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Messages - markus

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I looked at the sample of logs that I have since the release of Renaissance (about 70 games with Peasant and each pile).
There's a bit of variation between Teacher adding +Card and Pathfinding. The Teacher list is dominated by Villages, Governor is only near the top on the Pathfinding list.
Here are the top 30 sorted by Pathfinding targets (it counts each time the token gets placed on the pile by either player):

Eventually, I can also post the stats for the other tokens.

Dominion Articles / Re: A Different Way To Look at Dominion
« on: November 16, 2019, 09:58:06 am »
  • By not knowing when it is the optimal time for greening, but relying on your opponent to signal it, you're still giving up some of your win chances.
  • Greening first in the weaker position can make sense, if you rely on a bit of luck that you draw well in the next couple of turns.
  • A common situation is one where players build up to double-Province turns. In that case, being the first to green can give you quite an advantage: gaining 3 Provinces while your opponent only has 2 Provinces, puts them in a difficult situation on their next turn.

Masterpiece, Feodum, Delve and Tower

Some people would say that Ironworks or Rats also help, but I think that this combo is good enough on its own.

Rules Questions / Re: Multiple things happening at the same time
« on: October 10, 2019, 02:09:06 pm »
My opinion is: Road Network is mandatory. When it's my turn in turn order, I need to resolve it before it's the next player's turn. Before resolving Road Network, I'm allowed to trash Fool's Gold. I'm also allowed to trash afterwards. If someone else after me in turn order resolves something (e.g. Road Network draw), I get another chance to trash Fool's Gold.

Dominion Online at Shuffle iT / Re: Trader/Changeling interaction bug?
« on: August 25, 2019, 02:16:06 am »
The problem is that lightbulb reacted to the wrong gain (namely the Urchin gain). With indents the log looks like this:

Turn 4 - markus
m plays 3 Coppers. (+$3)
m buys an Urchin.
   m gains a Curse.
   m reacts with a Trader.
   m gains a Silver.
      m returns a Silver.
      m receives a Changeling.

So reacting was not in response to gaining Curse but to buying (and gaining) Urchin. In terms of clicking in the game: they gain the Curse first, but declline Trader; second they gain Urchin and use Trader and then use Changeling's ability.

This analysis rings hollow because 6$ is already one of the "swing" costs.  6$ on turn 3/4 is far from guaranteed.
Having played a bit with Captain, I agree. It sucks when your opponent hits $6 early on. Then the Captain will help a lot to get more Captains. (Artisan for example can't gain itself and makes it rather harder to hit $6 again.)
Overlord has a debt cost to make it available with fewer coins to everyone, but still be reasonably expensive to not run very often.

Captain reads a lot like a 7$
That seems like a fairer price but it would make it swingier I suppose, because hitting $7 is even more difficult than $6.

Wouldn't that argument apply to every cost card?
Forge and Expand are not cards you need too many of copies of (early on). Inheritance definitely has the problem that a player early on gets a significant lead. King's Court as well, if you connect it with an appropriate action. Bank is not a great card and Opulent Castle not available early on.
But Captain is likely to help you get another Captain and there's often a good reason to do so. Therefore, hitting $7 early snowballs more than with a $6 cost Captain.

Captain reads a lot like a 7$
That seems like a fairer price but it would make it swingier I suppose, because hitting $7 is even more difficult than $6.

Skill multiplier is not a very difficult concept: you are say 1 mu (roughly 7.5 levels) ahead of your opponent on the leaderboard. This has some implications for how much you win on an average board (73%). A skill multiplier of 0.8 means that with that card on the board, you only win as if the skill difference was 0.8*1 (resulting in 69%).
"The better player winning less than the worse player" would only happen if the skill multiplier was negative - that is by far not the case for any card, and I doubt that such a card will ever exist (e.g. "The weaker player tosses a coin and wins the game on heads.").

A high skill multiplier might mean that it's difficult to master the card, or it involves little luck such that small skill differences really matter, or that it's better known to good players (e.g. some players might know the base cards but not the expansions). A single number can't really tell apart 3 reasons, but for Black Market the total effect is that the better player wins more than expected. Hence, even if there was more "luck" involved, there is even more "skill" needed.

When Silver is the best thing to buy at $4 repeatedly, it's probably a good idea for the game to be shorter.

5/2 on a Cathedral board.

markus' stats show that players with a 5/2 on a Cathedral board have a 53% win rate, exactly the same as their win rate on boards without Cathedral.

I'm not sure you're reading the chart correctly (but maybe I'm not either) - seems to indicate a modest 5% decline in win rate?

You're both correct: the win rate with 5/2 or 2/5 on Cathedral boards is 53%, but that player tended to be the stronger one or first player more often in those almost 200 games. (That is just for random reasons.)
So actually that was not a better performance than expected. Due to the relatively small sample it's also well within the margin of error.

What we can conclude from that, however, that you're probably not losing like 40-60 or worse with 5/2 on Cathedral boards.

Dominion General Discussion / Re: Card Draw Statistics
« on: March 04, 2019, 02:14:07 am »
One thing is to check how the cards with varying draw do. I'm taking averages between players now to not have the "got lucky and won effect":

Scrying Pools have a net draw of 10.7 cards, which is 3.7 cards per gain. City Quarter has (10.6 | 4.6).

Seer has a net draw of 8.2 cards (3.8 per gain), putting it ahead of Laboratory (8.0 | 3.1) and Stables (7.5 | 3.1).
Menagerie is just behind those with 7.2 cards net draw (3.0 per gain). So a gained Menagerie draws basically the same as a Laboratory. Admittedly, you can't make it work on every board, but it seems to work quite often.
Wishing Well on the other hand is at (2.3 | 1.2), Patrician at (1.3 | 0.7).

2.8 Caravans basically draw the same as the 0.85 Sinister Plots over the course of the game (6.3 cards). Per gained Caravan that is only 2.3 cards.
Magpie is just behind it with 6.1 cards drawn. Most of the gains will be free, so let's look at the buys: 3.9 cards per buy. (Ok, some of them will be gained by Workshops making that number a bit too high.)

Experiment is lower with 4.9 cards drawn and let's say 1.4 cards per 2 gains. Yes, it's nice that you can hold on to them, but you had 1 dead card on that turn.
Expedition is further down with 4.3 cards and 1.9 cards per buy. It's even bought less often than Experiment (yes, discard attacks hurt it).

Library vs Scholar: they basically get gained the same amount. Library draws (3.5 | 6.3) compared to Scholar's (3.2 | 5.7). Scholar has the advantage of sifting (3.1 cards per game), Library of skipping Actions that you don't want.
For comparison, Cursed Village is at (8.5 | 4.3).

Dominion General Discussion / Card Draw Statistics
« on: March 03, 2019, 03:36:46 pm »
I’ve used my database of logs since the release of Renaissance to calculate statistics on draw and discard. (21,000 games with either the worse player having mu>1.3 or the better player having mu>1.8)
I’m tracking each time a card enters and leaves the hand of a player. (Or is played from somewhere else as if it entered your hand and was played immediately – Vassal, Throne Rooms, Band of Misfits,... see my notes below.) The results can be found in my stats sheet.

First, I’ll have a general look at the boards. I can check how many cards are drawn during the course of a game: 125 cards per player. The winner draws 136 cards compared to the loser’s 115 cards. (For example, playing a Village draws 1 card.)
This number is generally higher on boards with cards that increase your hand-size and also on boards with cantrips (playing each draws 1 card). Minion and Shepherd games top the list with 143 cards per player. On the other hand, if there’s trashing available, you don’t need to draw as many cards to get the game to an end. Donate is at the bottom of the list with only 92 cards. Other cards that can make a game short like Rebuild, Butcher and Salt the Earth are also listed there.

Most of this draw comes from drawing your 5 new cards during clean-up (75 cards). That’s more or less 15 turns drawing 5 cards each. (The exception would be Outpost turns and situations in which the deck contains fewer than 5 cards.) This number is 3 cards higher for the winner (the winner is more likely to have more turns).
Therefore, anything that makes the game longer like attacks will show up with a higher number there. Mountebank with 88 cards and Knights with 86 cards top the list. Donate with 60 cards and Governor with 62 cards are at the other end.

Hence, we’re left with 50 cards that are drawn by playing cards (or buying stuff). Some of that will be cantrips and when you play a Laboratory, your handsize only increases by 1. Therefore, I’m calculating “net draw”. It takes out the cost of playing the card to your handsize as well as discarding (Cellar) or trashing (Chapel) other cards from hand. Playing a Laboratory provides 1 card net draw, playing a Smithy 2 cards, playing a Warehouse -1 card. Summing up over all those cards with a positive net draw, I end up with 14 cards per player (winner 18, loser 12).
Margrave and Wharf are topping the list now, while Donate is still at the bottom, but you’ll also find Grand Market down there.

The second part of the table are the stats for the specific cards. I’ll present the stats from the winner’s perspective, noting that the loser drawing less is naturally also a sign of getting less lucky and not just being less skilled.
First in columns M and N, there is the total draw provided by the cards. Cards will be at the top if they draw a lot and are used a lot. (Counting House draws a lot per play, but unfortunately you often just ignore it.) Shepherd, Stables and Sauna/Avanto are the top with a draw of around 30 cards for the winner, Laboratory is at 21 cards and the Smithy family around 10 cards.
This can be split up into drawing on play, duration (Den of Sin and Wharf at the top), and on gain or trash effects (Villa, Fortress, Den of Sin and Ghost Town at the top.)
Next, I can look into how all this draw is used in practice. Columns O and P have the “discard” of cards from hand caused by this card. That could be discarding, putting on top of your deck, and trashing other cards from your hand. It could happen because you play the card, gain the card, call the card from the reserve mat, bought some event, etc.
Sifters are at the top of the list with Dungeon discarding 22 cards. Strong trashers end up with 8-10 cards. This discard number is decomposed into discarding and trashing further right in the table as well for whatever card that might be interesting (Count trashes 3.9 cards and discards 3.1 cards).
Another discard component that can be found there, is how often the card is “dead” in your hand (discarded during the clean-up phase). Because you either can’t, don’t need or don’t want to play it during your turn – not a good use of your draw. At the top of this list is the junk that you begin the game with (9.4 cards for Estates and 8.3 for Shelters). Cards that you typically can and want to play are below 1 in general.
Note that the measure is a bit too nice to terminal draw cards because cards that you draw dead with Smithy other than Smithies will count as a dead card in their respective row. But then it’s also partly Village’s fault that you can’t play it with 0 Actions left.

This allows me to calculate the net draw provided by each card. It is the draw minus the discard minus the number of plays and minus the number of being “dead” in hand. So the cards at the top of the list are the ones that provide you with a larger handsize. And the cards at the bottom better be useful in some other dimension to be worth the handsize reduction. Wharf wins with +19 cards, followed by City Quarter and Scrying Pool with around +15 cards for the winner. City Quarter and Scrying Pool are interesting because the loser only draws 6 cards with it. Partly, that’s because they gain fewer copies, but part of it will also be good or bad luck in aligning them in the right way. At the bottom there is Copper with -34 cards of course, followed by Ambassador (-20) and Forager, Remake around -15 cards. Artificer is the lowest card that doesn’t trash with -12 cards.

Some cards also affect the opponent’s handsize in a positive or negative way. I’m having those numbers in the decomposition of draw and discard. Minion tops both of those lists with the winner discarding 11.7 cards and drawing 9.3 cards due to their opponent’s Minion play.
I can add that effect on the opponent’s handsize to arrive at my preferred measure of card draw: subtract the cards that the opponent draws from net draw and add the cards that the opponent discards. Then, a usual Council Room play provides you with +2 cards relative to your opponent and a Militia play that makes them discard from 5 to 3 cards counts as +1 card. (Discarding your bad cards to Militia is not as bad of course as drawing fewer cards of course. But this exercise is just about drawing and discarding cards. Drawing a Curse to hand due to your opponent’s Torturer is usually not good, either…)
With this measure in columns S and T, Wharf keeps its top spot, but Margrave gets close to it with +19 cards as well. Ghost Ship also jumps up from +4 cards to +11 cards here, while Lost City loses from +9 cards to +6 cards.
For further statistics, you can download the sheet and calculate them from the available numbers (e.g. cards drawn per play or per gain).

The accounting exercise is that cards “drawn” equals cards “discarded” over the course of the game. There are some errors and omissions in the official log, woodcutter, and my code that I try to correct for. But some edge cases that I’m aware of and probably more that I’m not aware of are missed (e.g. gaining Ghost Town not to hand but top of deck with Armory).
I can check for each game and player how big the absolute difference between draw and discard is and I’m satisfied with it being only 0.07 cards on average per player and game. The worst boards in that sense include Plan or Innovation, because those uses are not logged, but the error is still below 0.3 cards per game. If you still see something that looks odd (yes, Horn of Plenty shouldn’t have 1/700 cards drawn on trash/gain) and significant, let me know.

The general rule is that I want to attribute the draw or discard to what ultimately caused it. For example, if you play a Workshop and gain a Ghost Town, the gain to hand is Ghost Town’s effect and not Workshop’s. If you trash a Rats, the card that you draw gets attributed to Rats and not the trasher. The exception are boons and hexes which do get added to the card that caused their receives.

Only stuff that happens to a player’s hand before and during their last turn counts. For example, if you Militia your opponent and end the game, their discard doesn’t count.

For most cards it should be obvious from the numbers what is what (for example, setting aside with Island counts as trashing as does returning with Ambassador).

Vassal, Summon, etc count as +1 card draw for whatever caused the other card to be played. For example Vassal finding a Village counts as 1 Vassal and 1 Village play, and 1 draw for Vassal and Village each. As a result, net draw is 0 (your hand size is the still the same). Similarly, Summon counts as 1 card duration draw if it plays the card on the next turn.
Throne Room family: if a Throne Room plays another card, Throne Room draws 1 card. (Think of it as Throne Room putting the played card into your hand and immediately playing it again.) Playing Throne Room – Village means: 1 Throne Room and 2 Villages played, 1 card drawn by Throne Room, 2 cards drawn by Villages. It all nets to 0 and indeed your handsize is the same afterwards.
With the same logic, King’s Court gets +2 cards, when it plays a card (King’s Court on Village nets 1 card).

Band of Misfits, Overlord, Necromancer: playing them also draws 1 card. Overlord as Village means 1 Overlord and 1 Village play, 1 card drawn by Overlord and 1 card drawn by Village for a net 0.
Inheritance gets the Necromancer treatment: playing an Estate inheriting Village counts as 1 Inheritance play and 1 Village play, Inheritance and Village each draw 1 card. So “Estate” in the list of cards is never played.

+card token: Pathfinding and Teacher get the cards drawn from the token that they placed as duration draw.

-card token: counts as -1 card draw (if eventually removed), making Raid, Relic and Borrow the only cards with negative contributions in the draw decomposition.

Outpost, Mission, Fleet: the extra turns are not attributed to the cards but would show up as more draw during clean-up for that player.

Clean-up, Expedition, Flag, River’s Gift: clean-up draw is the 5 (or 3 with Outpost) cards drawn during clean-up. The cards due to Expedition, Flag and River’s Gift show up as duration draw for Expedition, Flag Bearer and whatever led to River’s Gift.

Donate: checks whether the 5 cards that you draw afterwards are more or fewer than what you drew in the previous clean-up. Often that will result in a small discard when trashing down to fewer than 5 cards. If you only draw 4 cards after your next turn, it will show up as only 4 cards drawn in clean-up.

Yesterday I got matched with an opponent who, upon seeing the kingdom, pledged for not using Star Chart because it would slow down the game too much. I couldn't make heads or tails out of this and opened Star Chart anyway, causing him to resign immediately. I do think that he meant that every shuffle procedure takes longer. The number of rounds should be accelerated by Star Chart.
For the record, I was not that player.  8)

Turn numbers slightly decreases with Star Chart (but that's not significant). I suppose that getting faster to the attacks cancels out with getting faster to whatever cards speed up your deck building.

On average there are 9 shuffles in which each player may choose a card.

Ceterum censeo, I still find it annoying that you can see all but the remaining cards in the deck that you are about to draw.

I do have all the VP stats, but it's indeed a bad measure in my opinion. If I need those additional 2 VP, I'll take that Duchy with my win, otherwise I just end it as quickly as possible.

Linking this to another discussion: how many VP chips do you think that player 2 would need to start the game with to have a 50% win chance on average. I've seen 2.5 VP been suggested, maybe it's a bit higher. Misery's estimated effect is about half of first player advantage.

Just one word of caution with the stats ranking is that some hexes are close and the differences not statistically significant.

If you want to have one number: receiving Misery makes you go from 50% to 44% win chance. (95% confidence interval about [42%,46%]. Bad Omens for comparison would be [45%,49%].)

One part of the statistics I have is the impact factor inspired by trivialknot. It can be found for all cards here:

It looks at how much more or less other "cards" get bought, gained or trashed compared to the average game, distinguishing between the probability of doing that and the number. Each category is normalized to have mean 0 and standard deviation of 1.

Here are the landmarks only:

Dominion General Discussion / Re: A Question About First-Player Advantage
« on: February 26, 2019, 02:41:11 am »
I can often not really distinguish resigning from buying last Province for a loss. The games without resign are the ones with at least 2 Provinces left or 2 cards away from a 3-pile.

Even when Fortune Teller hits something, it is weaker than the -Card token, because you would draw into this junk anyways at some point. So the attack of FT is not really topdecking the junk but removing the non-junk cards before it.

Not if it causes a shuffle first.
Shuffling doesn't really matter for that purpose. It means that also your cards in hand miss the shuffle - maybe you would have even triggered that shuffle on your turn anyways.

Maybe you would have triggered the shuffle, or maybe you wouldn't. The point is that saying that it's just making you draw junk sooner than you would have isn't entirely correct - sometimes it also makes you see junk more frequently than you would have otherwise.
That's also true in the "sooner" argument. You shuffle earlie, when you discard non-junkl. So yes, you do draw junk more frequently. My point was not that the attack doesn't do anything, but that it's significantly weaker than the -Card token.

The Best + Cards (Top Half)

Comments for odd ranks are provided by lovestha, comments for even ranks by markus.

#19 ▲2 Nobles (Intrigue)
Weighted Average:
Unweighted Average:
Standard Deviation:

A very sad village, but still a village. A very sad source of VP, but still a source of VP. Only a little bit sad when it is how you are drawing cards, +3 cards is never bad. Getting all three in one package is very strong.
#18  Canal (Renaissance)
Weighted Average:
Unweighted Average:
Standard Deviation:

Being a project, you can't stack Canal as you love to do it with Bridges. The permanent cost reduction is still useful on the typical board and can be quite exciting with Workshops that suddenly can gain the shiny $5 cost cards.
#17 ▲1 Peddler (Prosperity)
Weighted Average:
Unweighted Average:
Standard Deviation:

No better place to put surplus buys than a peddler. But for more than $2 it is a pretty sad option. Its position in the $6+ list is a bit awkward, has anyone ever paid $6 for Peddler when they cared about the text on Peddler?
#16  Innovation (Renaissance)
Weighted Average:
Unweighted Average:
Standard Deviation:

The usefulness of Innovation depends on the board quite a bit. Preferably, there's a way to gain Action cards during the Action phase. Or there might be some cards that you can buy for a nice immediate effect. In contrast to other (expensive) projects, the only player to buy it doesn't have a great win performance in my stats sample (still ok!).
#15  Citadel (Renaissance)
Weighted Average:
Unweighted Average:
Standard Deviation:

The highest entry in this list of a Renaissance card. The reliability of a Throne Room every turn is great, having to play it first every turn is less awesome. Will not be surprised to see this rise a few slots next year.
#14 ▼1 Artisan (Base)
Weighted Average:
Unweighted Average:
Standard Deviation:

Artisan is a very nice gainer of $5 cost cards. Just get it as early as possible and you'll typically do fine.
#13 ▲1 Altar (Dark Ages)
Weighted Average:
Unweighted Average:
Standard Deviation:

The big trash and gain. The gain is big enough that you aren't sad to sacrifice early purchases to it. I am a bit sad when it is the only trashing in a kingdom, it is so very slow at that it's nearly not worth mentioning, it is more a side benefit to use in the late game to get rid of early trashers after they are no longer useful or to keep up with a weak junker.
#12 ▼2 Overlord (Empires)
Weighted Average:
Unweighted Average:
Standard Deviation:

Getting Overlord on turn 2 to play your preferred $5 cost on turn 3 or 4 is often the correct move. Later on, buying the $5 costs might be cheaper, but possibly you value the higher reliability of Overlord. Just be careful, that the card you want to play doesn't pile out.
#11 ▼6 Fortune (Empires)
Weighted Average:
Unweighted Average:
Standard Deviation:

Biggest cost in the game, but it's worth it. May not be available is the biggest down side with it staying hidden under Gladiator many games.
#10 ▲2 Dominate (Empires)
Weighted Average:
Unweighted Average:
Standard Deviation:

Dominate gains the 2 ranks that it lost last year to swap it's rank with Overlord again. It potentially provides a lot of VP, so you usually want to build a bit more...and then watch out for the 3-pile that ends the game before a Dominate gets even bought.
#9 ▲2 Grand Market (Prosperity)
Weighted Average:
Unweighted Average:
Standard Deviation:

One of everything and an extra coin doesn't sound like much, and you need to jump through hoops to get it? The deal is a lot better than it sounds. Jumping through the hoops can make it slow, but it is commonly worth it.
#8 ▲1 Border Village (Hinterlands)
Weighted Average:
Unweighted Average:
Standard Deviation:

In the best case, you only pay $1 more to get a Village with your $5 cost. Or you can Remodel into Border Village. If you are able to make use of its gain effect more often than your opponent, you're in a good shape to win the game.
#7 ▼1 Lost Arts (Adventures)
Weighted Average:
Unweighted Average:
Standard Deviation:

Turning a cantrip into a village gives a lot of flexibility to many kingdoms. The cost of 6 should be easy to achieve around the time that a deck needs to have a bunch of villages.
#6 ▲1 City Quarter (Empires)
Weighted Average:
Unweighted Average:
Standard Deviation:

Finding the right timing for your City Quarter gains is sometimes tricky. But in general you should get more than you think. If you also find a way to increase the action density in your hand, the deck can become quite explosive.
#5 ▲3 Inheritance (Adventures)
Weighted Average:
Unweighted Average:
Standard Deviation:

Cementing its place at 5th, Inheritance is obviously a very strong effect. Personally I put it a little bit lower as it is more situationally good than others it is ranking above. When the conditions are right for using it there is no doubt about its power.
#4 =0 Pathfinding (Adventures)
Weighted Average:
Unweighted Average:
Standard Deviation:

Pathfinding keeps its spot. It is the best of the rest with a significant distance to the top 3 on this list. The +card token is great...the sooner you're able to buy it the better.
#3 =0 Goons (Prosperity)
Weighted Average:
Unweighted Average:
Standard Deviation:

I'm still enjoying playing with Goons, that could make me a masocist. A useful attack with virtual VP, economy and +buys, it is a compelling payload for any deck. The attack does not stack but the rest of the abilities are very good in multiples. With a deck willing to buy many coppers/silvers the points ceiling for such a deck is very very high. Do not ignore. Obviously this is still the region of cards people are not sleeping on.
#2 =0 King's Court (Prosperity)
Weighted Average:
Unweighted Average:
Standard Deviation:

lovestha: Extremely powerful. Costing 7 is a lot, so it can be too slow. But it can play the role of village or simply amplify your payload. As it must collide with something it is probably wrong to open but otherwise it is a great card. Only clearly a trap when the kingdom doesn't support more than single provincing.

markus: Let's be clear. You almost always want it and you want it in big quantities.
#1 =0 Donate (Empires)
Weighted Average:
Unweighted Average:
Standard Deviation:

Infinite trash for just 8 debt?! Do we really need to say more about this most powerful option? As a self confessed player I'm sure the mistakes I'm making with Donate are: Not planning when to use it well enough; Not thinking about using it twice in a game.

Where's the top half?
It will be posted on the 22nd (in some suitable timezone).

Even when Fortune Teller hits something, it is weaker than the -Card token, because you would draw into this junk anyways at some point. So the attack of FT is not really topdecking the junk but removing the non-junk cards before it.

Not if it causes a shuffle first.
Shuffling doesn't really matter for that purpose. It means that also your cards in hand miss the shuffle - maybe you would have even triggered that shuffle on your turn anyways.

Even when Fortune Teller hits something, it is weaker than the -Card token, because you would draw into this junk anyways at some point. So the attack of FT is not really topdecking the junk but removing the non-junk cards before it.

I also thought that posting it in the wrong order and not starting with #1 is bad.
But having two threads is even worse.

43.5pp is not very meaningful. You need to argue which cards that are in between the two cards should be below Walled Village or above Wandering Minstrel.

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