Don't trust me! Get the data and do your own analysis,
http://councilroom.com/margin.txt.gzOr find bugs in the code!
https://github.com/rrenaud/dominionstats/blob/master/oneoff/process_margin_advantage.pyThe second column is the marginal difference between the first player and the second player in the median game when sorted by the score difference across all games on isotropic.
The third column is the marginal difference between first and second player with the first player skill bias removed (eg, pair up two players, only take the same number of games from when player A was first as when player B was first, if they only played one game, it will be thrown out, if A was first once, and B was first 10 times, take the 1 game from A, and 1 game at random from B).
The first player loses a half point for having more turns than player two.
You can view the third column as a reasonable upper bound on what a player should willing to bid. The games are played on iso with no bidding, so if there was bidding, the second player could use his point advantage to close games that he actually lost and turn them into wins (they whole point). Thankfully, the third column is quite a bit higher than my heuristic estimate of 1.5 points
.
rrenaud@kingscourt:~/dominionstats/oneoff$ python process_margin_advantage.py
from 1122324 sampled down to 329378
*all 1.0 2.5
Adventurer 0.5 2.5
Alchemist 1.0 3.0
Ambassador 1.0 3.5
Apothecary 1.0 3.0
Apprentice 1.0 2.5
Bank 1.0 3.0
Baron 0.5 2.5
Bazaar 1.0 2.5
Bishop 1.0 3.0
Black Market 1.0 3.0
Bridge 1.0 2.5
Bureaucrat 1.0 2.5
Caravan 1.0 2.5
Cellar 1.0 2.5
Chancellor 1.0 2.5
Chapel 0.5 3.0
City 0.5 3.0
Colony 1.0 4.0
Conspirator 0.5 2.5
Contraband 1.0 3.0
Coppersmith 1.0 2.5
Council Room 1.0 2.5
Counting House 1.0 3.0
Courtyard 1.0 2.5
Cutpurse 0.5 2.5
Duke 1.0 2.5
Embargo 1.0 2.5
Envoy 1.0 2.5
Expand 1.0 2.5
Explorer 1.0 2.5
Fairgrounds 1.0 3.5
Familiar 1.5 4.0
Farming Village 1.0 3.0
Feast 1.0 2.5
Festival 0.5 2.5
Fishing Village 1.0 3.0
Forge 1.0 3.0
Fortune Teller 1.0 2.5
Gardens 1.0 2.5
Ghost Ship 1.0 2.5
Golem 1.0 3.0
Goons 1.5 4.0
Grand Market 1.0 3.0
Great Hall 1.0 2.5
Hamlet 1.0 3.0
Harem 1.0 2.5
Harvest 1.0 3.0
Haven 1.0 2.5
Herbalist 1.0 3.0
Hoard 1.0 3.0
Horn of Plenty 1.0 3.0
Horse Traders 1.0 2.5
Hunting Party 1.0 3.0
Ironworks 0.5 2.5
Island 1.0 2.5
Jester 1.0 3.0
King's Court 1.0 3.5
Laboratory 1.0 2.5
Library 1.0 2.5
Lighthouse 1.0 2.5
Loan 0.5 3.0
Lookout 1.0 2.5
Market 1.0 2.5
Masquerade 0.5 2.5
Menagerie 1.0 3.0
Merchant Ship 1.0 2.5
Militia 1.0 2.5
Mine 1.0 2.5
Mining Village 1.0 2.5
Minion 1.0 2.5
Mint 1.0 3.0
Moat 0.5 2.5
Moneylender 1.0 2.5
Monument 1.0 3.0
Mountebank 1.0 3.5
Native Village 1.0 2.5
Navigator 1.0 2.5
Nobles 1.0 3.0
Outpost 1.0 2.5
Pawn 0.5 2.5
Pearl Diver 1.0 2.5
Peddler 1.0 3.0
Philosopher's Stone 1.0 2.5
Pirate Ship 0.5 2.5
Platinum 1.0 4.0
Possession 0.5 3.0
Potion 1.0 3.0
Quarry 1.0 2.5
Rabble 1.0 2.5
Remake 1.0 3.0
Remodel 0.5 2.5
Royal Seal 1.0 3.0
Saboteur 1.0 2.5
Salvager 1.0 2.5
Scout 0.5 2.5
Scrying Pool 1.0 3.0
Sea Hag 1.0 3.0
Secret Chamber 1.0 2.5
Shanty Town 1.0 2.5
Smithy 1.0 2.5
Smugglers 0.5 2.5
Spy 1.0 2.5
Stash 1.0 2.5
Steward 1.0 3.0
Swindler 1.0 3.0
Tactician 1.0 2.5
Talisman 1.0 3.0
Thief 0.5 2.5
Throne Room 1.0 2.5
Torturer 1.0 3.0
Tournament 1.5 4.0
Trade Route 0.5 2.5
Trading Post 1.0 2.5
Transmute 1.0 3.0
Treasure Map 1.0 3.0
Treasury 1.0 2.5
Tribute 0.5 2.5
University 1.0 2.5
Upgrade 1.0 2.5
Vault 1.0 3.0
Venture 1.0 3.0
Village 1.0 2.5
Vineyard 1.0 3.0
Warehouse 1.0 2.5
Watchtower 1.0 2.5
Wharf 1.0 3.0
Wishing Well 0.5 2.5
Witch 1.5 3.5
Woodcutter 1.0 2.5
Worker's Village 1.0 3.0
Workshop 1.0 2.5
Young Witch 1.5 3.5