Dominion Strategy Forum
Dominion => Dominion General Discussion => Topic started by: trivialknot on April 29, 2018, 02:46:42 am
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In another thread (http://forum.dominionstrategy.com/index.php?topic=18567.0), I suggested that you can estimate card power by measuring how much the presence of the card impacts what cards you gain. Well, ben_king kindly supplied some data, so I did it.
The Data
The data set consists of 140,000 game logs from Isotropic. All games are 2 players, pro rated, no bots, and each game has at least one player in the top 100 Isotropish rankings. It's the same data set ben_king used for this analysis (http://forum.dominionstrategy.com/index.php?topic=12341.0), and this too (http://forum.dominionstrategy.com/index.php?topic=12351.0). This data predates Adventures, so cards only go up to Guilds.
The Math
ben_king's first analysis calculated "gain percentages", the probability of gaining a card given that it was in the supply. What I'm calling the "impact factor" is a measure of how much the presence of a card changes the gain percentages of all supply piles (relative to their average gain percentage). For instance, if the presence of Duke increases the gain percentage of Duchy by 0.2, then I add 0.2 to Duke's impact factor.
Tricky details: Contributions to impact factor are weighted by how likely it is the cards will show up together. So Duchy makes a full contribution to Duke, because Duchy is in every game, but Count makes a much smaller contribution to Duke because Count is not in every game. The gain percentage of Duke makes a contribution to its own impact factor, calculated as (gain percentage)*(probability Duke is not in supply). Note that the whole calculation is based on supply piles, not kingdom cards, so I don't include Prizes or Black Market cards, but I do include Potion, Estate, Knights, etc. Yes, the impact factor of Estate must be zero, just think about it.
I am not claiming that the "impact factor" is a measure of the "strength" of a card. Maybe it is, maybe it isn't. Tell me what you think.
Update: I posted another list (http://forum.dominionstrategy.com/index.php?topic=18577.msg755632#msg755632) that's calculated without any weighting, and without contribution from non-kingdom piles.
The Results
Rank | Card | Impact | | Rank | Card | Impact |
1 | Rebuild | 2.97 | | 110 | Throne Room | 1.03 |
2 | Mountebank | 2.55 | | 111 | Cellar | 1.02 |
3 | Goons | 2.46 | | 112 | Market | 1.01 |
4 | Cultist | 2.43 | | 113 | Stonemason | 1.01 |
5 | Ill-Gotten Gains | 2.38 | | 114 | Ghost Ship | 1.00 |
6 | Ambassador | 2.36 | | 115 | Remodel | 1.00 |
7 | Governor | 2.23 | | 116 | Oasis | 0.99 |
8 | University | 2.19 | | 117 | Vagrant | 0.99 |
9 | Scrying Pool | 2.17 | | 118 | Haven | 0.98 |
10 | Tournament | 2.16 | | 119 | Great Hall | 0.98 |
11 | Familiar | 2.01 | | 120 | Watchtower | 0.98 |
12 | Minion | 2.00 | | 121 | Trading Post | 0.96 |
13 | Swindler | 2.00 | | 122 | Doctor | 0.96 |
14 | JackOfAllTrades | 1.99 | | 123 | Moneylender | 0.95 |
15 | Chapel | 1.96 | | 124 | Lookout | 0.95 |
16 | Masquerade | 1.94 | | 125 | Silk Road | 0.95 |
17 | Colony | 1.94 | | 126 | Inn | 0.92 |
18 | Platinum | 1.94 | | 127 | Smugglers | 0.92 |
19 | Soothsayer | 1.87 | | 128 | Pawn | 0.91 |
20 | Fishing Village | 1.84 | | 129 | Forge | 0.91 |
21 | Fool's Gold | 1.81 | | 130 | Rabble | 0.89 |
22 | Wharf | 1.80 | | 131 | Envoy | 0.88 |
23 | Marauder | 1.80 | | 132 | Sage | 0.88 |
24 | Witch | 1.80 | | 133 | Feodum | 0.86 |
25 | Sea Hag | 1.75 | | 134 | Horn of Plenty | 0.86 |
26 | Torturer | 1.75 | | 135 | Death Cart | 0.85 |
27 | King's Court | 1.74 | | 136 | Vault | 0.85 |
28 | Black Market | 1.68 | | 137 | Trade Route | 0.84 |
29 | Border Village | 1.63 | | 138 | Smithy | 0.84 |
30 | Tunnel | 1.60 | | 139 | Farmland | 0.84 |
31 | Steward | 1.57 | | 140 | Expand | 0.82 |
32 | Forager | 1.57 | | 141 | Wishing Well | 0.81 |
33 | Market Square | 1.55 | | 142 | Moat | 0.80 |
34 | Plaza | 1.52 | | 143 | Mint | 0.80 |
35 | Remake | 1.51 | | 144 | Council Room | 0.79 |
36 | Urchin | 1.51 | | 145 | Harem | 0.79 |
37 | Gardens | 1.50 | | 146 | Storeroom | 0.78 |
38 | City | 1.49 | | 147 | Advisor | 0.78 |
39 | Highway | 1.48 | | 148 | Pearl Diver | 0.78 |
40 | Wandering Minstrel | 1.45 | | 149 | Baron | 0.78 |
41 | Hunting Party | 1.44 | | 150 | Hunting Grounds | 0.77 |
42 | Alchemist | 1.43 | | 151 | Taxman | 0.77 |
43 | Worker's Village | 1.41 | | 152 | Scavenger | 0.77 |
44 | Lighthouse | 1.41 | | 153 | Catacombs | 0.76 |
45 | Conspirator | 1.41 | | 154 | Journeyman | 0.76 |
46 | Grand Market | 1.40 | | 155 | Potion | 0.76 |
47 | Ruins | 1.40 | | 156 | Cartographer | 0.75 |
48 | Baker | 1.40 | | 157 | Nomad Camp | 0.75 |
49 | Peddler | 1.39 | | 158 | Treasury | 0.75 |
50 | Hamlet | 1.38 | | 159 | Procession | 0.74 |
51 | Squire | 1.36 | | 160 | Develop | 0.74 |
52 | Young Witch | 1.34 | | 161 | Feast | 0.74 |
53 | Ironmonger | 1.33 | | 162 | Loan | 0.73 |
54 | Herald | 1.31 | | 163 | Band of Misfits | 0.71 |
55 | Vineyard | 1.31 | | 164 | Mystic | 0.70 |
56 | Upgrade | 1.31 | | 165 | Beggar | 0.70 |
57 | Prince | 1.31 | | 166 | Library | 0.69 |
58 | Bridge | 1.31 | | 167 | Noble Brigand | 0.68 |
59 | Nobles | 1.30 | | 168 | Rats | 0.68 |
60 | Fortress | 1.30 | | 169 | Workshop | 0.68 |
61 | Jester | 1.30 | | 170 | Bank | 0.68 |
62 | Junk Dealer | 1.29 | | 171 | Spy | 0.67 |
63 | Festival | 1.28 | | 172 | Armory | 0.67 |
64 | Count | 1.27 | | 173 | Venture | 0.67 |
65 | Duke | 1.27 | | 174 | Duchess | 0.67 |
66 | Fairgrounds | 1.25 | | 175 | Poor House | 0.67 |
67 | Knights | 1.25 | | 176 | Cutpurse | 0.66 |
68 | Candlestick Maker | 1.24 | | 177 | Oracle | 0.65 |
69 | Butcher | 1.24 | | 178 | Rogue | 0.65 |
70 | Hermit | 1.24 | | 179 | Mine | 0.64 |
71 | Bishop | 1.23 | | 180 | Pillage | 0.63 |
72 | Bandit Camp | 1.23 | | 181 | Stash | 0.63 |
73 | Margrave | 1.21 | | 182 | Woodcutter | 0.61 |
74 | Walled Village | 1.21 | | 183 | Talisman | 0.60 |
75 | Caravan | 1.20 | | 184 | Masterpiece | 0.59 |
76 | Apprentice | 1.20 | | 185 | Outpost | 0.59 |
77 | Apothecary | 1.19 | | 186 | Secret Chamber | 0.58 |
78 | Hoard | 1.18 | | 187 | Merchant Ship | 0.58 |
79 | Bazaar | 1.18 | | 188 | Graverobber | 0.58 |
80 | Village | 1.17 | | 189 | Fortune Teller | 0.58 |
81 | Haggler | 1.17 | | 190 | Saboteur | 0.57 |
82 | Warehouse | 1.16 | | 191 | Tribute | 0.57 |
83 | Counterfeit | 1.15 | | 192 | Herbalist | 0.55 |
84 | Salvager | 1.15 | | 193 | Bureaucrat | 0.55 |
85 | Laboratory | 1.14 | | 194 | Treasure Map | 0.54 |
86 | Embassy | 1.14 | | 195 | Cache | 0.54 |
87 | Merchant Guild | 1.14 | | 196 | Philosopher's Stone | 0.53 |
88 | Menagerie | 1.14 | | 197 | Mandarin | 0.52 |
89 | Crossroads | 1.12 | | 198 | Explorer | 0.52 |
90 | Stables | 1.11 | | 199 | Navigator | 0.52 |
91 | Ironworks | 1.11 | | 200 | Thief | 0.51 |
92 | Mining Village | 1.11 | | 201 | Pirate Ship | 0.50 |
93 | Spice Merchant | 1.11 | | 202 | Adventurer | 0.50 |
94 | Possession | 1.11 | | 203 | Transmute | 0.49 |
95 | Quarry | 1.10 | | 204 | Royal Seal | 0.48 |
96 | Farming Village | 1.09 | | 205 | Chancellor | 0.47 |
97 | Golem | 1.08 | | 206 | Harvest | 0.45 |
98 | Shanty Town | 1.08 | | 207 | Scout | 0.45 |
99 | Tactician | 1.07 | | 208 | Contraband | 0.42 |
100 | Trader | 1.07 | | 209 | Coppersmith | 0.39 |
101 | Monument | 1.05 | | 210 | Counting House | 0.38 |
102 | Scheme | 1.05 | | 211 | Copper | 0.00 |
103 | Courtyard | 1.05 | | 212 | Duchy | 0.00 |
104 | Embargo | 1.05 | | 213 | Silver | 0.00 |
105 | Island | 1.04 | | 214 | Gold | 0.00 |
106 | Native Village | 1.04 | | 215 | Curse | 0.00 |
107 | Militia | 1.04 | | 216 | Province | 0.00 |
108 | Altar | 1.03 | | 217 | Estate | 0.00 |
109 | Horse Traders | 1.03 | |
Edit: fixed Colony and Platinum, which were calculated incorrectly.
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This data predates Adventures, so cards only go up to Guilds.
More importantly than cards only going up to Guilds, the data was collected back when everyone sucked at the game.
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I don't think that this measure is useful. If I understand it correctly, it is high when you're more likely to gain all other cards in its presence.
Wouldn't that at first glance mean that the card is weak, because I'm more likely to want other cards?
Junkers make people gain Curses, Ruinss, etc, such that they end up high on the list, but not because people want to gain those cards.
Or it really favours engines, such that I want to gain a lot of different cards.
In the end, I can maybe explain why a card has a high or low impact factor, but I wouldn't know the reason, without knowing the card.
I think a more useful version would define categories for cards (Village, Smithy,...) and calculate the impact on those, e.g. am I more likely to gain Villages in the presence of Rebuild or not.
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I don't think that this measure is useful. If I understand it correctly, it is high when you're more likely to gain all other cards in its presence.
Wouldn't that at first glance mean that the card is weak, because I'm more likely to want other cards?
Junkers make people gain Curses, Ruinss, etc, such that they end up high on the list, but not because people want to gain those cards.
Or it really favours engines, such that I want to gain a lot of different cards.
In the end, I can maybe explain why a card has a high or low impact factor, but I wouldn't know the reason, without knowing the card. The theory is that this is a proxy for measuring how much a card changes what you'd be planning to do.
I think a more useful version would define categories for cards (Village, Smithy,...) and calculate the impact on those, e.g. am I more likely to gain Villages in the presence of Rebuild or not.
A card is high on the list if it is likely to change what cards you gain. So the impact factor goes up both if a card's presence makes you want to gain more of a card, or less of a card.
Things that gain other cards (Cursers, Ruins givers) may be over-represented. That's probably why Tunnel is so high, for example.
idk, I think there are some interesting things in there. Colony and Platinum being so high is some interesting commentary on how strategy changes in Colony games.
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I missed that the absolute amount of change is added up.
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Colony and Platinum being so high is some interesting commentary on how strategy changes in Colony games.
I don‘t think the presence of Colonies has a huge impact on the chosen strategy. If I understand the maths correctly, I assume that Colony games are merely longer, and therefore more cards are bought.
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Colony and Platinum being so high is some interesting commentary on how strategy changes in Colony games.
I don‘t think the presence of Colonies has a huge impact on the chosen strategy. If I understand the maths correctly, I assume that Colony games are merely longer, and therefore more cards are bought.
I don't know if Colony games are all that much longer by a number of turns metric. I think it's mostly that Colony games increase the amount you want to build, so you likely have more cards being gained overall.
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This data predates Adventures, so cards only go up to Guilds.
More importantly than cards only going up to Guilds, the data was collected back when everyone sucked at the game.
Man, forget Loan, look at Harem's placement here. Edit: okay maybe Harem wasn't so bad back before Adventures came out.
It feels like this metric is good at finding the cards that warp what you do on the board, but not so good at highlighting the cards where you naturally get one at convenience just because it's usually better than not getting it regardless of what you're doing, such as with Junk Dealer, Spice Merchant, Upgrade, Militia, and Ghost Ship.
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A card is high on the list if it is likely to change what cards you gain. So the impact factor goes up both if a card's presence makes you want to gain more of a card, or less of a card.
Things that gain other cards (Cursers, Ruins givers) may be over-represented. That's probably why Tunnel is so high, for example.
Correct, it looks at the absolute change in gain percentages. And I agree that it over-represents cards that make you gain other cards, especially Coppers, Curses, Ruins, Estates--things you wouldn't otherwise gain.
More importantly than cards only going up to Guilds, the data was collected back when everyone sucked at the game.
Also correct.
I don‘t think the presence of Colonies has a huge impact on the chosen strategy. If I understand the maths correctly, I assume that Colony games are merely longer, and therefore more cards are bought.
I don't look at the total number cards gained from each pile, just the percentage chance that at least one card was gained from each pile. I also tried analysis where I looked at the total number of cards gained. The number one ranked card was Ill-Gotten Gains, and well you can see which method I decided to stick with.
I think Colony is high primarily because it increases the gain percentage of 2 supply piles: Colony and Platinum.
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Have you considered other normalizations for kingdom piles? How does this list change if you give them the same weight as for basic supply piles?
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Have you considered other normalizations for kingdom piles? How does this list change if you give them the same weight as for basic supply piles?
Yes this is really easy to do, and I'm willing to post results for alternative analysis. The hard part is actually just thinking out a mathematical formula that makes sense.
The current formula is:
Impact(supply pile X) = Sum over supply pile Y abs( P(gain Y|X and Y are in supply) * P(Y is in supply|X is in supply) - P(gain Y|Y is in supply)*P(Y is in supply) )
I was thinking that I could try an alternate formula like this:
Impact(supply pile X) = Sum over supply pile Y abs( P(gain Y|X and Y are in supply) - P(gain Y|Y is in supply) )
This would eliminate the weight given to base cards (or e.g. Potions in the case of potion cards), but also it would eliminate the contribution of each card to its own impact factor. Is this calculation something people would be interested in seeing?
Another thing I wanted to do was take the impact vectors, and apply Principal Component Analysis. This would identify a few dimensions that can be used to differentiate cards. But I'm waffling on how I should define the impact vector.
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This data predates Adventures, so cards only go up to Guilds.
More importantly than cards only going up to Guilds, the data was collected back when everyone sucked at the game.
And the proof is that there are cards lower than Scout.
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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.
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.)
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) )
In that sense, I like the alternate formula more than the current one.
Wishlist:
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.
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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?
Wishlist:
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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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.
Rank | Card | Synergy Factor | Top synergy | | 2nd synergy | | Top anti-synergy | |
1 | Rebuild | 25.8 | Feodum | 0.25 | Feast | 0.24 | Laboratory | -0.34 |
2 | Chapel | 16.9 | Treasure Map | 0.29 | Market Square | 0.14 | Lookout | -0.42 |
3 | JackOfAllTrades | 16.9 | Feodum | 0.21 | Duke | 0.13 | Sea Hag | -0.30 |
4 | Governor | 16.8 | Rats | 0.19 | Militia | 0.18 | Bandit Camp | -0.34 |
5 | Cultist | 16.6 | Death Cart | 0.18 | Trader | 0.16 | Rabble | -0.27 |
6 | Masquerade | 16.6 | Possession | 0.15 | Bandit Camp | 0.12 | Sea Hag | -0.39 |
7 | Wharf | 16.6 | Bank | 0.18 | Quarry | 0.17 | Catacombs | -0.33 |
8 | University | 16.1 | Library | 0.30 | Journeyman | 0.26 | Quarry | -0.13 |
9 | Ill-Gotten Gains | 15.8 | Trader | 0.20 | Gardens | 0.17 | Festival | -0.22 |
10 | Minion | 15.2 | Lighthouse | 0.18 | Horse Traders | 0.17 | Ghost Ship | -0.31 |
11 | Goons | 14.3 | Quarry | 0.22 | Native Village | 0.22 | Hoard | -0.26 |
12 | Fishing Village | 13.8 | Envoy | 0.28 | Smithy | 0.26 | Village | -0.33 |
13 | Fool's Gold | 13.4 | Storeroom | 0.17 | Nomad Camp | 0.16 | Peddler | -0.19 |
14 | Fairgrounds | 13.1 | Death Cart | 0.19 | Spy | 0.18 | Chapel | -0.02 |
15 | Ambassador | 13.1 | Lighthouse | 0.17 | Native Village | 0.13 | Sea Hag | -0.37 |
16 | Mountebank | 12.6 | Trader | 0.23 | Watchtower | 0.22 | Witch | -0.30 |
17 | Tournament | 12.2 | Band of Misfits | 0.16 | Tactician | 0.10 | Bridge | -0.21 |
18 | Prince | 12.0 | Oracle | 0.30 | Quarry | 0.24 | Jester | -0.21 |
19 | Steward | 12.0 | Bandit Camp | 0.10 | Bazaar | 0.10 | Lookout | -0.26 |
20 | Forager | 11.9 | Poor House | 0.18 | Fool's Gold | 0.16 | Trade Route | -0.37 |
21 | Sea Hag | 11.9 | Moat | 0.17 | Lighthouse | 0.17 | Familiar | -0.32 |
22 | Border Village | 11.8 | Rabble | 0.26 | Journeyman | 0.24 | Nobles | -0.13 |
23 | Torturer | 11.7 | Lighthouse | 0.17 | University | 0.14 | Rabble | -0.27 |
24 | Remake | 11.5 | Poor House | 0.32 | Fortress | 0.13 | Moneylender | -0.28 |
25 | King's Court | 11.5 | Saboteur | 0.27 | Woodcutter | 0.21 | Bank | -0.17 |
26 | Scrying Pool | 11.4 | Storeroom | 0.21 | Woodcutter | 0.21 | JackOfAllTrades | -0.17 |
27 | Urchin | 11.4 | Fortress | 0.16 | Lighthouse | 0.10 | Lookout | -0.26 |
28 | Wandering Minstrel | 11.2 | Workshop | 0.21 | Armory | 0.19 | Farming Village | -0.30 |
29 | Walled Village | 11.2 | Hunting Grounds | 0.24 | Council Room | 0.23 | Advisor | -0.19 |
30 | Hunting Party | 11.2 | Altar | 0.15 | Horn of Plenty | 0.15 | Laboratory | -0.26 |
31 | Plaza | 11.0 | Library | 0.22 | Watchtower | 0.18 | Mining Village | -0.31 |
32 | Gardens | 10.9 | Beggar | 0.39 | Workshop | 0.26 | Apprentice | -0.13 |
33 | Swindler | 10.7 | Masterpiece | 0.30 | Chancellor | 0.28 | Fool's Gold | -0.16 |
34 | Tunnel | 10.5 | Storeroom | 0.28 | Embassy | 0.22 | Militia | -0.19 |
35 | Fortress | 10.4 | Procession | 0.20 | Develop | 0.19 | Worker's Village | -0.15 |
36 | Black Market | 10.3 | Fairgrounds | 0.17 | Quarry | 0.13 | Smugglers | -0.18 |
37 | City | 10.2 | University | 0.18 | Bridge | 0.16 | Cartographer | -0.18 |
38 | Worker's Village | 10.2 | Catacombs | 0.21 | Torturer | 0.21 | Mining Village | -0.21 |
39 | Witch | 10.2 | Lighthouse | 0.15 | Trader | 0.14 | Torturer | -0.26 |
40 | Highway | 10.1 | Talisman | 0.21 | Ironworks | 0.18 | Mystic | -0.19 |
41 | Familiar | 10.0 | Transmute | 0.25 | Golem | 0.20 | Witch | -0.13 |
42 | Vineyard | 9.9 | Herbalist | 0.24 | Rats | 0.23 | Cultist | -0.18 |
43 | Baker | 9.9 | Altar | 0.11 | Count | 0.09 | Treasury | -0.18 |
44 | Festival | 9.6 | Hunting Grounds | 0.22 | Watchtower | 0.21 | Market | -0.17 |
45 | Ironmonger | 9.6 | Workshop | 0.22 | Ironworks | 0.17 | Farming Village | -0.23 |
46 | Bazaar | 9.4 | Smugglers | 0.18 | Smithy | 0.16 | Treasury | -0.14 |
47 | Village | 9.4 | Rabble | 0.18 | Smithy | 0.18 | Shanty Town | -0.11 |
48 | Soothsayer | 9.4 | Lighthouse | 0.15 | Watchtower | 0.13 | Witch | -0.24 |
49 | Marauder | 9.3 | Lighthouse | 0.13 | Death Cart | 0.12 | Militia | -0.16 |
50 | Bridge | 9.3 | Native Village | 0.20 | Inn | 0.11 | Nomad Camp | -0.25 |
51 | Squire | 9.1 | Torturer | 0.20 | Rabble | 0.19 | Native Village | -0.14 |
52 | Margrave | 9.1 | Village | 0.15 | University | 0.15 | Ghost Ship | -0.16 |
53 | Hamlet | 9.0 | Library | 0.21 | Smithy | 0.19 | Native Village | -0.25 |
54 | Young Witch | 8.9 | Tunnel | 0.15 | Band of Misfits | 0.13 | Expand | -0.23 |
55 | Herald | 8.9 | Armory | 0.26 | Workshop | 0.25 | Mining Village | -0.13 |
56 | Grand Market | 8.9 | Quarry | 0.26 | Vault | 0.21 | Hoard | -0.18 |
57 | Embassy | 8.8 | Tunnel | 0.11 | Farmland | 0.07 | Catacombs | -0.18 |
58 | Bandit Camp | 8.8 | Envoy | 0.19 | Hunting Grounds | 0.16 | Festival | -0.18 |
59 | Farming Village | 8.7 | Torturer | 0.20 | Hunting Grounds | 0.16 | Mining Village | -0.20 |
60 | Upgrade | 8.5 | Rats | 0.31 | Poor House | 0.28 | Apprentice | -0.18 |
61 | Colony | 8.5 | Mine | 0.13 | Taxman | 0.12 | Duke | -0.24 |
62 | Platinum | 8.5 | Mine | 0.13 | Taxman | 0.12 | Duke | -0.24 |
63 | Duke | 8.4 | Beggar | 0.21 | Bureaucrat | 0.15 | Possession | -0.11 |
64 | Conspirator | 8.3 | Sage | 0.14 | Ironworks | 0.13 | Bank | -0.11 |
65 | Junk Dealer | 8.3 | Market Square | 0.11 | Quarry | 0.09 | Trading Post | -0.26 |
66 | Butcher | 8.3 | Rats | 0.23 | Fortress | 0.12 | Remodel | -0.18 |
67 | Caravan | 8.2 | Workshop | 0.26 | Ironworks | 0.23 | Advisor | -0.22 |
68 | Market Square | 8.2 | Apprentice | 0.17 | Vineyard | 0.11 | Worker's Village | -0.15 |
69 | Mining Village | 8.2 | Torturer | 0.18 | Rabble | 0.16 | Fortress | -0.16 |
70 | Lighthouse | 8.2 | Mint | 0.11 | Horn of Plenty | 0.08 | Moat | -0.20 |
71 | Bishop | 8.1 | Fortress | 0.19 | Rats | 0.18 | Gardens | -0.18 |
72 | Laboratory | 8.0 | Altar | 0.15 | University | 0.15 | Mystic | -0.15 |
73 | Salvager | 7.9 | Rats | 0.19 | Fortress | 0.12 | Remodel | -0.20 |
74 | Native Village | 7.8 | Bridge | 0.19 | Torturer | 0.15 | Pearl Diver | -0.16 |
75 | Knights | 7.8 | Moat | 0.16 | Rogue | 0.15 | Duke | -0.17 |
76 | Apprentice | 7.8 | Rats | 0.30 | Fortress | 0.16 | Gardens | -0.13 |
77 | Envoy | 7.7 | Inn | 0.14 | Worker's Village | 0.09 | Nomad Camp | -0.14 |
78 | Horn of Plenty | 7.7 | Spy | 0.16 | Journeyman | 0.15 | Workshop | -0.05 |
79 | Stash | 7.7 | Envoy | 0.15 | Scavenger | 0.13 | Market | -0.11 |
80 | Hermit | 7.7 | Market Square | 0.12 | Wishing Well | 0.11 | Sea Hag | -0.17 |
81 | Stables | 7.6 | University | 0.11 | Altar | 0.09 | Mystic | -0.16 |
82 | Trader | 7.6 | Feodum | 0.38 | Duke | 0.11 | Sea Hag | -0.18 |
83 | Quarry | 7.5 | Market | 0.16 | Forge | 0.15 | Trader | -0.09 |
84 | Crossroads | 7.5 | Torturer | 0.17 | Great Hall | 0.14 | Native Village | -0.14 |
85 | Alchemist | 7.4 | Possession | 0.22 | Transmute | 0.17 | Smithy | -0.12 |
86 | Tactician | 7.4 | Storeroom | 0.18 | Secret Chamber | 0.16 | Soothsayer | -0.11 |
87 | Peddler | 7.4 | Worker's Village | 0.13 | Salvager | 0.12 | Fool's Gold | -0.09 |
88 | Monument | 7.4 | Golem | 0.12 | Band of Misfits | 0.10 | Scavenger | -0.16 |
89 | Menagerie | 7.3 | Ironworks | 0.14 | Outpost | 0.13 | Envoy | -0.12 |
90 | Ruins | 7.3 | Fairgrounds | 0.09 | Watchtower | 0.09 | Baron | -0.12 |
91 | Haggler | 7.1 | Mining Village | 0.14 | Spy | 0.13 | Rogue | -0.11 |
92 | Count | 7.0 | Duke | 0.18 | Grand Market | 0.05 | Trading Post | -0.16 |
93 | Candlestick Maker | 7.0 | Vineyard | 0.16 | Peddler | 0.12 | Pawn | -0.21 |
94 | Ironworks | 7.0 | Silk Road | 0.23 | Gardens | 0.21 | Armory | -0.19 |
95 | Merchant Guild | 6.9 | Quarry | 0.10 | Golem | 0.09 | Nomad Camp | -0.12 |
96 | Embargo | 6.9 | Stash | 0.11 | Venture | 0.10 | Pawn | -0.11 |
97 | Golem | 6.9 | Apothecary | 0.17 | Saboteur | 0.12 | Throne Room | -0.07 |
98 | Throne Room | 6.8 | Armory | 0.13 | Band of Misfits | 0.13 | Mining Village | -0.08 |
99 | Procession | 6.8 | Adventurer | 0.17 | Catacombs | 0.15 | Horn of Plenty | -0.06 |
100 | Apothecary | 6.7 | Possession | 0.20 | Golem | 0.19 | Loan | -0.11 |
101 | Altar | 6.7 | Stash | 0.16 | Mystic | 0.16 | Expand | -0.10 |
102 | Spice Merchant | 6.7 | Fool's Gold | 0.11 | Market Square | 0.09 | Moneylender | -0.24 |
103 | Militia | 6.6 | Band of Misfits | 0.12 | Lighthouse | 0.11 | Cutpurse | -0.18 |
104 | Counterfeit | 6.6 | Fool's Gold | 0.10 | Envoy | 0.10 | Loan | -0.14 |
105 | Ghost Ship | 6.6 | Farming Village | 0.14 | Lighthouse | 0.13 | Militia | -0.11 |
106 | Feodum | 6.6 | Masterpiece | 0.41 | Trader | 0.30 | Throne Room | -0.10 |
107 | Market | 6.5 | Quarry | 0.19 | Conspirator | 0.11 | Band of Misfits | -0.10 |
108 | Horse Traders | 6.4 | Tunnel | 0.11 | Gardens | 0.10 | Nomad Camp | -0.15 |
109 | Warehouse | 6.4 | Tunnel | 0.17 | Treasure Map | 0.12 | Oasis | -0.18 |
110 | Rabble | 6.3 | University | 0.12 | Village | 0.12 | Library | -0.10 |
111 | Shanty Town | 6.3 | Rabble | 0.14 | Council Room | 0.13 | Wishing Well | -0.12 |
112 | Doctor | 6.3 | Venture | 0.09 | Merchant Ship | 0.08 | Lookout | -0.20 |
113 | Jester | 6.3 | Spy | 0.09 | Native Village | 0.08 | Rogue | -0.12 |
114 | Watchtower | 6.2 | Festival | 0.13 | Rats | 0.11 | Oracle | -0.11 |
115 | Nobles | 6.2 | Quarry | 0.20 | Trade Route | 0.13 | Harem | -0.14 |
116 | Courtyard | 6.2 | Worker's Village | 0.08 | Bandit Camp | 0.07 | Pearl Diver | -0.17 |
117 | Moneylender | 6.2 | Venture | 0.09 | Stash | 0.09 | Cutpurse | -0.14 |
118 | Inn | 6.1 | Torturer | 0.13 | Hunting Grounds | 0.13 | Cartographer | -0.10 |
119 | Vault | 6.1 | Grand Market | 0.10 | Tunnel | 0.09 | Envoy | -0.12 |
120 | Lookout | 6.1 | Mystic | 0.09 | Treasure Map | 0.09 | Loan | -0.18 |
121 | Silk Road | 6.0 | Workshop | 0.16 | Baron | 0.14 | Laboratory | -0.08 |
122 | Hoard | 5.9 | Harem | 0.13 | Silk Road | 0.12 | Conspirator | -0.09 |
123 | Smugglers | 5.9 | Apprentice | 0.10 | Duke | 0.09 | Workshop | -0.07 |
124 | Vagrant | 5.9 | Vineyard | 0.09 | Harem | 0.08 | Pearl Diver | -0.24 |
125 | Trading Post | 5.9 | Feodum | 0.12 | Grand Market | 0.10 | Altar | -0.11 |
126 | Possession | 5.9 | Apothecary | 0.20 | Alchemist | 0.17 | Conspirator | -0.09 |
127 | Island | 5.8 | Ironworks | 0.20 | Hoard | 0.10 | Remodel | -0.11 |
128 | Haven | 5.7 | Envoy | 0.10 | Treasure Map | 0.08 | Pearl Diver | -0.21 |
129 | Forge | 5.7 | Rats | 0.12 | Catacombs | 0.10 | Gardens | -0.11 |
130 | Beggar | 5.7 | Gardens | 0.25 | Counting House | 0.13 | Fortress | -0.08 |
131 | Journeyman | 5.7 | Horn of Plenty | 0.07 | Bank | 0.07 | Council Room | -0.12 |
132 | Masterpiece | 5.6 | Feodum | 0.32 | Gardens | 0.15 | Cellar | -0.08 |
133 | Remodel | 5.6 | Rats | 0.14 | Fool's Gold | 0.13 | Horn of Plenty | -0.08 |
134 | Stonemason | 5.5 | Catacombs | 0.10 | Feodum | 0.09 | Altar | -0.07 |
135 | Cellar | 5.5 | Tunnel | 0.12 | Bureaucrat | 0.08 | Pearl Diver | -0.15 |
136 | Smithy | 5.5 | Festival | 0.09 | Village | 0.09 | Envoy | -0.18 |
137 | Workshop | 5.4 | Gardens | 0.15 | Silk Road | 0.13 | Stonemason | -0.08 |
138 | Feast | 5.4 | Stash | 0.09 | Witch | 0.07 | Fortress | -0.07 |
139 | Storeroom | 5.2 | Tunnel | 0.12 | Tactician | 0.10 | Woodcutter | -0.11 |
140 | Pawn | 5.2 | Vineyard | 0.11 | Stash | 0.09 | Pearl Diver | -0.19 |
141 | Catacombs | 5.2 | University | 0.10 | Bank | 0.08 | Journeyman | -0.13 |
142 | Scheme | 5.2 | Conspirator | 0.12 | Armory | 0.09 | Wishing Well | -0.16 |
143 | Nomad Camp | 5.2 | Golem | 0.09 | Highway | 0.07 | Woodcutter | -0.10 |
144 | Rats | 5.2 | Apprentice | 0.14 | Butcher | 0.14 | Spice Merchant | -0.07 |
145 | Expand | 5.2 | Rats | 0.09 | Marauder | 0.08 | Bank | -0.09 |
146 | Library | 5.2 | Festival | 0.09 | University | 0.09 | Envoy | -0.10 |
147 | Armory | 5.2 | Advisor | 0.12 | Vineyard | 0.12 | Workshop | -0.12 |
148 | Venture | 5.1 | Altar | 0.09 | Bank | 0.08 | Graverobber | -0.10 |
149 | Trade Route | 5.1 | Band of Misfits | 0.08 | Scrying Pool | 0.07 | Develop | -0.11 |
150 | Baron | 5.0 | Silk Road | 0.10 | Cartographer | 0.07 | Nomad Camp | -0.11 |
151 | Treasury | 5.0 | University | 0.09 | Expand | 0.08 | Mystic | -0.10 |
152 | Hunting Grounds | 5.0 | Native Village | 0.10 | Worker's Village | 0.09 | Council Room | -0.09 |
153 | Sage | 5.0 | Trader | 0.07 | Golem | 0.07 | Wishing Well | -0.11 |
154 | Advisor | 4.9 | Armory | 0.19 | Ironworks | 0.14 | Spy | -0.09 |
155 | Scavenger | 4.9 | Stash | 0.20 | Lookout | 0.07 | Navigator | -0.12 |
156 | Council Room | 4.9 | Bank | 0.11 | Village | 0.09 | Library | -0.07 |
157 | Wishing Well | 4.9 | Mystic | 0.08 | Horn of Plenty | 0.07 | Sage | -0.10 |
158 | Moat | 4.9 | Harem | 0.07 | Festival | 0.07 | Pawn | -0.10 |
159 | Develop | 4.9 | Rats | 0.15 | Poor House | 0.13 | Envoy | -0.10 |
160 | Oasis | 4.8 | Tunnel | 0.13 | Soothsayer | 0.07 | Wishing Well | -0.12 |
161 | Woodcutter | 4.8 | Ill-Gotten Gains | 0.08 | Gardens | 0.08 | Baron | -0.06 |
162 | Pirate Ship | 4.8 | Oasis | 0.10 | Merchant Ship | 0.08 | Envoy | -0.12 |
163 | Adventurer | 4.8 | Stash | 0.08 | Venture | 0.08 | Peddler | -0.06 |
164 | Cutpurse | 4.7 | Hoard | 0.08 | Band of Misfits | 0.07 | Navigator | -0.09 |
165 | Great Hall | 4.7 | Ironworks | 0.19 | Silk Road | 0.13 | Sage | -0.10 |
166 | Talisman | 4.7 | Feodum | 0.11 | Highway | 0.09 | Smugglers | -0.07 |
167 | Taxman | 4.7 | Harem | 0.09 | Soothsayer | 0.08 | Moneylender | -0.08 |
168 | Bureaucrat | 4.6 | Feodum | 0.11 | Duke | 0.09 | Vineyard | -0.06 |
169 | Secret Chamber | 4.6 | Stash | 0.09 | Tactician | 0.08 | Poor House | -0.07 |
170 | Herbalist | 4.6 | Philosopher's Stone | 0.14 | Stash | 0.09 | Moat | -0.07 |
171 | Cache | 4.6 | Monument | 0.07 | Young Witch | 0.07 | Conspirator | -0.07 |
172 | Loan | 4.6 | Venture | 0.08 | Baker | 0.07 | Oracle | -0.07 |
173 | Mystic | 4.6 | Altar | 0.08 | Rebuild | 0.07 | Tribute | -0.10 |
174 | Band of Misfits | 4.6 | Duke | 0.07 | Margrave | 0.06 | Bishop | -0.10 |
175 | Mint | 4.5 | Fool's Gold | 0.08 | Harem | 0.06 | Trading Post | -0.08 |
176 | Transmute | 4.5 | Trader | 0.08 | Apothecary | 0.08 | Stash | -0.06 |
177 | Thief | 4.5 | Venture | 0.10 | Familiar | 0.08 | Stonemason | -0.07 |
178 | Harem | 4.5 | Silk Road | 0.13 | Hoard | 0.09 | Ironworks | -0.07 |
179 | Farmland | 4.5 | Trader | 0.09 | Silk Road | 0.07 | Band of Misfits | -0.06 |
180 | Philosopher's Stone | 4.4 | Herbalist | 0.14 | Duke | 0.09 | Throne Room | -0.11 |
181 | Mine | 4.4 | Harem | 0.09 | Catacombs | 0.08 | Band of Misfits | -0.05 |
182 | Bank | 4.4 | Venture | 0.12 | Tactician | 0.07 | Vineyard | -0.07 |
183 | Harvest | 4.4 | Hoard | 0.07 | Duke | 0.07 | Highway | -0.05 |
184 | Chancellor | 4.4 | Envoy | 0.10 | Stash | 0.10 | Quarry | -0.04 |
185 | Cartographer | 4.4 | Tunnel | 0.12 | Moneylender | 0.06 | Bazaar | -0.09 |
186 | Oracle | 4.4 | Ill-Gotten Gains | 0.09 | Venture | 0.07 | Fortune Teller | -0.09 |
187 | Rogue | 4.3 | Soothsayer | 0.08 | Doctor | 0.07 | Candlestick Maker | -0.07 |
188 | Pearl Diver | 4.3 | Cartographer | 0.07 | Jester | 0.07 | Lighthouse | -0.09 |
189 | Noble Brigand | 4.3 | Beggar | 0.09 | Venture | 0.07 | Ironworks | -0.05 |
190 | Duchess | 4.3 | Stash | 0.12 | Venture | 0.07 | Workshop | -0.08 |
191 | Contraband | 4.3 | Expand | 0.09 | Envoy | 0.08 | Festival | -0.06 |
192 | Spy | 4.3 | Doctor | 0.08 | Golem | 0.07 | Quarry | -0.07 |
193 | Outpost | 4.3 | Trading Post | 0.07 | Navigator | 0.07 | Horn of Plenty | -0.05 |
194 | Saboteur | 4.3 | Embargo | 0.07 | Sage | 0.07 | Armory | -0.07 |
195 | Royal Seal | 4.2 | Cartographer | 0.08 | Venture | 0.07 | Stash | -0.07 |
196 | Navigator | 4.2 | Tunnel | 0.08 | Farmland | 0.08 | Oasis | -0.07 |
197 | Tribute | 4.2 | Ghost Ship | 0.09 | Familiar | 0.07 | Pillage | -0.05 |
198 | Treasure Map | 4.2 | Chapel | 0.07 | Sea Hag | 0.07 | Throne Room | -0.08 |
199 | Death Cart | 4.1 | Rats | 0.11 | Band of Misfits | 0.07 | Nomad Camp | -0.08 |
200 | Scout | 4.1 | Harem | 0.08 | Band of Misfits | 0.07 | Quarry | -0.06 |
201 | Counting House | 4.1 | Beggar | 0.10 | Treasury | 0.08 | Tactician | -0.05 |
202 | Poor House | 4.1 | Vault | 0.09 | Island | 0.06 | Remake | -0.09 |
203 | Mandarin | 4.0 | Mint | 0.07 | Familiar | 0.07 | Envoy | -0.07 |
204 | Fortune Teller | 4.0 | Ill-Gotten Gains | 0.07 | Mystic | 0.06 | Poor House | -0.05 |
205 | Merchant Ship | 4.0 | Marauder | 0.06 | Inn | 0.06 | Harvest | -0.06 |
206 | Coppersmith | 3.9 | Apothecary | 0.07 | Council Room | 0.06 | Quarry | -0.07 |
207 | Pillage | 3.9 | Alchemist | 0.08 | Hoard | 0.06 | Saboteur | -0.06 |
208 | Graverobber | 3.9 | Rats | 0.08 | Marauder | 0.07 | Possession | -0.06 |
209 | Explorer | 3.9 | Duke | 0.07 | Silk Road | 0.06 | Envoy | -0.08 |
210 | Potion | 3.2 | Herbalist | 0.08 | Woodcutter | 0.07 | Quarry | -0.04 |
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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.
Yeah, to put it another way, if, in a game with Counting House, you're not much more likely to gain Counting House than you are in a game without Counting House, that's evidence that Counting House is a fairly low-impact card whose presence on the board doesn't usually matter.
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I love that Swindler's top synergies are terrible cards that you get Swindled into.
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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.
Yeah, to put it another way, if, in a game with Counting House, you're not much more likely to gain Counting House than you are in a game without Counting House, that's evidence that Counting House is a fairly low-impact card whose presence on the board doesn't usually matter.
But that runs against the idea of "how much does the presence of the card change the gain probabilities of cards?". By that definition, the presence of Counting House doesn't affect the probability of gaining Counting House conditional on it being present.
I wouldn't call it "synergy factor", if it sums up the absolute values of synergy and anti-synergy.
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Remake's top synergy card: Poor House ;)
Looking at the stats, it's a higher synergy pair than everything except Gardens/Beggar, Trader/Feodum, and Masterpiece/Feodum.
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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.
I know, that people can argue what defines a Village. I would suggest that you pick whatever definition you like. Given that most villages are uncontroversial, it shouldn't matter too much for the results.
I'm skeptical that PCA will deliver anything useful, but I'd be happy to be wrong about that.
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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.
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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.
Hey you can use your math to figure out categories.
1. Each card determines a category. You won't actually do each card, because we care about e.g. villages rather than e.g. Poor Houses.
2. So, pick a card, e.g. Village.
3. Iterate through all other cards.
4. For each card, calculate the sum of the absolute value of the differences between gain percentages for Village and the other card, for all other cards. For example, for Poor House, first you say, okay how much does Village change the gain percentage for Ironworks, how much does Poor House change the gain percentage for Ironworks, take the absolute value of the difference; then, Forager, how much does Village change the gain percentage for Forager, how much does Poor House change the gain percentage for Forager, and so on. In the end you have this number that says, how similar in changing gain percentages is Poor House to Village.
5. Sort from lowest to highest; the ones at the top are the most similar to the chosen card, e.g. Village.
6. Draw the line where it looks like it goes.
This of course includes power level; a card we recognize as a village might be so weak that it's beaten by cards we are sure aren't villages. Still, could be fun.
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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.
Hey you can use your math to figure out categories.
In other words, you have a matrix of interaction strengths. Treat each column (or row, or some combination to account for interactions in both directions) as a vector, and run a clustering algorithm on the results. (Donald suggests measuring distance with the 1-norm, but you could probably use any reasonable norm. You might need to lower the dimensionality by random projection first.)
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*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.
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*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.
Or like, on board where you go for a Stash deck and you buy Duchy, Duchess is a "might as well" addition. Or am I misinterpreting the statistic.
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Or like, on board where you go for a Stash deck and you buy Duchy, Duchess is a "might as well" addition. Or am I misinterpreting the statistic.
It's the other way around: on a board with Duchess, you're more likely to go for a Stash deck. (We don't know the number for Duchess on a Stash board.)
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Or like, on board where you go for a Stash deck and you buy Duchy, Duchess is a "might as well" addition. Or am I misinterpreting the statistic.
It's the other way around: on a board with Duchess, you're more likely to go for a Stash deck. (We don't know the number for Duchess on a Stash board.)
But there's overlap isn't there? Like, Masterpiece/Feodum has a similarly high synergy factor to Feodum/Masterpiece.
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Or like, on board where you go for a Stash deck and you buy Duchy, Duchess is a "might as well" addition. Or am I misinterpreting the statistic.
It's the other way around: on a board with Duchess, you're more likely to go for a Stash deck. (We don't know the number for Duchess on a Stash board.)
But there's overlap isn't there? Like, Masterpiece/Feodum has a similarly high synergy factor to Feodum/Masterpiece.
Yes, you'd usually expect that. For Feodum/Masterpiece both cards are not getting gained much without the other, but gained a lot when they are both present. For Capital/Mandarin I'd expect that Capital increases gain% of Mandarin more than the other way around.
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*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).
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Thanks to ceviri and his tool (http://forum.dominionstrategy.com/index.php?topic=18336.0), I got some logs from the new client since the Nocturne release. There are about 1100 logs that feature either me (75%) or RTT as a player.
The small sample means that you can expect some outliers for random reasons, but the results look fine enough to me that I'm posting them. You can find them here (https://docs.google.com/spreadsheets/d/1M2L7hcY3sbA33OwuZhgPYJWVlMFgJYBdK8cnkbJHmbo/edit#gid=1032809554).
Small sample also means that I'm calculating the impact factor a bit differently than trivialknot, but the idea is still to see how much the buy% or gain% of other cards changes in absolute terms when card/event/landmark X is on the board. Results are normalized to have mean 0 and standard deviation 1.
One thing to note is that a card being on the bottom means that it doesn't affect the chance that at least one of the players buys/gains the other cards much. That could be, because it's a dud as for many cards in the original list. Or because it doesn't affect the average strategy much.
Probably, Herald is at the bottom for random reasons. But you could make a case that with Herald on the board you often play it the same as "on average" and you gain some Heralds in addition.
PS: There's a bunch of other stuff, I've been calculating with those logs, which you can find on the other sheets. Feel free to ask, if there are any questions.
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Yeah, Herald is basically a helper card that usually doesn't encourage you to buy things you weren't going to buy anyway. I don't think it's a coincidence that Lost City, which is basically a Herald that never duds, is also near the bottom. Though Scheme is near the top, and that's also just a helper card, so... dunno.
One thing I am surprised by is how low Stonemason is, considering the way it changes how you gain stuff, like Alms, which is near the top.
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Similar to Alms, Stonemason also has the property that it changes gains less than buys. It was below average on the list for gains with cards up to Guilds as well.