechanics like shuffling, which I think is far easier to track and understand when you're doing the shuffling physically.  It's designed for timed play, which solves the slow-rolling problem.  And it seems much more amenable to AI.

I couple things I'm less fond of: It's very math-y.  And I tend to prefer games that are about parallel building up, rather than direct confrontation.

I don't have a great understanding of the strategy, but this morning I had the realization that it's sort of like Temporum, where everything has a "par" value.  In Temporum the expected value of a turn is $8, with cards = crowns = $4, but you might make more or less depending on tactics.  In Prismata, there's a "par" interest rate of 33% a turn, so that 3 of anything this turn is worth 4 next turn.  We also have Gaussite ~ Replicase ~ $1, Behemium ~ $2, and a single point of damage/defense is worth a bit more than $2.  I tried calculating the values of a few basic units, and it seems that Gauss Cannons are about par, Tarsiers are above par, Walls are only better than par if they absorb damage.  Rhinos just seem weak...

Dominion General Discussion / Re: Card alchemy revelation....
« on: May 16, 2018, 06:26:42 pm »
Card alchemy revelation?

Rules Questions / Re: Inheritance interaction
« on: May 12, 2018, 12:24:30 pm »
I don't think the other player's card can ever end up in play through this mechanism.
Oh, it surely can!  Suppose your opponent inherited Caravan Guard.  And somewhere in your action chain, after Ambassadoring the Estate, you play an Attack, and your opponent responds by playing several Estates, one of which may or may not have been the Estate you gave to them. 8)

Dominion General Discussion / Re: Playing to lose?
« on: May 12, 2018, 12:16:26 pm »
In addition to valuing 2nd place, players might also value:
1. Winning as many times as possible.  So, whenever victory/loss is assured, end the game as quickly as possible
2. Spend as much time in winning games as possible.  So, whenever loss is assured, end the game quickly.  And whenever anyone else does the same, complain they are being bad sports.  It's true that their behavior is just as likely to help you as hurt you, but overall it makes you spend less time in winning games.

Rules Questions / Re: Inheritance interaction
« on: May 12, 2018, 12:06:21 pm »
The lose-track change would change Throne / Feast in the original main set; I'm not doing it. People don't know the lose track rule, and the main set rulebook said Throne / Feast worked. For new games this would be a thing to consider; Dominion does not want to mess with that.

I think you can lose track harder and still have Throning Feast work. One way would be to use last-known information for things you lost track of. Throne plays a card in your hand twice. That card's not in your hand anymore after the first play? (Actually true whatever it plays; Feast wouldn't even be a special case.) Ok, just play whatever that card was back when it was in your hand. Throne wants to play an Estate that used to be in your hand but has somehow maybe ended up around the world and in the supply or in your opponent's deck or maybe is still in your hand and nobody really knows for sure where it is? Just play whatever the Estate was when it was in your hand.

There would be complications with BoM, though. The way BoM works now, I guess a Throne would always end up playing it as BoM both times (because that's what it was in your hand) so you'd always get to choose an action to emulate for both plays. If you wanted to change that, maybe you could revert BoM to its old behavior and have it become Feast or whatever as you play it; then Throne would remember it as Feast and play it as Feast twice... which was how that originally worked anyway, I think. (To me, either one of those options seems like an improvement over the current situation where sometimes a Throned BoM is stuck as one card and sometimes it's not.)

Using last-known information would also, I guess, make things like Transmute and Procession work like Ritual and care what stuff looks like just before you trash it, not what it turns into afterwards.
I like this way of dealing with the problem--not as a modification of Throne Room et al., but a modification of the lose track rule.  Whenever you need to do something to a card that you have lost track of, then not only do all "move" effects fail, you also treat the card as if its name/types/abilities have not changed since losing track.

Although, as noted, this changes the behavior of several interactions.  If you TR-BoM as Feast, then the second time you play the card, you're forced to play as Feast again, since that's what it was when you lost track of it.  If you Procession-BoM as Lighthouse, then you gain a $3-cost, since the card only cost $2 when you lost track of it.  Actually, I think the Procession interaction shouldn't work, since Procession itself put the card in the trash, and as long as it's still in the trash it shouldn't lose track.

Rules Questions / Re: Inheritance interaction
« on: May 12, 2018, 11:50:35 am »
Another way to treat Throne room is like this:
1. Choose an action card from hand.
2. Create a pointer to the physical copy of the card.
3. Store a virtual copy of the card (ie remember its instructions and name and types)
4. Play the card being pointed to.
5a. If the card has moved (even if it later returns to play), then play the virtual copy of it.
5b. If the card has not moved, then play it.
I fear the body of rules you'd then need to create for how a "virtual copy" of a card behaved in every possible circumstance would then be second only to Possession in its baroque intricacy. Specimen question: is a virtual card in play for the purpose of pricing Peddler?
You can treat the "virtual" card as the original card, which you have lost track of.  So, you play it, but whenever there's an effect that moves its location, that effect fails. So, it fails to go in to play, and it doesn't affect Peddler.

I like Inheritance. I've never imagined it needs a fix. As Donald points out, the problem is, MANDARIN, which moves cards from play. I also agree that we will never see this lunatic interaction again.

You can create the interaction without Mandarin.

Play King's Court, choosing Band of Misfits
--Play Band of Misfits as Mining Village, trash it
--Play Band of Misfits as Throne Room, choosing Herald
----Play Herald, playing Lurker to gain Band of Misfits
----Play Herald, playing Throne Room, choosing Band of Misfits
------Play Band of Misfits as Lighthouse twice
--Play Band of Misfits again.  But is it a Lighthouse now?

So, do these interactions actually work on Dominion Online?  I'd love to see a video of that.

Rules Questions / Re: Inheritance interaction
« on: May 11, 2018, 10:48:22 pm »
So, Throne Room currently works is like this:
1. Choose an action card from hand.
2. Create a pointer to the physical copy of the card.
3. Play the card being pointed to.
4. Play it again.

The intention is that the card can change its identity or abilities somewhere between steps 3 and 4.  So if you throne a BoM and it becomes a Lighthouse in step 3, then in step 4 you play the Lighthouse.  The problem is that with Inheritance, sometimes you don't even know whether the card has changed its ability.

I'm pretty sure you can recreate this problem even without Inheritance:
Play Throne Room, choose Overlord.
--Play Overlord as Crown, choose Herald.
----Play Herald, which plays University to gain Mandarin.
----Play Herald, which plays Throne Room, choosing an Overlord from your hand.
------Play the Overlord as Lighthouse twice.
--Play Overlord again, but is it a Lighthouse now?

Another way to treat Throne room is like this:
1. Choose an action card from hand.
2. Create a pointer to the physical copy of the card.
3. Store a virtual copy of the card (ie remember its instructions and name and types)
4. Play the card being pointed to.
5a. If the card has moved (even if it later returns to play), then play the virtual copy of it.
5b. If the card has not moved, then play it.

This would have the same behavior with TR-BoM-Feast, but wouldn't have the accountability/uncertainty problems.  It's a bit convoluted, but for what it's worth, this is probably how I'd play it if it ever came up IRL.  ETA: ...which it won't.

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.

Dominion General Discussion / Re: Data Mining: Card Impact Factor
« on: May 01, 2018, 05:18:41 pm »
*ok, I have no idea why Duchess promotes Stash.

I do! When you gain a bunch of terminals for free, you don't have so much terminal space left so you'll buy Stash or Venture instead of a terminal $5. I don't think this effect would be at all visible today, but I'm like 90-93% sure that was really the reason in 2014.
I guess that makes sense.

FWIW there's less data for the promo cards, so they tend to have larger error margins.  That's why the promo cards show up disproportionately in the top synergies lists (and also why I had to remove Prince/Walled Village).

Dominion General Discussion / Re: Data Mining: Card Impact Factor
« on: April 30, 2018, 06:49:09 pm »
Now that I have both these lists, here are my thoughts on interpretation.

The "Impact factor", while not perfect, is the best objective measure of "card strength" that I have seen so far.  In the gain percentage list, the top three cards were Tournament, Governor, and Border Village; here they are Rebuild, Mountebank, Goons.  And that seems to me a little more on point.  I bet if you compared this to the 2014 Qvist rankings you would find that they are a closer match.

But there is an obvious bias towards cards that either force or incentivize you to gain copper/curse/estate/ruins/potion.  I think dumping 10 curses into players decks should rightfully be considered impactful, but maybe not quite this much.

The synergies and anti-synergies are very interesting, and you can think up a reason for why almost every card on that list is there.*  I'm not sure the sum absolute value of synergies is especially meaningful though.

*ok, I have no idea why Duchess promotes Stash.

The synergy factor looks like the most promising data for PCA.  My prediction is that the first principal component will be "terminals vs villages".  The most villagey cards will be strong villages that encourage even weak terminal draw and weak terminal payload, while discouraging weak villages.  The least villagey cards will be strong terminal draw that encourage even weak villages, while discouraging weak terminal draw.

Dominion General Discussion / Re: Data Mining: Card Impact Factor
« on: April 30, 2018, 01:25:06 pm »
Introducing the synergy factor!

The synergy factor of a supply pile is the sum of the absolute changes in the gain percentages of other kingdom piles, due to this supply pile's presence.  That means I don't count the contribution from base cards, Potions, Ruins, Platinum/Colonies, or from the card itself.  The math also ends up excluding the contribution of potion cards to Potion, and the contribution of Looters to Ruins.  Finally, I left out Prince and Walled Village because there's less data for them and it was impacting statistics in a bad way. 

Furthermore, for each card I show the top 2 synergies, and top anti-synergy.  While these are interesting, keep in mind the error margins can be larger than the differences between the top few synergies.

RankCardSynergy FactorTop synergy          2nd synergy          Top anti-synergy         
2Chapel16.9Treasure Map0.29Market Square0.14Lookout-0.42
3JackOfAllTrades16.9Feodum0.21Duke0.13Sea Hag-0.30
4Governor16.8Rats0.19Militia0.18Bandit Camp-0.34
5Cultist16.6Death Cart0.18Trader0.16Rabble-0.27
6Masquerade16.6Possession0.15Bandit Camp0.12Sea Hag-0.39
9Ill-Gotten Gains15.8Trader0.20Gardens0.17Festival-0.22
10Minion15.2Lighthouse0.18Horse Traders0.17Ghost Ship-0.31
11Goons14.3Quarry0.22Native Village0.22Hoard-0.26
12Fishing Village13.8Envoy0.28Smithy0.26Village-0.33
13Fool's Gold13.4Storeroom0.17Nomad Camp0.16Peddler-0.19
14Fairgrounds13.1Death Cart0.19Spy0.18Chapel-0.02
15Ambassador13.1Lighthouse0.17Native Village0.13Sea Hag-0.37
17Tournament12.2Band of Misfits0.16Tactician0.10Bridge-0.21
19Steward12.0Bandit Camp0.10Bazaar0.10Lookout-0.26
20Forager11.9Poor House0.18Fool's Gold0.16Trade Route-0.37
21Sea Hag11.9Moat0.17Lighthouse0.17Familiar-0.32
22Border Village11.8Rabble0.26Journeyman0.24Nobles-0.13
24Remake11.5Poor House0.32Fortress0.13Moneylender-0.28
25King's Court11.5Saboteur0.27Woodcutter0.21Bank-0.17
26Scrying Pool11.4Storeroom0.21Woodcutter0.21JackOfAllTrades-0.17
28Wandering Minstrel11.2Workshop0.21Armory0.19Farming Village-0.30
29Walled Village11.2Hunting Grounds0.24Council Room0.23Advisor-0.19
30Hunting Party11.2Altar0.15Horn of Plenty0.15Laboratory-0.26
31Plaza11.0Library0.22Watchtower0.18Mining Village-0.31
33Swindler10.7Masterpiece0.30Chancellor0.28Fool's Gold-0.16
35Fortress10.4Procession0.20Develop0.19Worker's Village-0.15
36Black Market10.3Fairgrounds0.17Quarry0.13Smugglers-0.18
38Worker's Village10.2Catacombs0.21Torturer0.21Mining Village-0.21
44Festival9.6Hunting Grounds0.22Watchtower0.21Market-0.17
45Ironmonger9.6Workshop0.22Ironworks0.17Farming Village-0.23
47Village9.4Rabble0.18Smithy0.18Shanty Town-0.11
49Marauder9.3Lighthouse0.13Death Cart0.12Militia-0.16
50Bridge9.3Native Village0.20Inn0.11Nomad Camp-0.25
51Squire9.1Torturer0.20Rabble0.19Native Village-0.14
52Margrave9.1Village0.15University0.15Ghost Ship-0.16
53Hamlet9.0Library0.21Smithy0.19Native Village-0.25
54Young Witch8.9Tunnel0.15Band of Misfits0.13Expand-0.23
55Herald8.9Armory0.26Workshop0.25Mining Village-0.13
56Grand Market8.9Quarry0.26Vault0.21Hoard-0.18
58Bandit Camp8.8Envoy0.19Hunting Grounds0.16Festival-0.18
59Farming Village8.7Torturer0.20Hunting Grounds0.16Mining Village-0.20
60Upgrade8.5Rats0.31Poor House0.28Apprentice-0.18
65Junk Dealer8.3Market Square0.11Quarry0.09Trading Post-0.26
68Market Square8.2Apprentice0.17Vineyard0.11Worker's Village-0.15
69Mining Village8.2Torturer0.18Rabble0.16Fortress-0.16
70Lighthouse8.2Mint0.11Horn of Plenty0.08Moat-0.20
74Native Village7.8Bridge0.19Torturer0.15Pearl Diver-0.16
77Envoy7.7Inn0.14Worker's Village0.09Nomad Camp-0.14
78Horn of Plenty7.7Spy0.16Journeyman0.15Workshop-0.05
80Hermit7.7Market Square0.12Wishing Well0.11Sea Hag-0.17
82Trader7.6Feodum0.38Duke0.11Sea Hag-0.18
84Crossroads7.5Torturer0.17Great Hall0.14Native Village-0.14
86Tactician7.4Storeroom0.18Secret Chamber0.16Soothsayer-0.11
87Peddler7.4Worker's Village0.13Salvager0.12Fool's Gold-0.09
88Monument7.4Golem0.12Band of Misfits0.10Scavenger-0.16
91Haggler7.1Mining Village0.14Spy0.13Rogue-0.11
92Count7.0Duke0.18Grand Market0.05Trading Post-0.16
93Candlestick Maker7.0Vineyard0.16Peddler0.12Pawn-0.21
94Ironworks7.0Silk Road0.23Gardens0.21Armory-0.19
95Merchant Guild6.9Quarry0.10Golem0.09Nomad Camp-0.12
97Golem6.9Apothecary0.17Saboteur0.12Throne Room-0.07
98Throne Room6.8Armory0.13Band of Misfits0.13Mining Village-0.08
99Procession6.8Adventurer0.17Catacombs0.15Horn of Plenty-0.06
102Spice Merchant6.7Fool's Gold0.11Market Square0.09Moneylender-0.24
103Militia6.6Band of Misfits0.12Lighthouse0.11Cutpurse-0.18
104Counterfeit6.6Fool's Gold0.10Envoy0.10Loan-0.14
105Ghost Ship6.6Farming Village0.14Lighthouse0.13Militia-0.11
106Feodum6.6Masterpiece0.41Trader0.30Throne Room-0.10
107Market6.5Quarry0.19Conspirator0.11Band of Misfits-0.10
108Horse Traders6.4Tunnel0.11Gardens0.10Nomad Camp-0.15
109Warehouse6.4Tunnel0.17Treasure Map0.12Oasis-0.18
111Shanty Town6.3Rabble0.14Council Room0.13Wishing Well-0.12
112Doctor6.3Venture0.09Merchant Ship0.08Lookout-0.20
113Jester6.3Spy0.09Native Village0.08Rogue-0.12
115Nobles6.2Quarry0.20Trade Route0.13Harem-0.14
116Courtyard6.2Worker's Village0.08Bandit Camp0.07Pearl Diver-0.17
118Inn6.1Torturer0.13Hunting Grounds0.13Cartographer-0.10
119Vault6.1Grand Market0.10Tunnel0.09Envoy-0.12
120Lookout6.1Mystic0.09Treasure Map0.09Loan-0.18
121Silk Road6.0Workshop0.16Baron0.14Laboratory-0.08
122Hoard5.9Harem0.13Silk Road0.12Conspirator-0.09
124Vagrant5.9Vineyard0.09Harem0.08Pearl Diver-0.24
125Trading Post5.9Feodum0.12Grand Market0.10Altar-0.11
128Haven5.7Envoy0.10Treasure Map0.08Pearl Diver-0.21
130Beggar5.7Gardens0.25Counting House0.13Fortress-0.08
131Journeyman5.7Horn of Plenty0.07Bank0.07Council Room-0.12
133Remodel5.6Rats0.14Fool's Gold0.13Horn of Plenty-0.08
135Cellar5.5Tunnel0.12Bureaucrat0.08Pearl Diver-0.15
137Workshop5.4Gardens0.15Silk Road0.13Stonemason-0.08
140Pawn5.2Vineyard0.11Stash0.09Pearl Diver-0.19
142Scheme5.2Conspirator0.12Armory0.09Wishing Well-0.16
143Nomad Camp5.2Golem0.09Highway0.07Woodcutter-0.10
144Rats5.2Apprentice0.14Butcher0.14Spice Merchant-0.07
149Trade Route5.1Band of Misfits0.08Scrying Pool0.07Develop-0.11
150Baron5.0Silk Road0.10Cartographer0.07Nomad Camp-0.11
152Hunting Grounds5.0Native Village0.10Worker's Village0.09Council Room-0.09
153Sage5.0Trader0.07Golem0.07Wishing Well-0.11
156Council Room4.9Bank0.11Village0.09Library-0.07
157Wishing Well4.9Mystic0.08Horn of Plenty0.07Sage-0.10
159Develop4.9Rats0.15Poor House0.13Envoy-0.10
160Oasis4.8Tunnel0.13Soothsayer0.07Wishing Well-0.12
161Woodcutter4.8Ill-Gotten Gains0.08Gardens0.08Baron-0.06
162Pirate Ship4.8Oasis0.10Merchant Ship0.08Envoy-0.12
164Cutpurse4.7Hoard0.08Band of Misfits0.07Navigator-0.09
165Great Hall4.7Ironworks0.19Silk Road0.13Sage-0.10
169Secret Chamber4.6Stash0.09Tactician0.08Poor House-0.07
170Herbalist4.6Philosopher's Stone0.14Stash0.09Moat-0.07
171Cache4.6Monument0.07Young Witch0.07Conspirator-0.07
174Band of Misfits4.6Duke0.07Margrave0.06Bishop-0.10
175Mint4.5Fool's Gold0.08Harem0.06Trading Post-0.08
178Harem4.5Silk Road0.13Hoard0.09Ironworks-0.07
179Farmland4.5Trader0.09Silk Road0.07Band of Misfits-0.06
180Philosopher's Stone4.4Herbalist0.14Duke0.09Throne Room-0.11
181Mine4.4Harem0.09Catacombs0.08Band of Misfits-0.05
186Oracle4.4Ill-Gotten Gains0.09Venture0.07Fortune Teller-0.09
187Rogue4.3Soothsayer0.08Doctor0.07Candlestick Maker-0.07
188Pearl Diver4.3Cartographer0.07Jester0.07Lighthouse-0.09
189Noble Brigand4.3Beggar0.09Venture0.07Ironworks-0.05
193Outpost4.3Trading Post0.07Navigator0.07Horn of Plenty-0.05
195Royal Seal4.2Cartographer0.08Venture0.07Stash-0.07
197Tribute4.2Ghost Ship0.09Familiar0.07Pillage-0.05
198Treasure Map4.2Chapel0.07Sea Hag0.07Throne Room-0.08
199Death Cart4.1Rats0.11Band of Misfits0.07Nomad Camp-0.08
200Scout4.1Harem0.08Band of Misfits0.07Quarry-0.06
201Counting House4.1Beggar0.10Treasury0.08Tactician-0.05
202Poor House4.1Vault0.09Island0.06Remake-0.09
204Fortune Teller4.0Ill-Gotten Gains0.07Mystic0.06Poor House-0.05
205Merchant Ship4.0Marauder0.06Inn0.06Harvest-0.06
206Coppersmith3.9Apothecary0.07Council Room0.06Quarry-0.07
209Explorer3.9Duke0.07Silk Road0.06Envoy-0.08

Dominion General Discussion / Re: Data Mining: Card Impact Factor
« on: April 30, 2018, 11:18:28 am »
I don't like the own-effect of the impact factor, because the presence of the card in the kingdom shouldn't affect the average probability to gain it.
It made sense to me because the idea was to see how much the card changes your gains, and surely the presence of a card changes your ability to gain itself.  But I can calculate it the other way too.

But shouldn't it be smaller for cards that show up more frequently (Platinum), as it boils down to:
P(gain X|X is in supply) * (1 - P(X is in supply)),
and P(X is in supply) is higher for Platinum? (It can be offset by a higher probability of gaining Platinum.)
Not quite.  The own-effect for Duke is about %Duke*0.95, and the own-effect for Platinum/Colony is (%Platinum+%Colony)*0.875.

The other thing that I noticed with the current formulat is that a card Y that is gained independently of all other cards, still contributes to their impact factors:
P(gain Y|Y is in supply) * (P(Y is in supply|X is in supply) - P(Y is in supply) )
That is technically true, but what I didn't tell you is that P(Y is in supply|X is in supply) is just a number I hard-coded in.  I didn't bother taking into account the fact that if X takes up a slot in the kingdom, it decreases the probability of Y.  But that's a really good point, if my formula includes such an effect, does the formula even make sense?

1) Also show a version that excludes Copper, Curse, Ruins, Estate (am I missing something?)
2) For each card, show the top 3 cards that contribute the most in a positive or in a negative way to the impact factor.
3) I (still) would like to see the impact factor (and number of cards gained from that pile) for categories of cards.

4) Analysis with games from Shuffle iT.
I can do 1) and 2) fairly easily, although I'm thinking that I should also remove the other base cards and Potion.  I feel like it doesn't make sense to put synergy with Duchy on the same level as synergy with Count, because Duchy is in every game.  I could keep in Platinum and Colony because those are only 2.5x as likely to show up.

For 3) the difficulty is whose card categories do I use?  I hope that the PCA analysis, when I do it, will provide some insight into card categories.

AFAIK Shuffle IT data doesn't exist.

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