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Subject: Lots of Simulations; Village is Bad rss

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Charles Connaughton
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I have been tweaking my Monte Carlo simulations recently to try and get some more concrete data on the timing associated with buys; it should be obvious that when you buy a particular card can be just as important and what you end up buying.

You can count several different things to differentiate the different stages a game goes through as it progresses; you can count turns, or the number of silver and gold you have bought so far. The most universally useful (I.E., gives the most consistently good results across multiple strategies) seems to be the number of times you have reshuffled your deck. This is intuitive, as the only time your deck changes in aggregate power level is when you shuffle all of the buys from the last few turns back into a new deck. In just the same way that whether you buy something on turn 1 or turn 2 does not matter at all, all of the turns between reshuffles are essentially identical; there is noise in individual draws, but what order those draws take place doesn't matter in a fishbowl and only matters in practice if opponents are reshuffling faster or slower alongside playing attacks.

So I have been looking at two main variables - what cards you should buy, and what pass through your deck you should buy them at.


For example, the two Smithy deck gives (using 50,000 games; don't have the 1000000 game tests in front of me):

Smithy(1,2): Mean = 14.88
Smithy(1,3): Mean = 14.76
Smithy(1,4): Mean = 14.74
Smithy(1,5): Mean = 14.78
Smithy(1,6): Mean = 14.88

[Smithy(1,4) means you buy the first Smithy on your first time through the deck, and the second no earlier than your 4th time through the deck. Mean is the average time to 4 provinces.]

If you run the simplest Smithy strategy and buy both as fast as possible, the deck isn't all that much faster than just buying one Smithy. But if you wait until your fourth time through the deck (give or take; there's some judgment that doesn't get into simulations) there is a significant increase in how fast you get to four provinces with buying the second Smithy.

You won't reproduce the above numbers using just that change, because I did the same thing with Provinces. The "Big Money" algorithm loses a bit less than 0.1 turns by buying Provinces in the 3rd time through the deck. You should definitely wait until your 4th time through the deck to buy Provinces (and possibly a bit slower; 4 and 5 is too close to the error bounds to call without millions of cycles). The above numbers take that into account, as do all the ones below.


Now that it's all set up, time for the fun stuff.

Smithy / Village

I've seen more discussion of this strategy than any other so I wanted to take a good look at it, and see where the optimization took place with the above parameters taken into account. I didn't have time to do every single iteration of how many to buy and when, so I used a pseudo-relaxation algorithm; start with an even distribution with a bunch of each, and tweak one variable at a time to find a local minimum, with the maximum reshuffle at which to buy things is 10 (which, in practice, you never get to).

So the algorithm ran 10,000 point simulations to get close, then 100,000 point simulations to verify; starting with this distribution:

Smithy(1,4,7,10);Village(1,4,7,10)

After a few hours of running through permutations, it kicked out the optimal Smithy/Village play as:

Smithy(1,4,8,10);Village(8,10,10,10)

Which is to say, you do not buy any Villages in Smithy/Village unless something has gone horribly, horribly wrong. 8 is about the point where everything starts to blend together due to noise.

To confirm, I re-seeded the relaxation with this distribution:

Smithy(1,1,1,1);Village(1,1,1,1)

(I.E., buy the two as fast as possible), and let it see what it found to be the best strategy from that starting point:

Smithy(1,4,7,9);Village(9,9,10,10)

Which tells me I wasn't finding a false minimum.

The proper number of Villages to play in Smithy/Village, with no other cards, is apparently *0*.

(There might be something to buying that 3rd Smithy in the late late game if things have gone horribly wrong. I don't know.)


To explore this further, I added several other cards to the mix, one at a time - Festival, Market, and Laboratory. All are straightforward to simulate to a reasonable degree of accuracy.

So, trying these:

Smithy(1,4,7,10);Village(1,4,7,10);Festival(1,4,7,10)

Optimizes down to:

Smithy(1,2,4,7);Village(6,9,10,10);Festival(1,2,2,2)

Or, buy Festival every single time you can, buy 3 Smithies as fast as possible, and avoid Villages. I looked into the Village at 5-8 with the same numbers, and they're virtually indistinguishable - on the off chance you only get 3 coins late in the game with that many Smithies and Festivals, you're probably better off buying an Estate, or nothing at all.

Next up - Market.

Smithy(1,4,7,10);Village(1,4,7,10);Market(1,4,7,10)

Relaxes to:

Smithy(1,4,6,9);Village(9,9,10,10);Market(1,2,2,2)

Market is also, apparently, a huge savage beating. Like Festival, you buy the hell out of it, with a couple Smithies, and treat Villages like a leper colony.


One more, this time with Lab:

Smithy(1,4,7,10);Village(1,4,7,10);Laboratory(1,4,7,10)

Reduces to:

Smithy(1,6,9,10);Village(8,9,10,10);Laboratory(3,4,4,6)


This one surprised me. Apparently if the only cards on the board are Smithy and Laboratory, and you draw 5/2, the best opening is *Smithy*, not Laboratory. Grabbing early Labs doesn't do nearly as much for you, it seems, as just grabbing the cash. Whether this is because of the interactions with the Smithy before you have a big deck, or that Labs don't start pulling their weight until you have several Silvers, I don't know.

But I do know this - the Village still sucks horribly.


My opinion of Village has fallen dramatically since I was first introduced to the game; but until now I wasn't prepared to say that it was the weakest of the 3 cost cards in the initial 25. But it sure looks that way. All of the prototypical Village strategies, apparently, are optimal when you do not buy any Villages at all. I suppose this makes sense, when you consider how fast the game gets when you start playing tight; how few buys you really have before the rush on provinces; and how many Villages and actions you need to have before you start putting together any sort of combo.

I am currently running a simulation using Smithy, Council Room, and Village; it isn't done yet, but at the moment there is a single copy of Village in the deck, bought on the 4th pass through the deck. This one is interesting, and it looks like there might be multiple local minima. Also, that deck is FAST. It's doing some weird stuff in how it likes cards, putting in Smithies than pulling them back out. It might be unstable.

So, as it stands now, I'm trying to look for situations in which Village excels. Where is the card good? When do you want to play it? Am I approaching things wrong, am I putting it in the wrong situation, or is Village as bad as it appears?
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Mike Ellis
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David desJardins
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IMHO, the Village only makes sense in very action-heavy decks, which aren't what you are going to get from this kind of simulation. I'd be looking at cases where you're getting rid of some of your starting Copper and Estates, one way or another.
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Mason Louie
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cxensign wrote:
My opinion of Village has fallen dramatically since I was first introduced to the game; but until now I wasn't prepared to say that it was the weakest of the 3 cost cards in the initial 25.

...

So, as it stands now, I'm trying to look for situations in which Village excels. Where is the card good? When do you want to play it? Am I approaching things wrong, am I putting it in the wrong situation, or is Village as bad as it appears?


I think you miss the point of Village. Its point is simple-- enable combinations. No combinations, no reason for Village. Weak combinations, weak Village. And finally, strong combinations, strong complaints.

So I'm not surprised that basically a money deck is best without a Village. That's like saying Gardens suck when you play a mean Chapel deck. It's true, but uninteresting.

Your inquiry for interesting combos is a better direction. But there are two factors your methodology doesn't cover. First, is that Donald goes to great lengths to ensure no single dominating combination (or most likely handful of combinations) just like for single cards ignoring Chapel whiners. So you'll have a hard time pinning down the ultimate combo by design.

Second, is that combinations are inherently riskier than singleton plays, ie there's variance, cause it depends on others. Which means it can tilt one way or the other. If you look at it mechanically, you weigh the odds and just play, the solitaire complaint. However the game gives a lot of power backed by volition such that it becomes possible to change your luck.

Simple example: is Cellaring for 4 cards the same in all circumstances? How about for 3 cards? How about during early game? Mid game? Late game? What and when you pick greatly affects the outcome as does the contents of your discard piles. And this doesn't take into consideration the business of messing with your opponents. Do I want to mess with them first and then play personal actions or the other way around or some other combo?

What's especially tricky and when done correctly, brilliant about Village is that it allows dynamic, sweeping, but still feasible changes to your strategy. A good player will do this depending on their draws and what others do. A simple robot will simply lump a crappy draw or formidable opponent. A bad player will overdo changing their luck such that their actions smother them.
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Jeff Petersen
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I could see the point that Village doesn't help a Smithy deck all that much... because Smithy decks are ridiculously one-sided in strategy: all you care about is getting to 8 treasure in a turn, but no more. Unless you're playing with additional buy actions, you're not going to gain much benefit from a village, smithy, smithy turn.

Similarly, Lab isn't a good card to combo with Smithy. It doesn't provide a buy (which Market, Festival, and Council Room all do), so heaping on an action combo isn't going to improve the strategy.

Also, you're essentially creating situations where you're comparing Village to a bunch of 5 cost cards and finding out that it's not as good as they are. Of course it's not. Moreover, you're comparing it to cards that pretty much cover the basic ability of village in and of themselves.

I'd suggest trying to do the method with other cards that don't do the same thing. Try it with cheaper cards. I'm quite curious to see what Woodcutter, Remodel, or Workshop do.
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Matt Sargent
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Quote:
So, as it stands now, I'm trying to look for situations in which Village excels. Where is the card good? When do you want to play it? Am I approaching things wrong, am I putting it in the wrong situation, or is Village as bad as it appears?


Village excels when your deck is stuffed full of action cards. I don't have any definitive answers to your questions, but consider the following strategy, using the "basic" set:

Do not buy treasure. Buy villages, smithies, and one each of militia, mine, and market. Buy the militia on turn 1/2, and buy the mine and market as soon as possible. Buy enough villages and smithies so that it is likely you will draw your entire deck on your turn. Don't buy provinces until you can buy two a turn. Then buy provinces.

I'm fairly certain this beats two smithies, but it's somewhat harder to simulate. Your simulations are giving you excellent information, but remember their assumptions: the player will buy money; the player will buy provinces as soon as possible; and single player only (disregarding the drawback of council room, for example). The decks that village does well in do not conform to those assumptions.
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Gareth B
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Village isn't bad - others have already adequately covered that you need to have some powerful terminal actions in the deck before you see the benefit of being able to play them every turn.

I have a few more comments though.

There are 86 points available in 2er; looking at a sample of the BSW score database, an average score in 2er might be close to 35. It might be premature to be ending the simulation at 27 points. Even six provinces ties with 2 provinces and 8 duchies.

In 2er with the basic set, simple smithy has problems facing an action-heavy village/smithy/remodel/cellar setup that arranges to play militia as often as possible, and every turn after the Nth. Not only does discarding two cards every turn cramp the ability of simple smithy to hit its 8 coin, but also the action deck usually gets to control when the game ends.

You could factor into your simulation the effect of being hit by militia at a specified frequency, but it's much harder to factor in the lack of control over the end condition being met.
 
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Paul King
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Your results aren't that surprising.

The whole point of village is to be able to play two Action cards that don't give extra actions. If you only have two Smithies in your deck then all a Village will do is let you play both instead of only one - if you have the Village in hand. And without an extra buy even that may not be much help.

Festival, Market and Laboratory are all extra action cards so Village isn't much help there either (It's only helpful if you start with Smithy and Village - and a Festival is probably as good as the Village anyway). Festival is better than Village in this set-up because it DOES give an extra buy, Market also gives an extra buy, but it doesn't let you chain Smithies.

Laboratory differs from Smithy in that you draw one card less, but get +1 action. If you only have one action card in your deck a Smithy is better than a Laboratory (because you have no use for the extra action). Laboratory doesn't start pulling it's weight until you have several of them, because chaining is the only advantage it has - you need at least 3 to do better than a Smithy.

Council Room gives an extra buy so I think that it will be more likely to benefit from Village than Smithy.

So yes, I think that you are putting Village into situations where it isn't that helpful. You probably also need to model the benefits of the attack cards to see the full benefit.
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Charles Connaughton
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A couple quick notes;

One, I'm starting the simulation by feeding it a strategy to buy lots and lots of Smithies and Villages. The result it's giving back is that the strategy gets faster as you pull more and more Villages and Smithies out of the deck, until you're back to Smithy(1,4). You can do that with any arbitrarily large number of Smithies and Villages. It keeps telling you to pull them out and buy Silver. If you have ideas for other terminal actions you think I should feed it, let me know, and I'll plug them in as best I can manage.

What this tells me is that Village does not make a bunch of terminal actions good - it requires very specific conditions to be good. I want to identify what those conditions are, because the canon appears to be wrong. If Smithy/Village beats Smithy/Silver, it's because of a key 3rd cog in the combo that isn't immediately obvious.


Second, it seems like the big advantages an experienced player has over a simulation in the relevant situations come from underbuying at the right time, and from timing the estate / duchy buys at the end. Mostly this serves to pad the score a bit at the end, and pulls in the variance in the long tail. A series of hands that is going to hit 4 Provinces on turn 13 largely plays itself. It's the ones that the simulation is going to hit on turn 18-20 that an experienced player can salvage into a 16 where the player starts to matter. Basically experience pulls in the variance and pulls wins out of bad hands, but good hands tend to play themselves.
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Branko K.
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cxensign wrote:
The most universally useful (I.E., gives the most consistently good results across multiple strategies) seems to be the number of times you have reshuffled your deck.


This means that the deck chokeful of Chancellors is made of pure win.
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Adrian Brooks
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Against the tide of "This isn't very surprising"s, I'm going to say I think what you've done is worthwhile. I've certainly played a game with with the theory that village/smithy is getting me screeds of cards, and hence money. The obvious flaw is then getting too much money, so you want more buys; the two extra buy cards you've tried both provide more actions too, though, making village somewhat redundant. I'd guess that your simulation with village/smithy/woodcutter (or just village/woodcutter, for that matter) will show more village love, particularly if that second/third buy is allowed to be a duchy.
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Paul King
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When I say that the results are not surprising I'm not saying that the simulations weren't worth doing (expectations can be wrong !). I am saying that they aren't a good measure of the effectiveness of the Village.
 
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David desJardins
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cxensign wrote:
What this tells me is that Village does not make a bunch of terminal actions good - it requires very specific conditions to be good. I want to identify what those conditions are, because the canon appears to be wrong. If Smithy/Village beats Smithy/Silver, it's because of a key 3rd cog in the combo that isn't immediately obvious.


What "canon" are you talking about? I never heard anyone before suggest that lots of Smithies and Villages is a particularly good strategy. Are you presenting this as some sort of well-accepted notion that you need to refute?
 
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Lots of players, but especially new ones, love the village. Hence the term "village idiots" thrown around the forums. I've found it common to have my opponents buy 4-5 villages in a game, terminal actions or not. And I have seen it posited that in the "basic" setup, the village/smithy combo is among the best strategies available. This is likely the "canon" referred to.

It is great to see a computer simulation confirming this is not the case. Better to just buy one or two smithies and a bunch of treasure. The points about the +Buy lacking are also well made.

This thread basically reconfirms the notion that in a basic strategy you want few, highly focused action cards in a deck with a coin density > 1.5 and then a keen timing of when to switch to duchy/estate as the endgame draws near. This can be varied with remodel and gardens, of course, but I have personally been finding the remodel easier to beat as my action buying has diminished.
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Matt Sargent
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Your examples imply that you cap the number of villages bought at four. If so you'll want to increase that ... village/smithy doesn't become good until you can draw your entire deck, and it won't be able to do that without five or six of each.

You current simulations use the following rules (I'm assuming): if 3 buy silver, if 6 buy gold. I think it would be interesting if instead you used these rules: if 3 buy village if 6 buy two villages. Then search for what additional action cards go best with those rules.
 
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Dan Schaeffer
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noon wrote:
You current simulations use the following rules (I'm assuming): if 3 buy silver, if 6 buy gold. I think it would be interesting if instead you used these rules: if 3 buy village if 6 buy two villages. Then search for what additional action cards go best with those rules.


Where does the extra buy come from to buy two Villages?
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Matt Sargent
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Golux13 wrote:
noon wrote:
You current simulations use the following rules (I'm assuming): if 3 buy silver, if 6 buy gold. I think it would be interesting if instead you used these rules: if 3 buy village if 6 buy two villages. Then search for what additional action cards go best with those rules.


Where does the extra buy come from to buy two Villages?


Probably Market or Festival. Depends on what additional action cards you're using. The point is to find what cards are ideal for a deck that doesn't buy money, but uses action cards to increase its buying power. If you have six money, and only one buy, you'd just buy one village, unless your buying schedule told you to buy one of the cards whose efficacy was being tested.
 
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cxensign wrote:

So, as it stands now, I'm trying to look for situations in which Village excels. Where is the card good? When do you want to play it? Am I approaching things wrong, am I putting it in the wrong situation, or is Village as bad as it appears?


I am pretty sure that Village is not as bad as you indicate (and is in fact often good), but I dont understand your methodology enough to know why.


Obviously many people overvalue village. However, it is also clear from experience that there are times where it is very strong, and efficient.


Lets ask the question: When is Village good, and when is it bad?

Drawing a Village in your 5 card hand never hurts you. At worst it just cycles. It is pretty much always a net positive to add it to your deck. The times when it is bad is when it is not nearly as efficient to add it to your deck, as adding something else, which will increase your deck strength by a greater degree.


A Village is very good when you have two other action cards (in your hand plus draws that you are able to make). It is neutral, when you draw it with zero or one other action (again counting additional draws of the village and that action card). Adding a card that ends up being neutral is worse than adding a card which helps you when you draw it, so in these times it is bad.



From your initial deck, obviously if you buy a Village, it does nothing right now. It only cycles through your deck and draws yo ua random card. A Smithy, when drawn, gives 3 cards, clearly much better at this point.

Once your deck alreayd contains actions cards, however, Village becomes stronger. When you have 2 smithies, adding a smithy results in a lot more 'dead' smithy cards, where you draw two at once, or draw one when playing the other. Drawing a Village, however, allows playing both, gaining even more cards. In these cases, the village actually can end up being worth 4 cards (the one it draws and the three the smithy draws), and in fact much more if those draws continue to chain more actions.


What Village does is it rises greatly in value the more action cards you have in your deck, and the more draw cards you have in your deck. (And especially, if you eliminate poor non-action/non-draw cards from your deck).

Decks that fill up with action cards and no +Action providers generally become terrible, as you end up with many hands with dead cards. Adding a Village to that deck is very helpful. (Decks with all villages are also terrible, they do nothing when not combined with multiple useful action cards). The value of an action scales based on the actions in your deck, and the value of a draw scales based on the strength of your deck.


If you run a simulation, it might looks like the best strategy is to fill your deck with silver and gold, and a few smithies (up until a certain % of your deck is smithies such that you dont often draw two). You might refer to this as the default strategy or the money strategy.

You have to compare this against a deck that ends up alwyas drawing its entire deck each turn and playing all actions, which provides $11, two buys, and a workshop effect, such that you can buy Province+Village and Workshop for a Smithy, so that your deck never loses the ability to draw itself each turn.


You need to simulate the two strategies on the basis of which one allows you to reach a victory state in the shortest number of turns (an example of a victory state being 50% of the provinces plus one, or maybe, 'all the gardens'.
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David desJardins
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Alexfrog wrote:
Once your deck alreayd contains actions cards, however, Village becomes stronger. When you have 2 smithies, adding a smithy results in a lot more 'dead' smithy cards, where you draw two at once, or draw one when playing the other. Drawing a Village, however, allows playing both, gaining even more cards.


But, if you've only got one Village, you're nearly as likely to draw it with one of your Smithies, in which case it's dead weight that does hurt you.
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Andrew Hardin
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The basic problem with the Village (and this is likely to change more with some of the newer cards) is that the Village helps you do something you usually shouldn't do (buy lots of Action Cards).

To gain any real advantage from a Village you have to buy a Village, and then buy 2 Action cards. You have just eaten up 3 buys that aren't Coin. Unless those 2 Action cards are really incredible together you could have gotten away with only playing 1.

So the Village needs lots of Action cards. If the game had 40 Provinces and each stack had infinite supply then lots of Action cards would be the way to go. Instead you have no more than 12 Provinces and most stacks have 10 cards.

Instead, you are lucky to play more than 20 turns in a game. Buying a Village and 2 Action Cards is going to require 3 buys. You now have 17 other turns in which to do things. Buy 4 more villages and you are now looking at 13-14 more turns. Buying enough Action cards to make it worth all those buys and you are looking at 8 turns. But you still haven't bought any Treasure (unless you bought a lot of +2 Coin cards). Not exactly a lot of time to catch up with the player who has bought his 4th or 5th Province. Especially if your opponent plays anything with the same quality as Big Money and is hitting 4 Provinces by Turn 16-17.

So in many, many games the Village is an expensive card for what you get.

- Lex
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Andrew Mitchell
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yeah,
village in a fast deck = bad, particularly near the start... it is likely that a silver is better.
village in a smithy deck = bad, as there is a good chance of picking up a useless village with your smithy.

Generally a smithy or similar deck is highly biased against buying more actions because if you only pick up the smithy in your initial deck then you really don't want more actions to pick up with your smithy.

Village does have uses, but they are rare.
Their relative utility value increases against, e.g. thief, where it dilutes your deck (as far as the opponents are concerned but not where you sit)
My favourite combo... chapel + village + workshop + gardens is one that needs village and I often 'pay' 4 for it in that deck (with workshop).
 
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Robert
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So, as a math teacher, someone who actually teaches AP statistics, it's very interesting to me to see these kinds of analysis .

The thing is, for all that I enjoy and understand that statistics are a huge part of these kinds of games, I find that my primary action when playing them is to... relax a bit from my "job" and potentially miss out on the subtle strategies in favor of "just having fun".

That said, I'm still really enjoying looking through the strategies and seeing how the cards interact. This is a game that is almost as fun to watch as it is to play.

-Esch
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Chris Taylor
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I agree with you Robert. As an engineer who does research, it is nice to play a relaxing game and leave the numbers at work. With that being said it is a ton of fun to keep track of numbers and the statistics and beat someones pants off at a game like this
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Alex Rockwell
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While 'several villages + a number of action cards' is too slow if you just acquire 1 card per turn, it can be a superior strategy when you are acquiring cards throug hextra buys and/or workshops.

Workshop and Village clearly go well together, as the Village allows the play of workshop + other cards, and the workshop gets the many action cards you need to combine with the village.

Village isnt always awesome, but there are card sets where it is awesome.

I guess its not awesome in a cardset of only money, point cards, village and smithy, based on the simulation. That doesnt mean that its not good when combined with some other action cards.
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Matt N

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armitch wrote:

Village does have uses, but they are rare.
Their relative utility value increases against, e.g. thief, where it dilutes your deck (as far as the opponents are concerned but not where you sit)
My favourite combo... chapel + village + workshop + gardens is one that needs village and I often 'pay' 4 for it in that deck (with workshop).

Good point about the thief; I wonder if village + whatever is more powerful in a 4+ player game where thieves are much stronger. Maybe the lame village + moat would make more sense in an attack-heavy situation.

I don't understand "chapel + village + workshop + gardens" at all. Why would you ever use a chapel in a workshop + gardens deck... other than curses.
 
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