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[rrenaud]

First, two very big, fairly similar looking pictures.

http://mine.councilroom.com/~rrenaud/grouped_by_prob_wgag.png
http://mine.councilroom.com/~rrenaud/grouped_by_wgag.png

And then some code.

https://github.com/rrenaud/dominionstats/commit/0a97f05263bc709b1f410639cb6843b62e8c5288

Basic idea, form vectors out of the card conditional win stats.  Feed these vectors to hierarchical clustering algorithm.  Look at pictures.  Decide if groupings are sane (sometimes, throne room, king's court) or crazy (throne room, king's court, colony?).

I could perhaps compare this against Empathy's method here:
http://forum.dominionstrategy.com/index.php?topic=647.msg8951#msg8951

or even try combining them to get card features and play features.

Is this going to be useful for anything?  I am not sure.  It could perhaps help in defining useful encoding of game states for machine learning algorithms.

[Qvist]

That worked surprisingly well. Well done. I did not have time to look at the code so I'm not sure what your code exactly does.
It worked pretty well: Curser in one group, villages in another, etc.
But still I like to point out what I noticed.

Saboteur + Woodcutter, that seems odd! Maybe that just means, both are equally bad. And Nomad Camp is nowhere near Woodcutter.
Mandarin + Noble Brigand seems also very odd. They both have something to do with treasure cards and have on buy effects, maybe that's the reason. Thief is definitely too far away from Noble Brigand.

Reaction cards seem also very odd grouped together. Moat + Herbalist? Both cost $2 and are bad, so that's the reason? Generally speaking it tends to put these cards together that costs the same if you look at Embargo, Pearl Diver, Pawn and Haven...

I can also not explain Expand + Goons + Tournament.

You really have interesting ideas. Keep it going, I like it.

[DG]

Interestingly, it puts wharf with the +1 action drawing cards rather than with the terminal drawing cards. The wishing well is with the 2 cost cards. The caravan is with other ironworks favourites, mining village and great hall. That's quite insightful considering how it was put together. Does the quantity of cards purchased/gained affect these stats?

[theory]

What if you got rid of the visualization and had it output a text dump?  Create a ranked list of some card groupings, from the closest (Gardens/Silk Roads), to the most distant (wtf is up with Adventurer?).

[rrenaud]

Adventurer is a crazy card, no one understands it! (or it's just mostly ignored...)

[rrenaud]

Here is the data by gain rate.  Maybe there is some kind of bug causing the flatness on the right side?  I removed Archivist from the data set.  I am running the card combo stats thing over the most recent 4 months, but that hasn't finished yet.

http://mine.councilroom.com/~rrenaud/grouped_by_gain_rate.png

Here is gain rate with the other stats:

http://mine.councilroom.com/~rrenaud/grouped_by_wgag_gain_rate_prob.png

[blueblimp]

Just a suggestion... could you rotate the picture 90 degrees? It's pretty hard to read as-is.

[rrenaud]

You can view it okay with chrome and zooming around.  I am just calling a function to render the graph, so I don't really have any control over how it looks (except for controlling its inputs).  I can try producing different graphs for different costs.  Maybe that will make the graph more easy to see.

If I just rotate it, the card labels are going to be oriented incorrectly.

Edit: looks like there is an orientation flag to the function I am calling.  http://docs.scipy.org/doc/scipy/reference/generated/scipy.cluster.hierarchy.dendrogram.html

I'll play with it later.

[rrenaud]

There is definitely something wrong with adventurer.  Good catch theory!  Maybe I'll debug it when I get home from work.

Otherwise, here is the closest cosine distances for vectors based on card conditional chance of being gained and card conditional win rates.

Adventurer : Merchant Ship, Mandarin, Rabble, Council Room, Embassy, Expand, Venture, Smithy, Minion, Goons
Alchemist : Treasury, Minion, Laboratory, Caravan, Highway, Bazaar, Menagerie, City, Governor, Nobles
Ambassador : Chapel, Masquerade, Remake, Steward, Apprentice, Salvager, Shanty Town, Upgrade, Spice Merchant, Stables
Apothecary : Potion, Alchemist, Spice Merchant, Scrying Pool, Conspirator, Golem, Stables, Moneylender, Peddler, Highway
Apprentice : Chapel, Ambassador, Haven, Caravan, Laboratory, Highway, Scheme, Hunting Party, Menagerie, Nobles
Bag of Gold : Platinum, Colony, Grand Market, Goons, Expand, Harem, Farmland, Tournament, King's Court, Hoard
Bank : Harem, Fishing Village, Platinum, Hoard, Goons, Expand, Festival, Tournament, Island, Bazaar
Baron : Bishop, Remodel, Swindler, Horse Traders, Monument, Black Market, Bridge, Young Witch, Salvager, Steward
Bazaar : Farming Village, Fishing Village, Festival, Highway, Laboratory, Mining Village, Village, Worker's Village, Caravan, Border Village
Bishop : Monument, Island, Tournament, Salvager, Swindler, Militia, Bridge, Remodel, Expand, Young Witch
Black Market : Swindler, Steward, Bridge, Salvager, Jester, Monument, Remodel, Masquerade, Bishop, Courtyard
Border Village : Fishing Village, Farming Village, Worker's Village, Festival, Mining Village, Caravan, Hamlet, Bazaar, Lighthouse, Shanty Town
Bridge : Monument, Black Market, Tournament, Salvager, Haggler, Nomad Camp, Bishop, Horse Traders, Wharf, Island
Bureaucrat : Trader, Baron, Jack of All Trades, Noble Brigand, Navigator, Cutpurse, Pirate Ship, Explorer, Monument, Horse Traders
Cache : Hoard, Royal Seal, Stash, Venture, Harem, Platinum, Tribute, Fool's Gold, Mandarin, Bank
Caravan : Island, Mining Village, Fishing Village, Tournament, Farming Village, Great Hall, Laboratory, Nobles, Worker's Village, Hamlet
Cartographer : Laboratory, Hunting Party, Stables, Minion, Treasury, Governor, Nobles, Market, Caravan, Bazaar
Cellar : Warehouse, Haven, Crossroads, Oasis, Island, Hamlet, Pawn, Great Hall, Lighthouse, Embargo
Chancellor : Fortune Teller, Black Market, Oracle, Develop, Steward, Cutpurse, Duchess, Swindler, Smithy, Courtyard
Chapel : Ambassador, Steward, Remake, Shanty Town, Spice Merchant, Moneylender, Masquerade, Island, Caravan, Salvager
City : Farming Village, Bazaar, Mining Village, Festival, Laboratory, Hamlet, Village, Fishing Village, Shanty Town, Lighthouse
Colony : City, Platinum, Lighthouse, King's Court, Nobles, Farmland, Bazaar, Border Village, Great Hall, Farming Village
Conspirator : Peddler, Tournament, Pawn, Highway, Hunting Party, Nobles, Governor, Bridge, Wishing Well, Grand Market
Contraband : Royal Seal, Tribute, Treasury, Festival, Mine, Market, City, Bazaar, Platinum, Minion
Copper : Gardens, Great Hall, Embargo, Courtyard, Duchess, Smithy, Island, Chapel, Remodel, Nobles
Coppersmith : Baron, Cutpurse, Navigator, Smugglers, Moneylender, Black Market, Duchess, Nomad Camp, Feast, Bishop
Council Room : Rabble, Smithy, Embassy, Envoy, Margrave, Wharf, Courtyard, Torturer, Bridge, Merchant Ship
Counting House : Philosopher's Stone, Gardens, Duke, Trader, Duchess, Silk Road, Fairgrounds, Tunnel, Watchtower, Trade Route
Courtyard : Smithy, Embargo, Black Market, Envoy, Haven, Steward, Torturer, Bishop, Bridge, Salvager
Crossroads : Fishing Village, Farming Village, Island, Cellar, Hamlet, Mining Village, Worker's Village, Caravan, Tournament, Haven
Curse : Colony, Quarry, City, Throne Room, Highway, Peddler, King's Court, Scheme, Inn, Village
Cutpurse : Militia, Monument, Swindler, Black Market, Baron, Haggler, Bishop, Bridge, Moneylender, Horse Traders
Develop : Steward, Remake, Black Market, Trading Post, Masquerade, Trade Route, Swindler, Remodel, Upgrade, Lookout
Diadem : Colony, Grand Market, Platinum, Goons, Nobles, Highway, King's Court, Expand, Tournament, Conspirator
Duchy : Great Hall, Island, Nobles, Cellar, Caravan, Fishing Village, Shanty Town, Silk Road, Harem, Warehouse
Duke : Gardens, Farmland, Tunnel, Harem, Silk Road, Fairgrounds, Great Hall, Island, Colony, Nobles
Duchess : Bishop, Monument, Island, Black Market, Courtyard, Swindler, Great Hall, Embargo, Nobles, Cellar
Embargo : Haven, Pawn, Caravan, Chapel, Cellar, Salvager, Pearl Diver, Courtyard, Great Hall, Island
Embassy : Rabble, Torturer, Smithy, Wharf, Courtyard, Margrave, Council Room, Envoy, Ghost Ship, Vault
Envoy : Smithy, Torturer, Rabble, Courtyard, Council Room, Embassy, Margrave, Oracle, Black Market, Militia
Estate : Haven, Chapel, Great Hall, Scheme, Cellar, Crossroads, Shanty Town, Ambassador, Apprentice, Highway
Expand : Tournament, Goons, Island, Platinum, Nobles, Festival, Market, Monument, Bishop, Grand Market
Explorer : Hoard, Merchant Ship, Vault, Monument, Mandarin, Bishop, Jack of All Trades, Noble Brigand, Jester, Harvest
Fairgrounds : Gardens, Farmland, Silk Road, Nobles, Harem, Colony, Great Hall, City, Island, Goons
Familiar : Sea Hag, Witch, Young Witch, Tournament, Governor, Torturer, Mountebank, Swindler, Crossroads, Ambassador
Farming Village : Mining Village, Fishing Village, Bazaar, Worker's Village, Festival, Border Village, Walled Village, Village, Caravan, Hamlet
Farmland : Harem, Platinum, Island, Fishing Village, Great Hall, Expand, Nobles, Tournament, Caravan, Lighthouse
Feast : Horse Traders, Bridge, Monument, Island, Salvager, Caravan, Embargo, Tournament, Bishop, Nomad Camp
Festival : Worker's Village, Market, Bazaar, Farming Village, Fishing Village, Hamlet, Border Village, Mining Village, Caravan, Tournament
Fishing Village : Farming Village, Mining Village, Bazaar, Border Village, Worker's Village, Caravan, Festival, Village, Shanty Town, Island
Followers : Goons, Merchant Ship, Margrave, Tournament, Monument, Militia, Bishop, Caravan, Torturer, Jester
Fool's Gold : Fishing Village, Mining Village, Farming Village, Caravan, Tournament, Bazaar, Island, Crossroads, Highway, Laboratory
Forge : Steward, Remake, Upgrade, Trade Route, Chapel, Salvager, Shanty Town, Masquerade, Oasis, Ambassador
Fortune Teller : Black Market, Swindler, Steward, Courtyard, Remodel, Bridge, Smithy, Haggler, Oracle, Duchess
Gardens : Silk Road, Great Hall, Island, Fairgrounds, Farmland, Tunnel, Shanty Town, Harem, Cellar, Duke
Ghost Ship : Margrave, Torturer, Haggler, Witch, Militia, Wharf, Rabble, Jester, Embassy, Mountebank
Gold : Harem, Platinum, Fishing Village, Bank, Goons, Island, Caravan, Festival, Bazaar, Hoard
Golem : City, Inn, Throne Room, Potion, King's Court, Farming Village, Village, Shanty Town, Native Village, Colony
Goons : Tournament, Nobles, Expand, Wharf, Grand Market, Island, Market, Caravan, Festival, Platinum
Governor : Minion, Laboratory, Hunting Party, Tournament, Nobles, Bazaar, Treasury, Highway, Market, Caravan
Grand Market : Festival, Tournament, Market, Goons, Nobles, Bazaar, Border Village, Platinum, Governor, Expand
Great Hall : Island, Caravan, Fishing Village, Haven, Nobles, Shanty Town, Lighthouse, Mining Village, Hamlet, Farming Village
Haggler : Jester, Bridge, Monument, Tournament, Ghost Ship, Militia, Wharf, Bishop, Witch, Vault
Hamlet : Worker's Village, Festival, Haven, Pawn, Farming Village, Fishing Village, Caravan, Border Village, Mining Village, Lighthouse
Harem : Platinum, Island, Fishing Village, Farmland, Goons, Nobles, Tournament, Festival, Great Hall, Expand
Harvest : Merchant Ship, Mandarin, Rabble, Vault, Monument, Black Market, Smithy, Jester, Embassy, Haggler
Haven : Pawn, Pearl Diver, Hamlet, Caravan, Embargo, Cellar, Great Hall, Lighthouse, Chapel, Laboratory
Herbalist : Bridge, Pawn, Black Market, Salvager, Nomad Camp, Bishop, Courtyard, Market, Wharf, Monument
Highway : Bazaar, Laboratory, Caravan, Farming Village, Governor, Nobles, Treasury, Tournament, Peddler, Fishing Village
Hoard : Harem, Bank, Platinum, Goons, Tournament, Farmland, Bishop, Fishing Village, Expand, Tunnel
Horn of Plenty : Outpost, Haggler, Conspirator, Bridge, Mountebank, Ghost Ship, Goons, Witch, Quarry, Tournament
Horse Traders : Bridge, Feast, Monument, Nomad Camp, Expand, Salvager, Remodel, Bishop, Island, Black Market
Hunting Party : Laboratory, Stables, Governor, Cartographer, Wharf, Minion, Tournament, Nobles, Caravan, Witch
Ill-Gotten Gains : Island, Chapel, Steward, Cellar, Swindler, Bishop, Harem, Warehouse, Crossroads, Lighthouse
Inn : Farming Village, Village, City, Bazaar, Hamlet, Mining Village, Worker's Village, Fishing Village, Throne Room, Border Village
Ironworks : Workshop, Talisman, Trade Route, Swindler, Bridge, Monument, Haggler, Tournament, Remodel, Bishop
Island : Caravan, Great Hall, Tournament, Fishing Village, Bishop, Nobles, Warehouse, Mining Village, Crossroads, Farming Village
Jack of All Trades : Bishop, Monument, Swindler, Merchant Ship, Island, Militia, Tournament, Tunnel, Steward, Salvager
Jester : Haggler, Merchant Ship, Bridge, Torturer, Black Market, Vault, Margrave, Monument, Swindler, Bishop
King's Court : Throne Room, Border Village, Bazaar, Festival, Farming Village, City, Platinum, Fishing Village, Highway, Lighthouse
Laboratory : Minion, Cartographer, Hunting Party, Governor, Caravan, Treasury, Bazaar, Nobles, Market, Stables
Library : Rabble, Council Room, Watchtower, Smithy, Embassy, Envoy, Minion, Merchant Ship, Torturer, Courtyard
Lighthouse : Fishing Village, Caravan, Farming Village, Border Village, Hamlet, Mining Village, Shanty Town, Great Hall, Island, Pawn
Loan : Lookout, Spice Merchant, Moneylender, Ambassador, Remake, Chapel, Steward, Mint, Masquerade, Trading Post
Lookout : Loan, Remake, Steward, Chapel, Forge, Moneylender, Spice Merchant, Ambassador, Trading Post, Masquerade
Mandarin : Merchant Ship, Monument, Bishop, Vault, Expand, Harvest, Goons, Island, Harem, Duchess
Market : Festival, Worker's Village, Caravan, Laboratory, Tournament, Nobles, Hamlet, Grand Market, Treasury, Bazaar
Margrave : Wharf, Ghost Ship, Torturer, Militia, Goons, Bridge, Tournament, Hunting Party, Witch, Jester
Masquerade : Steward, Ambassador, Remake, Chapel, Swindler, Salvager, Sea Hag, Trading Post, Moneylender, Young Witch
Menagerie : Caravan, Laboratory, Nobles, Governor, Minion, Scheme, Hunting Party, Haven, Apprentice, Wharf
Merchant Ship : Monument, Jester, Bishop, Vault, Minion, Goons, Tournament, Bridge, Expand, Haggler
Militia : Margrave, Monument, Bishop, Tournament, Haggler, Salvager, Bridge, Black Market, Torturer, Jester
Mine : Black Market, Jester, Merchant Ship, Treasury, Steward, Haggler, Smithy, Trading Post, Bridge, Stables
Mining Village : Farming Village, Fishing Village, Caravan, Worker's Village, Bazaar, Festival, Border Village, Village, Hamlet, Island
Minion : Laboratory, Governor, Treasury, Hunting Party, Caravan, Nobles, Cartographer, Tournament, Stables, Market
Mint : Spice Merchant, Moneylender, Chapel, Stables, Ambassador, Hunting Party, Wharf, Shanty Town, Remake, Loan
Moat : Pawn, Lighthouse, Courtyard, Embargo, Nobles, Smithy, Haven, Black Market, Pearl Diver, Caravan
Moneylender : Spice Merchant, Remake, Chapel, Steward, Masquerade, Ambassador, Swindler, Salvager, Black Market, Mint
Monument : Bishop, Tournament, Bridge, Militia, Island, Haggler, Merchant Ship, Expand, Swindler, Salvager
Mountebank : Witch, Wharf, Hunting Party, Tournament, Governor, Haggler, Torturer, Border Village, Island, Margrave
Native Village : Village, Farming Village, Walled Village, Hamlet, Inn, Bazaar, Mining Village, Lighthouse, Fishing Village, City
Navigator : Cutpurse, Nomad Camp, Horse Traders, Monument, Baron, Bridge, Smithy, Fortune Teller, Black Market, Remodel
Nobles : Caravan, Tournament, Laboratory, Island, Market, Wharf, Great Hall, Goons, Governor, Minion
Noble Brigand : Monument, Bishop, Militia, Merchant Ship, Pirate Ship, Fool's Gold, Bridge, Mandarin, Black Market, Tournament
Nomad Camp : Bridge, Horse Traders, Monument, Herbalist, Black Market, Bishop, Woodcutter, Salvager, Feast, Remodel
Oasis : Warehouse, Cellar, Island, Pawn, Hamlet, Haven, Upgrade, Lighthouse, Great Hall, Chapel
Oracle : Envoy, Smithy, Rabble, Courtyard, Council Room, Embassy, Fortune Teller, Black Market, Torturer, Steward
Outpost : Conspirator, Bridge, Haggler, Possession, Upgrade, Tournament, Peddler, Pawn, Black Market, Mountebank
Pawn : Haven, Pearl Diver, Hamlet, Caravan, Lighthouse, Embargo, Cellar, Scheme, Nobles, Great Hall
Pearl Diver : Pawn, Haven, Hamlet, Cellar, Lighthouse, Embargo, Scheme, Crossroads, Caravan, Great Hall
Peddler : Highway, Conspirator, Governor, Scheme, Bazaar, Laboratory, Hunting Party, Nobles, Farming Village, Menagerie
Philosopher's Stone : Trader, Fairgrounds, Golem, Gardens, Colony, Silk Road, Forge, City, Ill-Gotten Gains, Duke
Pirate Ship : Noble Brigand, Thief, Monument, Mine, Black Market, Bishop, Nomad Camp, Bridge, Mandarin, Fool's Gold
Platinum : Festival, Fishing Village, Border Village, Bazaar, Harem, Expand, Farming Village, Grand Market, Lighthouse, Caravan
Possession : Conspirator, Bridge, Outpost, Goons, Tournament, Grand Market, Potion, Margrave, Haggler, Pawn
Potion : Highway, Farming Village, Tournament, Throne Room, Bazaar, Alchemist, City, Caravan, Peddler, Scheme
Princess : Grand Market, Colony, Goons, Platinum, Expand, Nobles, Tournament, King's Court, Conspirator, Governor
Province : Platinum, Colony, Lighthouse, Nobles, Border Village, Fishing Village, Caravan, Farmland, Great Hall, City
Quarry : Peddler, Throne Room, Pawn, Tournament, Farming Village, Hamlet, Highway, Feast, Conspirator, Crossroads
Rabble : Embassy, Smithy, Council Room, Envoy, Torturer, Margrave, Courtyard, Ghost Ship, Wharf, Merchant Ship
Remake : Steward, Chapel, Moneylender, Masquerade, Ambassador, Trading Post, Spice Merchant, Upgrade, Salvager, Swindler
Remodel : Salvager, Bishop, Black Market, Bridge, Steward, Island, Swindler, Monument, Horse Traders, Chapel
Royal Seal : Treasury, Venture, Tribute, Bazaar, Stash, Minion, Laboratory, Harem, Festival, Platinum
Saboteur : Black Market, Mine, Jester, Bridge, Merchant Ship, Treasury, Market, Tribute, Tournament, Smithy
Salvager : Island, Chapel, Bishop, Steward, Bridge, Tournament, Black Market, Masquerade, Pawn, Caravan
Scheme : Pawn, Shanty Town, Haven, Hamlet, Caravan, Nobles, Lighthouse, Farming Village, Island, Menagerie
Scout : Highway, Farming Village, Crossroads, City, Bazaar, Island, Shanty Town, Cartographer, Haven, Oasis
Scrying Pool : Conspirator, Wishing Well, Peddler, Alchemist, Menagerie, Potion, Governor, Minion, Highway, Hunting Party
Sea Hag : Young Witch, Swindler, Masquerade, Steward, Familiar, Remake, Witch, Ambassador, Chapel, Moneylender
Secret Chamber : Cellar, Horse Traders, Moat, Oasis, Pearl Diver, Pawn, Lighthouse, Embargo, Warehouse, Black Market
Shanty Town : Fishing Village, Chapel, Caravan, Farming Village, Lighthouse, Island, Hamlet, Great Hall, Border Village, Mining Village
Silk Road : Gardens, Farmland, Great Hall, Island, Shanty Town, Caravan, Fishing Village, Lighthouse, Cellar, Chapel
Silver : Fishing Village, Caravan, Mining Village, Island, Great Hall, Farming Village, Shanty Town, Fool's Gold, Tournament, Lighthouse
Smithy : Envoy, Courtyard, Rabble, Torturer, Black Market, Margrave, Embassy, Council Room, Militia, Monument
Smugglers : Swindler, Black Market, Baron, Steward, Remodel, Bishop, Moneylender, Monument, Jack of All Trades, Duchess
Spice Merchant : Moneylender, Chapel, Remake, Stables, Ambassador, Shanty Town, Mint, Caravan, Scheme, Steward
Spy : Mining Village, Farming Village, Caravan, Worker's Village, Walled Village, Lighthouse, Treasury, Island, Great Hall, Village
Stables : Hunting Party, Laboratory, Cartographer, Minion, Chapel, Caravan, Nobles, Spice Merchant, Governor, Shanty Town
Stash : Royal Seal, Venture, Tribute, Cache, Hoard, Treasury, Harem, Contraband, Platinum, Fool's Gold
Steward : Masquerade, Remake, Chapel, Swindler, Black Market, Ambassador, Salvager, Moneylender, Trading Post, Upgrade
Swindler : Steward, Black Market, Masquerade, Sea Hag, Bishop, Young Witch, Salvager, Monument, Chapel, Remake
Tactician : Laboratory, Wharf, Caravan, Menagerie, Cartographer, Chapel, Minion, Nobles, Hunting Party, Stables
Talisman : Remodel, Remake, Ironworks, Warehouse, Salvager, Cellar, Island, Crossroads, Bridge, Steward
Thief : Pirate Ship, Noble Brigand, Nomad Camp, Adventurer, Black Market, Mine, Monument, Spy, Mandarin, Herbalist
Throne Room : King's Court, Farming Village, Village, Mining Village, Worker's Village, Lighthouse, City, Hamlet, Shanty Town, Bazaar
Torturer : Margrave, Witch, Smithy, Envoy, Ghost Ship, Jester, Embassy, Wharf, Rabble, Militia
Tournament : Goons, Island, Caravan, Nobles, Wharf, Monument, Market, Festival, Fishing Village, Bishop
Trade Route : Steward, Remake, Upgrade, Forge, Salvager, Remodel, Swindler, Black Market, Chapel, Oasis
Trader : Horse Traders, Bishop, Jack of All Trades, Expand, Duchess, Ill-Gotten Gains, Monument, Island, Remodel, Harem
Trading Post : Remake, Steward, Masquerade, Ambassador, Chapel, Swindler, Upgrade, Moneylender, Sea Hag, Salvager
Transmute : Apothecary, Golem, Potion, Philosopher's Stone, Possession, Scout, Forge, University, Vineyard, Upgrade
Treasure Map : Fool's Gold, Venture, Tournament, Monument, Treasury, Merchant Ship, Minion, Governor, Bishop, Tribute
Treasury : Laboratory, Minion, Bazaar, Market, Governor, Caravan, Highway, Nobles, Festival, Farming Village
Tribute : Treasury, Highway, Minion, Laboratory, Royal Seal, Bazaar, Festival, Alchemist, Market, Cartographer
Trusty Steed : Grand Market, Platinum, Bazaar, Highway, Festival, Goons, Tournament, Governor, Expand, King's Court
Tunnel : Island, Great Hall, Caravan, Fishing Village, Tournament, Lighthouse, Bishop, Harem, Monument, Nobles
University : Quarry, Potion, Throne Room, Outpost, Mountebank, Border Village, King's Court, Conspirator, Peddler, Farming Village
Upgrade : Ambassador, Salvager, Remake, Steward, Warehouse, Oasis, Crossroads, Tournament, Masquerade, Hamlet
Vault : Jester, Haggler, Merchant Ship, Bishop, Monument, Wharf, Embassy, Torturer, Margrave, Ghost Ship
Venture : Minion, Laboratory, Treasury, Fool's Gold, Bazaar, Fishing Village, Mining Village, Caravan, Cartographer, Farming Village
Village : Farming Village, Fishing Village, Bazaar, Mining Village, Native Village, Walled Village, Worker's Village, Shanty Town, City, Hamlet
Vineyard : Highway, Potion, Gardens, Colony, Conspirator, King's Court, City, Scrying Pool, Throne Room, Fairgrounds
Walled Village : Farming Village, Mining Village, Village, Fishing Village, Worker's Village, Bazaar, Native Village, Festival, Border Village, City
Warehouse : Cellar, Oasis, Island, Hamlet, Crossroads, Haven, Chapel, Tournament, Nobles, Salvager
Watchtower : Moat, Smithy, Courtyard, Menagerie, Envoy, Rabble, Nobles, Council Room, Minion, Steward
Wharf : Tournament, Margrave, Hunting Party, Nobles, Witch, Island, Caravan, Market, Goons, Laboratory
Wishing Well : Haven, Pawn, Scheme, Pearl Diver, Apprentice, Menagerie, Peddler, Conspirator, Nobles, Governor
Witch : Mountebank, Wharf, Tournament, Torturer, Hunting Party, Margrave, Haggler, Governor, Familiar, Island
Woodcutter : Nomad Camp, Bridge, Herbalist, Horse Traders, Black Market, Council Room, Margrave, Remodel, Monument, Jester
Worker's Village : Festival, Hamlet, Farming Village, Fishing Village, Market, Mining Village, Caravan, Border Village, Bazaar, Island
Workshop : Ironworks, Talisman, Woodcutter, Smugglers, Fortune Teller, Trade Route, Remodel, Black Market, Swindler, Baron
Young Witch : Sea Hag, Swindler, Bishop, Masquerade, Steward, Familiar, Witch, Moneylender, Monument, Salvager

[WanderingWinder]

I'm guessing there's some index issue with adventurer, as it's first alphabetically and seems to be getting a 'perfect' no distance-score. But that's without really looking at any of your code

[werothegreat]

I'm guessing there's some index issue with adventurer, as it's first alphabetically and seems to be getting a 'perfect' no distance-score. But that's without really looking at any of your code

Maybe rrenaud has a crush on theory, and is using this "glitch" to tell him he's special.

[DStu]

Otherwise, here is the closest cosine distances for vectors based on card conditional chance of being gained and card conditional win rates.

For those of us not working at google, that means? If I read you code correctly, 'vector' means '2d vector (card, condition) for each card/condition pair'. And you measure the closest distance to what? Between "chance of being gained" and "conditional win rate"? That means you are looking for the pairs where the gain-rate reproduces the win-rate?

[DG]

Saboteur + Woodcutter, that seems odd! Maybe that just means, both are equally bad.

The grouping of saboteur with woodcutter, ironworks, workshop may signify that saboteur is good at deck reduction when deck expansion is important. Alternatively it might be strong when some key cards cost 4, such as gardens or silk roads.

The results seems less intuitive once gain rates are considered. I regret suggesting those now .

[timchen]

Otherwise, here is the closest cosine distances for vectors based on card conditional chance of being gained and card conditional win rates.

For those of us not working at google, that means? If I read you code correctly, 'vector' means '2d vector (card, condition) for each card/condition pair'. And you measure the closest distance to what? Between "chance of being gained" and "conditional win rate"? That means you are looking for the pairs where the gain-rate reproduces the win-rate?

I imagine this means that for every card, you have a list of other cards' win rate and gain rate when this card is present. This forms a vector in ~300 dimensions. Calculate the inner product of two such vectors shows how similar the two card is.

I don't work at google and I didn't look at the code  so maybe I am entirely wrong.

[RobBennett]

I started playing Dominion a few months ago and love both the game and this site. It is a truly amazing resource and it has greatly added to my experience of the game.

I would be grateful if someone could explain in language that means something to people who have no background in statistics what sorts of relationships are being explored here. My sense is that this thread is telling me something important about the various cards. But I do not possess the background needed to know with any sort of precision whatsoever what that something is.

Rob

[WanderingWinder]

I started playing Dominion a few months ago and love both the game and this site. It is a truly amazing resource and it has greatly added to my experience of the game.

I would be grateful if someone could explain in language that means something to people who have no background in statistics what sorts of relationships are being explored here. My sense is that this thread is telling me something important about the various cards. But I do not possess the background needed to know with any sort of precision whatsoever what that something is.

Rob

Oh, well, I don't think the thread is actually telling you something really important about cards. But if you want a really really simplified version - cards which are closer together, cards which are clustered together, are similar to each other.

Welcome to the forum!

[pst]

Adventurer : Alchemist, Ambassador, Apothecary, Apprentice, Bag of Gold, Bank, Baron, Bazaar, Bishop, Black Market

So Adventurer loves cards that begin with A or B? Curiouser and curiouser.

[WanderingWinder]

Adventurer : Alchemist, Ambassador, Apothecary, Apprentice, Bag of Gold, Bank, Baron, Bazaar, Bishop, Black Market

So Adventurer loves cards that begin with A or B? Curiouser and curiouser.

No.
If you read the post before theory edited it, every single card had adventurer as the first match; i.e. adventurer was getting a 'perfect' score for every card. And its own list is then just alphabetical.

[RobBennett]

Welcome to the forum!

Thanks.

And thanks for your articles and posts, Wandering. I have learned from them. I am especially grateful for your recent comments on multi-player games as I play mostly three-player games (with my two boys).

Rob

[theory]

An easy layman description of that grouping might just be, "These are cards that the Council Room robot considers to be similar." 

It's interesting to see the obvious similarities (Crossroads/Fishing Village) and the not-so-obvious that become obvious with a little thought (Throne Room + all the Villages).

[rrenaud]

I imagine this means that for every card, you have a list of other cards' win rate and gain rate when this card is present. This forms a vector in ~300 dimensions. Calculate the inner product of two such vectors shows how similar the two card is.

I don't work at google and I didn't look at the code  so maybe I am entirely wrong.

That's basically it.  Except the vector I form is the current cards win rate and chance of being purchased when the other cards are in the set, rather than the other cards chance of being purchased given this card is in the set.  There is also a preprocessing step where I subtract out the means and divide by the standard deviation, so all the vectors are roughly on the same scale.  So instead of the data saying, man, fishing village is awesome with everything, it says fishing village is relatively more awesome given torturer is available.

[rrenaud]

Maybe rrenaud has a crush on theory, and is using this "glitch" to tell him he's special.

When I want to profess my man-crush (bromance?) on theory, I do it much more directly than writing subtle bugs ;P.

[popsofctown]

Oh I bet.  I bet you use explicitly caught exceptions with verbose error messages

[werothegreat]

Oh I bet.  I bet you use explicitly caught exceptions with verbose error messages

Error 69: Administrator can't stop thinking about theory.

[Captain_Frisk]

Oh I bet.  I bet you use explicitly caught exceptions with verbose error messages

Error 69: Administrator can't stop thinking about theory.

Rule 34 applied to dominion strategy administrators?  Terrifying.