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Messages - trivialknot

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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.

Dominion General Discussion / Re: Data Mining: Card Impact Factor
« on: April 29, 2018, 12:40:25 pm »
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.

Dominion General Discussion / Re: Data Mining: Card Impact Factor
« on: April 29, 2018, 10:44:08 am »
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.

Dominion General Discussion / Data Mining: Card Impact Factor
« on: April 29, 2018, 02:46:42 am »
In another thread, 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, and this tooThis 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 that's calculated without any weighting, and without contribution from non-kingdom piles.

The Results

RankCardImpact         RankCardImpact
1Rebuild2.97110Throne Room1.03
5Ill-Gotten Gains2.38114Ghost Ship1.00
9Scrying Pool2.17118Haven0.98
10Tournament2.16119Great Hall0.98
12Minion2.00121Trading Post0.96
16Masquerade1.94125Silk Road0.95
20Fishing Village1.84129Forge0.91
21Fool's Gold1.81130Rabble0.89
25Sea Hag1.75134Horn of Plenty0.86
26Torturer1.75135Death Cart0.85
27King's Court1.74136Vault0.85
28Black Market1.68137Trade Route0.84
29Border Village1.63138Smithy0.84
32Forager1.57141Wishing Well0.81
33Market Square1.55142Moat0.80
35Remake1.51144Council Room0.79
39Highway1.48148Pearl Diver0.78
40Wandering Minstrel1.45149Baron0.78
41Hunting Party1.44150Hunting Grounds0.77
43Worker's Village1.41152Scavenger0.77
46Grand Market1.40155Potion0.76
48Baker1.40157Nomad Camp0.75
52Young Witch1.34161Feast0.74
54Herald1.31163Band of Misfits0.71
58Bridge1.31167Noble Brigand0.68
62Junk Dealer1.29171Spy0.67
66Fairgrounds1.25175Poor House0.67
68Candlestick Maker1.24177Oracle0.65
72Bandit Camp1.23181Stash0.63
74Walled Village1.21183Talisman0.60
77Apothecary1.19186Secret Chamber0.58
78Hoard1.18187Merchant Ship0.58
80Village1.17189Fortune Teller0.58
85Laboratory1.14194Treasure Map0.54
87Merchant Guild1.14196Philosopher's Stone0.53
92Mining Village1.11201Pirate Ship0.50
93Spice Merchant1.11202Adventurer0.50
95Quarry1.10204Royal Seal0.48
96Farming Village1.09205Chancellor0.47
98Shanty Town1.08207Scout0.45
101Monument1.05210Counting House0.38
106Native Village1.04215Curse0.00
109Horse Traders1.03

Edit: fixed Colony and Platinum, which were calculated incorrectly.

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

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

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

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

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

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

A few problems with this procedure:
a) We're trusting top players to make good decisions.
b) You'd need a really large data set.  Possibly impractically large.
c) This ignores decisions that don't involve gaining cards, or gaining the same cards at different times.  Special mention to events.
d) Many cards (e.g. junkers, Cache) force you to gain cards without it necessarily being a "decision", and this might cause their power to be inflated.
e) This would still underestimate the power of e.g. walled village, but I'm okay with this.

Variants and Fan Cards / Re: "Demon", the Druid of Hexes
« on: April 10, 2018, 12:18:37 am »
The rotating demon, for sure, is slow.  It's at least as slow as the veto demon, because you are effectively vetoing a hex, but now you also have think about the long-term implications of that choice.

I agree with LastFootnote that the thing to try is just two boons, opponent chooses one.  $4 for a terminal silver seems reasonable.

I think beyond Delusion and Envy, the other one you need to worry about is War.  I just tried flipping up the top two hexes and they were Delusion+War and doesn't that sound nasty?

Dominion Articles / Re: Duration Draw and Stop Card Capacity
« on: April 09, 2018, 11:19:22 am »
I read this article a while back, and my main response was, "What's so special about 100% reliability?"  I mean, reliability is great and all, and having more duration draw and fewer stop cards will certainly get you reliability.  But the difference between 70% and 90% reliability is more important than the difference between 90% and 100%.  If kicking off wins you games, then an increase of 20% will win you twice as many games as an increase in 10%.

The situation where stop card capacity seems most important is when your draw is based mostly on cantrips.  Say I have 10 peddlers and 4 stop cards, my reliability is 100%.  But if I add a single stop card, suddenly my reliability is 33%.

Variants and Fan Cards / Re: "Demon", the Druid of Hexes
« on: April 09, 2018, 10:54:39 am »
Another idea is that the set-aside hexes could rotate.  Like, whenever someone plays a Demon, they discard a hex of their choice and draw a new one.  There are plenty of ways to do this, but here's one:

Rotating Demon
Action - Attack
Each other player receives a set-aside hex of their choice.  Draw and set aside a hex, and then discard a set-aside hex.
Setup: Set aside 2 hexes

I think it's more interesting without the +Buy.

There's an interesting deck you can build which is like a golden deck, but it accumulates coin tokens instead of VP tokens, and then greens all at once.  And you can still do that, if there are other sources of +Buy.  But if +Buy is limited, then there's the interesting question of when you stop accumulating coin tokens and start cashing out.  So I think it's more interesting if the availability of +Buy varies from kingdom to kingdom--ie if the +Buy comes from other cards, and not from Savings.

The first thing that jumps out to me about Shield is, you can't call it unless opponents play attacks.  So if the on-play effect is too strong, then opponents will be disincentivized from ever playing attacks, since they don't want to allow you to get Shield off your mat.  And if it's too weak, then it's basically useless when there aren't attacks.  I'm not sure where the happy medium is.

Let's Discuss ... / Re: Let's Discuss Nocturne Cards: Conclave
« on: April 03, 2018, 03:48:06 pm »
Games with Conclave as the only splitter are super neat.  Sometimes there's a particular terminal you want to play a lot of--say, Bridge--but the maximum number of times you can play it is equal to 2 plus the number of distinct non-terminal actions in the kingdom, and you can't do it very reliably.  And what if instead of Bridge, it was Bridge Troll, then you got yourself a Conclave/Duration nombo, what fun.

Other fun interactions:
Conclave/Guide, or Conclave/Ratcatcher.  You can get unlimited +action this way, but if you call reserve cards from your mat, it doesn't work that turn.
Conclave/Enchantress.  Great when your opponent has 2 identical terminals and a Conclave.
Conclave/draw-to-X.  Disappearing money is great with draw-to-X, but generally you want to play multiple copies of the draw-to-X card.

Variants and Fan Cards / Re: Crystal
« on: April 03, 2018, 03:22:23 pm »
Turning copper-silver-gold into triple-gold doesn't look too strong to me.  If you're drawing deck, you can also pull off T-map or Windfall, and get golds that way, and that's not considered too powerful.

Treasure Map and Windfall add Golds to your deck; this just produces money, so not sure they're comparable. Activating Treasure Map or Windfall isn't something you do every turn, nor would you want to.
Right the mechanics are different, but T-Map, Windfall, and Crystal all fill the role of "ways to quickly increase payload when you're drawing your deck and can handle lots of non-terminal stop cards".  It's not obvious to me that buying two $4-costs and having them collide once is significantly harder than buying a $6-cost and $5-cost, and then having them collide with silver and copper every single turn.

Anyways, I feel like the cost of Crystal hardly matters, since most of the cost is in supporting it.  It could cost $2, and you still wouldn't spam it.

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