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Subject: The best Prestige Building is.... rss

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Jeff Dawson
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I haven’t seen much written about which Prestige Buildings are the best. The Cathedral (25PP) is clearly best from a psychological point of view. I have seen players visibly shrink as they are crushed by the Cathedral, especially if they were angling to build it themselves. But how much have they really “gained” by building the Cathedral. I would like to look at this from a statistical point of view.

First of all we have to look at how much resources are worth at the end of the game. Gold is worth 3 Prestige Points (PP) at the end of the game. Resources are worth 1/3 PP. Therefore gold is worth 9 times as much as any other resource, relatively speaking. Even if you never intend to build a Prestige Building, you should almost always take gold over a resource. (I know there are tactical exceptions and situations in which this is not true, but I am shocked at how often a player will take the farm or other wood building when the gold mine is safe and there is no tactical reason not to take it. When I ask them why they didn’t take the gold mine, they say “I won’t be able to build a Prestige Building anyway”.) Gold is very valuable in itself, even if it cannot be invested into a Prestige Building.

Using the conversion at the end of the game (3 Resource Cubes = 1PP and 1 Gold = 3PP) we can calculate the Resource Investment at the end of the game in terms of PP. We can then calculate the ROI in terms of PP and Royal Favors (FV). We can also calculate the PP/FV net gain in constructing the Prestige Building. (For the sake of this discussion I am going to ignore the value of the Library and Hotel in gaining $1/$2 in phase 1. This is a generally negligible benefit in the last couple of rounds of the game. If built earlier, it may enter into consideration.)

Building Cost Inv Return ROI Net Gain
Granary 3F+1G 4 10PP 2.5 6PP
Weaver 3C+1G 4 12PP 3.0 8PP
Library 3W+1G 4 10PP+$1(Ph1) 2.5 6PP
Theatre 3W+2G 7 14PP+1FV 2.0+1FV 7PP + 1FV
Statue 2S+1G 3 2/3 7PP+1FV 1.91+1FV 3-4PP + 1FV
Hotel 3S+2G 7 16PP+$2(Ph1) 2.29 9PP
College 3S+2G 7 14PP+1FV 2.0+1FV 7PP + 1FV
Monument 4S+2G 7 1/3 14PP+2FV 1.91+2FV 6-7PP + 2FV
Cathedral 5S+3G 10 2/3 25PP 2.34 14-15PP


So what do we see? Shockingly the building with the greatest ROI is the Weaver. Even the Granary and the Library have a better ROI then the Cathedral. In fact the Weaver + Granary/Library Net as many PP as the Cathedral for one less gold and one more resource. Interesting option if you cannot get that 3rd gold or get beat to the Cathedral.

Now it seems like some players devalue the Cathedral because it does not return a Royal Favor, but not all favors are created equal. If you upgrade to a Prestige Building in the Tower End Game scoring, I will argue in most cases that this favor is worth at most 1PP. Let’s look at it. Let’s say you get 2 favors in the tower scoring. Assuming that you are using the building track to construct a Prestige Building that returns a favor, you have 2 favors left (one from your building and one from the scoring bonus). One goes to the PP track (which is hopefully at 4PP or 5PP by now) and one that has to be thrown away on the money track or resource track, yielding at most 1PP. So what does that mean? I think in order for the Favor Producing Prestige Buildings to be worthwhile, they need to be constructed before the last round of the game, so that you can use your favors on the PP track or money if they need it.

So what’s the bottom line? I think if you are going to build only one Prestige Building, the Cathedral gives you the best bang for the buck (if you can afford it), yielding 14-15PP. This is much better than any other building in terms of Net Gain. A favor, in general, can earn at most 5PP at this point in the game. If you are going to build more then one Prestige Building, a Favor Producing Building in the 2nd to last round and a smaller Granary or Weaver in the Last round, this may be better then the Cathedral. However, if you build more then one Prestige on the building track it will cost you the additional favor. :)


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Jeff Dawson
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OK that chart was terrible. I am not sure this is much better.


Building \ Cost \ Inv \ Return \ ROI \ Net Gain
Granary \ 3F+1G \ 4 \ 10PP \ 2.5 \ 6PP
Weaver \ 3C+1G \ 4 \ 12PP \ 3.0 \ 8PP
Library \ 3W+1G \ 4 \ 10PP+$1(Ph1) \ 2.5 \ 6PP
Theatre \ 3W+2G \ 7 \ 14PP+1FV \ 2.0+1FV \ 7PP + 1FV
Statue \ 2S+1G \ 3 2/3 \ 7PP+1FV \ 1.91+1FV \ 3-4PP + 1FV
Hotel \ 3S+2G \ 7 \ 16PP+$2(Ph1) \ 2.29 \ 9PP
College \ 3S+2G \ 7 \ 14PP+1FV \ 2.0+1FV \ 7PP + 1FV
Monument \ 4S+2G \ 7 1/3 \ 14PP+2FV \ 1.91+2FV \ 6-7PP + 2FV
Cathedral \ 5S+3G \ 10 2/3 \ 25PP \ 2.34 \ 14-15PP
 
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David
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Use the CODE tags for a fixed-width font.

Makes tables much easier to write. 'Draw' your table/chart in an editor with a fixed-width font and then just paste
into your message and surround with the [c ] and [/c ] tags.
 
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Jeff Dawson
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Building Cost Inv Return ROI Net Gain
Granary 3F+1G 4 10PP 2.5 6PP
Weaver 3C+1G 4 12PP 3.0 8PP
Library 3W+1G 4 10PP+$1(Ph1) 2.5 6PP
Theatre 3W+2G 7 14PP+1FV 2.0+1FV 7PP + 1FV
Statue 2S+1G 3 2/3 7PP+1FV 1.91+1FV 3-4PP + 1FV
Hotel 3S+2G 7 16PP+$2(Ph1) 2.29 9PP
College 3S+2G 7 14PP+1FV 2.0+1FV 7PP + 1FV
Monument 4S+2G 7 1/3 14PP+2FV 1.91+2FV 6-7PP + 2FV
Cathedral 5S+3G 10 2/3 25PP 2.34 14-15PP
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Adam Smiles
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What your calculations don't take into account is the availability of each resource. For example, you calculate that the Weaver has a better net gain and a better ROI than the Granary. But you assume that aqcuiring 3 cloth is equally challenging as acquiring 3 food. This is rarely the case in an actual game.
 
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Brian Bankler
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A nice article, but I'm not sure ROI matters. Exactly where else are you going to invest your gold? [If you play with the optional jeweller, perhaps, but that's not standard]. You could invest a set of cubes for 3VP, so they should really be valued somewhere between 1/3rd and 1 (depending on how many sets that prestige building really costs you).

So, it depends on if you could send those cubes to the castle. And if your sending those cubes block others from building, then each cube is arguably worth 2VP. (3 cubes --> 3VP, and prevent 3VP).

The prestige buildings, while good, are not as automatic as I had originally thought. But you should still be angling for them (via residences and gold, both of which are good in their own right).
 
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Jeff Dawson
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asmiles wrote:
What your calculations don't take into account is the availability of each resource. For example, you calculate that the Weaver has a better net gain and a better ROI than the Granary. But you assume that aqcuiring 3 cloth is equally challenging as acquiring 3 food. This is rarely the case in an actual game.


No, you are right. I was simply considering how much of a gain you made as a result of constructing the Prestige Building, and not the relative value of the cubes in the course of the game. At the end of the game, the value of the production cubes are all the same...1/3 PP.

In fact I agree with you, I think the net gain of the weaver is higher then the granary or library BECAUSE cloth is generally more valuable, using it for jousting and other things. In fact I hardly use wood or stone for anything other then sending to the castle and building Prestige Buildings.
 
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Robert Rossney
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I'm not going to say this is a better evaluation, but it builds in more factors, and makes its assumptions explicit:

-----Cost------ ------Return------- -----Total----
Building Rsrc Type Gold PP Income Favor Cost Return ROI
Granary 3 Food 1 10 7 10 1.43
Library 3 Wood 1 10 1 7 11 1.57
Statue 2 Stone 1 7 1 7 11 1.65
Weaver 3 Cloth 1 12 7 12 1.72
Theatre 3 Wood 2 14 1 10 18 1.80
Hotel 3 Stone 2 16 2 10 18 1.80
College 3 Stone 2 14 1 10 18 1.80
Cathedral 5 Stone 3 25 14 25 1.83
Monument 4 Stone 2 14 2 10 22 2.13

Cost assumptions:
PP cost of 1 resource 0.33
PP cost of 1 gold 3.00
PP cost of architect action: 3

Value assumptions:
PP value of income: 1
PP value of favor: 4


The assumptions are almost all dubious. Here's my rationale for the values that I've assigned them

I assume that a favor is worth 4PP based on the idea that if you take 2 favors, one will be 5PP and one will be a gold. This is obviously dependent on which favors you've already taken, and on which you plan to take in the final scoring.

(To give an idea of how hard this is to calculate: If I currently plan to take one favor on the PP track at the end of the game, moving me from 4 to 5, a favor now is worth 5PP to me: 4PP plus the 1PP bump it gives to the end-of-game favor.)

I cost the architect action at 3PP just because. Sometimes it will cost more (taking a favor that could otherwise have gotten you 5PP, for instance). Most of the time this value's not calculable except as a wild guess. But the previous analysis costs it at 0, and I'm sure that's not right.

I value income at 1PP per $1/turn, which is obviously way too much if you're building the library or hotel on the last turn. But if you build them on the 3rd-to-last turn, that figure's probably too low.

I think I'm probably valuing favors too highly. But the end results seem intuitively correct to me: the ROI of the prestige buildings that cost more than one gold are all clustered together, the monument's two favors make it very valuable, and the one-gold buildings give you a profitable way of soaking up your excess resources at the end of the game but aren't as profitable as the two-gold buildings.
 
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David desJardins
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I think a generic cube is worth considerably more than 1/3 VP. Something around 1 VP would be about right. The fact that you only get 1/3 VP for cubes left at the end of the game, just means that everyone is trying not to have cubes left over at the end of the game!

I also think that the difference between the value of the inputs and the value of the output, is more important than the ratio.
 
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Michelle Zentis
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Your analysis is very interesting, and I'll have to take a look at it later when I have more time to ponder it. However, one thing that you're not considering when comparing one building to a combination of two buildings is that each blue building costs TWO worker-turns to build -- one to build the residence, and the second to build the prestige building itself. I've probably played around 10 games of Caylus, always with 4 or 5 players, and I've seen ONE person have the opportunity to build more than one prestige building (and not for lack of trying). There should be a way to factor the opportunity cost of those two worker-turns in to the calculations.
 
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Brian Bankler
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caesarmom wrote:
Your analysis is very interesting, and I'll have to take a look at it later when I have more time to ponder it. However, one thing that you're not considering when comparing one building to a combination of two buildings is that each blue building costs TWO worker-turns to build -- one to build the residence, and the second to build the prestige building itself. I've probably played around 10 games of Caylus, always with 4 or 5 players, and I've seen ONE person have the opportunity to build more than one prestige building (and not for lack of trying). There should be a way to factor the opportunity cost of those two worker-turns in to the calculations.


This is true enough, but building the residence is usually a good idea anyway. Assuming you build the residence with 3+ turns left, you earn 2VP + $3 (which you spent to build it $1 direct, $1 worker, $1 cube). The earlier the residence, the better the investment. Now, if you had to buy a residence and the residence hurt you, that wouuld be tougher.

But usually the only time the residence is wrong is when it is late enough (and touchy enough) that you are better off just building two stone buildings when you take your 4th and 5th advance on the construction track and take 12 VPs directly, or if you can use your worker elsewhere to generate a large chunk of VPs.

In a five-player game, more players will be trying to 'make the leap' (residence + prestige in one turn), but with fewer players, you'll see more people with 2 or more residences try to convert. And if several players are on the construction track, they can usually do it. (Win the castle on the final turn or joust for a residence, convert to a blue in the final scoring).
 
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Jeff Dawson
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DaviddesJ wrote:
I think a generic cube is worth considerably more than 1/3 VP. Something around 1 VP would be about right. The fact that you only get 1/3 VP for cubes left at the end of the game, just means that everyone is trying not to have cubes left over at the end of the game!


This is true. I kind of overstated that point. A cube is more valuable then 1/3 PP (The end game value). In fact it is probably worth 1-1.25 PP on the average. My point was that all things being equal, if you are first to place a worker, I believe it is best to take the gold mine, as long as it is safe, in most situations. At that point of the game, by the time your turn rolls around again, there will be a good wood production building (at least) left on the board to take, and probably more than one depending on the flow of the game and the number of players. I'm just shocked how often a player will pass on the gold mine and take a wood production building. That's all.
 
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Lucas Kruijswijk
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I want to mention about my rule of thumb in another thread.

I think Caylus is for a large part to correctly value things. However, you have to think a few moves ahead,
but then still you need to have some simple rules to value the situation.

Of course, there is more tactical play with a few players (2 or 3) then with 5 players. With 5 players you don't have enough control for tactics.

I my rule of thumb I value the things as follows:
- 1 coin = 0.5 VP
- 1 resource = 1.5 VP
- 1 gold = 3.5 VP
- 1 favor = 2.5 VP

Favors are the most difficult to value, because they are cumulative. The principle of the rule of thumb does not work here. Furthermore, with a few players, there are more favors for each player and this gives the favors a greater value.

To take the values at the end of the game as rule of thumb, is not so good idea. Having resources at the end of the game is the greatest waste. You can easily put them in the castle, to get more points and maybe an additional favor.

The rule thumb gives the average you get out of the thing. Sometimes you get more, sometimes you get less.

In Caylus you have less 'investments' as in Catan or Puerto Rico. I am certain that people will disagree with me, but that are good arguments for this statement. In Catan and Puerto Rico, your income is almost totally dependent on your investments. In Caylus that is not the case. If your investments are a total disaster, you can still put a worker on a building that produces three goods as any other player can do.

Given the fact that investments are less dominant, you get another model. You don't get VP's from your earlier investments, but you get VP's just from the turn.

Each turn gives you a number of VP's (probably not converted yet, but resources, money etc.). And you should try to maximize that. The first workers earn more VP's than later workers. Of course, if you think a few turns ahead, you can improve on your score.

Therefore, the absolute value is more important than the 'Return on Investment'. Thinking in 'Return on Investment' assumes a investment model, while investment in Caylus is not dominant.

Given this system, building the Cathedral is very good. You get lot of points from it. And this is also my experience in the game. The person that builds the Cathedral has a good end score.

However, you should take into account that you need a Green building first. Building a green building is something that does not give you much VP. The investment is at least 2 coins and 1 resource, so that is according to the rule of thumb 2.5 VP and you get back 2VP and maybe some coins during the game. So, it is rather neutral buy. If you can do this with one of your last workers, this is okay, but if the situation forces you to do this with one of your first workers, then you choose not to take another more profitable building. This can be expensive and these cost should be counted as part of the cost of building the blue building.

The way things are valued, should be adopted to the real situation and it should be combined with tactical play. I am totally aware, that in some situations things can be very different.

Strategy consists of the things that DO have investments (such as the favors) and objectives that can give lot of points (such as building the Cathedral).

Regards,

Lucas
 
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Dan The Man
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Let's fiddle with some valuations here, just for fun.

Caveat: it all depends on what tiles are out and what stage of the game you are in, and where the provost is and is likely to be...

That being said, here we go:

***$1 can be worth MORE THAN 3 VP (1 worker = $1, 1 gold = 3VP)***

One can get 1F 2W 2S 1C for 2 workers, building 12 VP of stone and 4 VP of wood buildings for 3 more workers, totalling 16 VP for $5, or 3.2 VP/$.

One can get 1F 2W 2S 1C for 2 workers, build a church (3 VP) and a 6VP stone bldg with the favor, and build 4 VP in the castle, totalling 13 VP for $4, or 3.25 VP/$ (plus maybe a favor).

One can get 2S 1C for 1 worker, building the church (3 VP) and a 4 VP wood building with the favor for 1 more worker, or 3.5 VP/$.

One can get 6R for 2 workers, get 3 gold for 6R and 2 more workers, or 2.25 VP/$.

VPs can be bought for $1 each at the Church and Bank ($1 for worker).

One can get 1C 5S for 3 workers, 3 gold for $4, Residence for $2, Prestige for $1, or 27 VP for $10, or 2.7+VP/$ (ratio goes up the longer you own the residence).

One can get 2F 2S 2C for 2 workers, castle 6 - 8 VP for 1 worker, or 2 - 2.67 VP/$ (plus 0 - 2 favors).

One can get 3F 2W 2S 2C for 3 workers, castle 9 - 12 VP for 1 worker, or 2.25 - 3 VP/$ (plus 0 - 3 favors).

At dungeon, 3R (castle) can be had for 3 workers, so 5 VP/$4 = 1.25 VP/$ (plus 0 - 2 favors).

At dungeon, 2R (wood bldg.) can be had for 3 workers, so 4 VP/$3 = 1.3+ VP/$ (plus VPs generated by building tile during game).

One can get 2C for 1 worker, 2 jousts = 10 VP for $4, or 2 VP/$.

1 worker at the mine translates to 3 VP/$.

THE ABOVE can be construed as medium to best case scenarios.

OVERVIEW: $1 is worth a MINIMUM of 1 VP, even considering expenses not covered above, like Merchant Guild or Stables or Provost or costly workers, etc.

Looked at another way: a game is 9 - 18 turns long. Scores of 90 VP are common. Assuming a conservative $5 per turn means 1 - 2 VP/$.

CONCLUSION: you should be generating a minimum of 1 VP/$, or you may not be playing optimally, or are in a very competitive game! Being short on money can cost you a whole lot more than that!
 
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Sean McCarthy
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DnaDan56 wrote:
Let's fiddle with some valuations here, just for fun.

Caveat: it all depends on what tiles are out and what stage of the game you are in, and where the provost is and is likely to be...

That being said, here we go:

***$1 can be worth MORE THAN 3 VP (1 worker = $1, 1 gold = 3VP)***

One can get 1F 2W 2S 1C for 2 workers, building 12 VP of stone and 4 VP of wood buildings for 3 more workers, totalling 16 VP for $5, or 3.2 VP/$.


OK, I think this is very funny. You say you can get 3 VPs for $1, huh? Therefore 1$ > 1VP? Well, I can do better.

By placing on the trading post, I get the best exchange rate in the game: $1 = $3. That's right, I can now get infinite $ and thus infinite points! Take that, Mr. "90 points"!

Oh, wait. That would cost an infinite number of worker placements, wouldn't it? Hmmm. Perhaps there is a resource that is missing from your analysis. Perhaps this resource is time.

When you go on the gold mine, you are not spending $1 for 3 points. You are spending your first turn (and $1) to get those 3 points. When you place on the trading post, you are spending a turn to get $2. Based on my experience, you usually don't go on the trading post until your 3rd or fourth turn if you're at the gold mine. So, I think it's fair to say that in the mid or late game, a bad turn is worth $2. A good turn is worth a lot more.

In regards to money vs VP, look at the exchange rate you get at the church or bank, but consider the fact that it costs a turn. that turn could be worth, we'll say for the sake of argument, $2-3. Clearly, a $ is worth less than a point. But we already knew that, otherwise the point track would be pointless (figuratively).

Quote:
CONCLUSION: you should be generating a minimum of 1 VP/$, or you may not be playing optimally, or are in a very competitive game! Being short on money can cost you a whole lot more than that!


This may be true, but it's not meaningful. What you are really getting each turn is a lot of placement opportuinities, plus $2. The chance to place your workers is worth a lot more than the money income in the grand scheme of things.

 
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Ian MacInnes
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There was a time when I thought gold was at least as good as 3 cubes. That was clearly wrong. Now I am not even sure it is worth more than 2 cubes in most situations. The key to strong Caylus play is cube advantage. It allows you to late pick the castle and get the favour regardless (screwing whoever might have dared go in before you). Obviously this works better with fewer players. Unlike PR, Caylus is not usually won and lost through prestige buildings. Prestige building focus will often cost people the much more important castle builds. You should not even think about prestige buildings until the last couple of turns (though the favour buildings, such as the theater and monument, are nice on the penultimate turn). Just view them as a decent bonus. You are better served by focusing on stone buildings till they are gone. They are a better deal than the lower end prestige buildings.
 
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Alex Rockwell
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I think gold should be valued at 3 points, and other cubes at more than 1 point. Probably 1.3 to 1.5.

Favors are highly variable. In the best case, the 2 gold and 4 stone building is worth: 14 + 2 favors = 14 + 5 + pay a cube for 6, so it costs GGSSSSC for 25 points, where C is a wood or food to build with. This is better than GGGSSSSS for theCathedral for 25. But it requires more favor setup.

My favorite buildings are the GGWWW for 14+ favor, the GGSSS for 14+favor, and best of all, the GGSSSS for 14+2 favor. They generally end up being cheaper ways to get 19 points (or 25) than the cathedral.

GGWWW or GGSSS for 19 is similar to GGGSSSSS for 25. You save a G (3 pts) and 2 cubes (3 pts), and get 6 points less, but its easier to do.

Cathedral is best for someone without the points track advanced. Statue is the best little building, at 12 points for GSS, as opposed to 10-12 for GFFF GWWW or GCCC.

If I was to rate them in power terms, in terms of how much gian was produced over what you input, I would say:

GGSSSS (14+2F)
GGSSS and GGWWW (14+F)
GGGSSSSS (25)
GSS (7+F)
GGSSS (Hotel/16+$2)
GCCC (12)
and the dregs:
GWWW (10+$1)
GFFF (10)


Of course, the favor buildings require the proper setup to be the best. But with the setup they are the best.
 
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Sean McCarthy
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In two-player, I can see that the 2-favor building could be pretty good, but it's never been really useful in my experience. (You rarely have points track and building track both, and even when you have building track, you're often using said track to make it in the first place, or there are no good buildings left to build.)

In multiplayer, the most common stone buildings I've seen are the 16-pointer and the cathedral, or sometimes the statue. The WWWGG is good too, and the cloth and food ones are nice when that's what you have.
 
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