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Subject: Perfected Puerto Rico rss

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David Bergan
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Update: I created a New Price Sheet that factors performance (final VP totals) into the repricing. It hasn't been vetted through years of play yet, but the math should be sound, and the concept is slightly better than the original. As of right now, I would recommend this sheet over the original one.


What follows is a 2-year long project that our group has been dedicated to and we all think is conclusively a better way to play Puerto Rico. The math involved has been refined to a T and it certainly breathes new life into an already great game. Please try it out in your group and give us any feedback.



Abstract

There are only two "flaws" to standard format of Puerto Rico... (1) certain buildings aren't worth their printed price, and thus tend to get passed over; and (2) the strategy in the game can feel like it becomes stagnant because there is so little variation from one game to the next (only the plantation choices are different each game)

Both of these can be overcome by using a pricing system that I invented which changes how much it costs to purchase the small violet buildings from one game to the next. Prices change according to how often the building is purchased... something that gets purchased frequently (like, every game) will go up in cost, while buildings that are neglected will go down in cost. Thus, you can't rely on one single strategy game-after-game because the buildings it relies on will become increasingly more expensive. And as the cost of less popular buildings go down (small wharf, university) players will start to wonder how they can incorporate them into their play. Each game ends up with a totally unique price sheet, and it is up to the players' adaptability to improvise new ways to win. For example, rather than relying on the consensus of strategy guides that the small market is one of the best cheap violet buildings, players will have to evaluate if the small market is still worth picking up when it costs twice, or thrice, as much.



Rules

All standard rules apply, except

1) Play includes all of the violet buildings from the original game and the expansion. This means there are 24 types of small violet buildings (and 2 copies of each type) and 7 large violet buildings to choose from each game. Since all the buildings do not fit on the game board, use this Expansion Tile Sheet.

2) At the beginning of the game, the prices for the small violet buildings are determined by this Pricing Sheet. Our group marks the new prices on the building tiles themselves so that you don't have to consult the sheet throughout the game. Note that there are tabs in the worksheet for 3-player games, 4-player games, etc. This is done because each is different and buildings that are more often purchased in a 5-player game (like the office) should not affect the prices for a 3-player game.

Update: I created a New Price Sheet that factors performance (final VP totals) into the repricing. It hasn't been vetted through years of play yet, but the math should be sound, and the concept is slightly better than the original. As of right now, I would recommend this sheet over the original one.


3) At the end of the game, the pricing sheet is updated by recording how many building tiles are left on the board (unpurchased) for each type of small violet building. (i.e. You record "2" if no one bought that building during the game, "0" if both copies of that building were bought.) The sheet then generates the new prices to be used in the next game.



Results

Our group has been playing this way for almost 2 full years. We don't get a ton of games in, but you can download our results to see what direction the prices went for us. Be sure to unhide all the columns to see how many games we played.




FAQ

I ran out of room on the pricing sheet.

Copy the last three columns (i.e. columns R-T, it looks like 2 columns unless you un-hide "S") and paste them to the right. The formulas will still be correct no matter how many times you add new columns this way.


Your rules allow for the Forest House and Hacienda simultaneously, which is widely consider a broken combo and specifically banned by the rules for the expansion.

Well, if the combo is really a world-beater, then the prices for those buildings will go through the roof and that strategy will no longer be viable. In our group, we've tried the combo many times (at regular price) and no one has consistently been able to win with it.


Why does the pricing sheet have the starting prices for the Factory and University switched around?

I've heard that the game creator once said that the only thing he would change to original version of Puerto Rico was switching these prices. And to me that makes sense given that (a) the University is hardly ever taken at 8, (b) the Factory is almost always taken at 7, and (c) in the expansion he created the Specialty Factory at a price of 8.


Why aren't the production plants and big buildings included in the price sheet?

Varying the price of the production plants would be chaotic, since their printed cost is tied directly to the trading value of their good. The point of changing prices is to create incentive to use different buildings, but the production buildings don't need incentive.

The original version of the price sheet did include the big buildings, but as I discussed this on a forum, a friend convinced me otherwise, saying:

I think this is a waste of time for the large buildings. Look at it this way:
- They have no function other than to give points at the end of the game
- They are worth different values to different players, depending on strategy
- Their uneven value rewards the player who buys first, who has given up other opportunities (say, a harbor) to get first pick. The guy who gets stuck with the Fortress either spent his money on something else, or got the last big building.



So how exactly does the price sheet work?

As players take buildings, the cost of those buildings go up for future games. The buildings that aren't taken slowly go down in price. The updated price sheet also figures in the final VP count... so that the winner's building choices has a greater impact on future prices than the loser's building choices.

For more precise details, and an explanation of the math involved, go here.


Thanks for your consideration,
David
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Pete
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Simplicity is not overrated.

Pete (thinks the price sheet overcomplicates things, especially if you play P.R. only occasionally)
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Branko K.
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You misspelled "tweaked and needlessly complicated" with "perfected".

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Jamie Pollock
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I believe the only required change is as the game creator has already stated - University to 7 and Factory to 8. With regards to the Office, this is a building which gets more valuable with fewer players. For instance, when we play the official 2-player version, we've found the Office to be pretty good since the trading house is much harder to empty.
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Maciej Welc
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Jambo wrote:
I believe the only required change is as the game creator has already stated - University to 7 and Factory to 8.

This perfectly implements K.I.S.S. rule.
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L. Scott Johnson
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I'd stick to the KISS rule, myself.

But for the groups that prefer this adaptive method, I'd suggest three things to improve the convergence to the "perfect" costs:

1. Use a separate spreadsheet for different number of players. (Track purchases for 3p separately from purchases in 4p, e.g.)

2. Do not track buildings that could be occupied but never were occupied (i.e., the buildings built at the end of the game just for their base VPs).

3. Weight buildings built and occupied by the player who wins winner more than those built by other players.
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L. Scott Johnson
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dbergan wrote:
There are only two "flaws" to standard format of Puerto Rico... (1) certain buildings aren't worth their printed price, and thus tend to get passed over; and (2) the strategy in the game can feel like it becomes stagnant because there is so little variation from one game to the next (only the plantation choices are different each game)


If you're using the expansion, which is the case for your analysis, then the second point isn't true. Different selections of available buildings produce a large variation from one game to the next.
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Adam K
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I like the idea how things change depending on how previous games were played... The problem is that PR isn't that frequently played and it might take a while before the game gets changed drastically.
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Tibs
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Eh, I have a much more wide-reaching rule that changes the stagnant tactics and fixes mis-priced buildings:

Quote:
• University is 7 and Factory is 8.
• Buy the expansion, and randomly pick which buildings will be used for any game, based on price (e.g: Small Market OR Aqueduct. Small Warehouse OR Storehouse. Any two of the following: Hacienda, Construction Hut, Forest House, Black Market. Five of the seven large buildings, etc.).

That's it.


And for a little more security:

•Don't use Hacienda and Forest House in the same game (exploitable)
•Don't use Office and Trading House in the same game (Office is worse if the small and large markets aren't drawn. Plus they're too similar)
•Don't use Factory and Specialty Factory in the same game (two buildings in one game that make money based on products is boring.)


Also there are the new buildings in the new release to look forward to, and I have a few custom-buildings of my own to complement them. With all of them mixed together, there will be three times as many small purple buildings as in the base game, allowing—even requiring—players to alter their strategies from game to game.
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David Bergan
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Dear Friends who think this is over-complicated,


Playing this variant is not complicated. There are only 3 rule changes:


1) Play includes all of the violet buildings from the original game and the expansion. This means there are 24 types of small violet buildings (and 2 copies of each type) and 7 large violet buildings to choose from each game. Since all the buildings do not fit on the game board, use this Expansion Tile Sheet.

2) At the beginning of the game, the prices for the small violet buildings are determined by this Pricing Sheet. Our group marks the new prices on the building tiles themselves so that you don't have to consult the sheet throughout the game. Note that there are tabs in the worksheet for 3-player games, 4-player games, etc. This is done because each is different and buildings that are more often purchased in a 5-player game (like the office) should not affect the prices for a 3-player game.

3) At the end of the game, the pricing sheet is updated by recording how many building tiles are left on the board (unpurchased) for each type of small violet building. (i.e. You record "2" if no one bought that building during the game, "0" if both copies of that building were bought.) The sheet then generates the new prices to be used in the next game.


What is so complicated about that?


True, it is fairly complicated to understand all the math involved with what is going on, but if you just trust me and try playing a few sessions this way I really do think you would like it better.

Kind regards,
David
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David Bergan
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Rulemonger wrote:
I'd stick to the KISS rule, myself.

But for the groups that prefer this adaptive method, I'd suggest three things to improve the convergence to the "perfect" costs:

1. Use a separate spreadsheet for different number of players. (Track purchases for 3p separately from purchases in 4p, e.g.)


Ummm... did you even download my price sheet? It already has tabs for 3-player, 4-player, and 5-player.



Rulemonger wrote:
2. Do not track buildings that could be occupied but never were occupied (i.e., the buildings built at the end of the game just for their base VPs).


I disagree. The base VPs (and number of quarries you can use to buy a building) are inherent functions of the building. Buying something even for its base VPs should affect the future price. In fact when the University gets cheap (like, say, 5 dubloons) it is often taken late-game because it is worth 3 VPs and you can use 3 quarries to get it. If it continued to get cheaper because it wasn't occupied, then it would be broken.


Rulemonger wrote:
3. Weigh buildings built and occupied by the player who wins winner more than those built by other players.


My philosophy was to add incentive to purchase buildings that were never taken by anybody... not to discourage people particularly from using the buildings that the winner had just used. You could certainly add in a factor like this, but it sounds like more complicated bookkeeping, and I'm not sure it would really make things more fun or interesting. Just my opinion...

Kind regards,
David
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David Bergan
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LupusX wrote:
I like the idea how things change depending on how previous games were played... The problem is that PR isn't that frequently played and it might take a while before the game gets changed drastically.


True it does take a while for drastic changes... if all the prices moved a ton, it wouldn't be stable. We intentionally leaned toward stability.
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L. Scott Johnson
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dbergan wrote:
Rulemonger wrote:
I'd stick to the KISS rule, myself.

But for the groups that prefer this adaptive method, I'd suggest three things to improve the convergence to the "perfect" costs:

1. Use a separate spreadsheet for different number of players. (Track purchases for 3p separately from purchases in 4p, e.g.)


Ummm... did you even download my price sheet? It already has tabs for 3-player, 4-player, and 5-player.


Um, no. As I said: I'll stick to the KISS rule. So I'd have no reason to download the spreadsheet and open it.

It was just a constructive suggestions in addition to that, and one that you've apparently already implemented.

dbergan wrote:
Rulemonger wrote:
3. Weigh buildings built and occupied by the player who wins winner more than those built by other players.


My philosophy was to add incentive to purchase buildings that were never taken by anybody... not to discourage people particularly from using the buildings that the winner had just used. You could certainly add in a factor like this, but it sounds like more complicated bookkeeping, and I'm not sure it would really make things more fun or interesting. Just my opinion...


Oh. I thought your philosophy was to perfect the costing of the buildings. Sorry about that, then.
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David Bergan
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kungfro wrote:
Eh, I have a much more wide-reaching rule that changes the stagnant tactics and fixes mis-priced buildings:

Quote:
• University is 7 and Factory is 8.
• Buy the expansion, and randomly pick which buildings will be used for any game, based on price (e.g: Small Market OR Aqueduct. Small Warehouse OR Storehouse. Any two of the following: Hacienda, Construction Hut, Forest House, Black Market. Five of the seven large buildings, etc.).

That's it.


And for a little more security:

•Don't use Hacienda and Forest House in the same game (exploitable)
•Don't use Office and Trading House in the same game (Office is worse if the small and large markets aren't drawn. Plus they're too similar)
•Don't use Factory and Specialty Factory in the same game (two buildings in one game that make money based on products is boring.)


Also there are the new buildings in the new release to look forward to, and I have a few custom-buildings of my own to complement them. With all of them mixed together, there will be three times as many small purple buildings as in the base game, allowing—even requiring—players to alter their strategies from game to game.


That's fine if you prefer playing that way, but we prefer having all the options (small violet buildings) available in every game.

We don't want new strategies that come from being denied certain buildings (like if the Harbor isn't available) but rather from players understanding just how valuable every building really is. So if the Harbor is priced at 9 or 10... it's still there, but is it worth paying 1 or 2 more dubloons to get it to work for me in this situation? Or if specialty factory is at 6, can you really get away with all-indigo production? Our way requires much more nuance in understanding the combos and strategies... rather than simply trying to make a strategy work because you only have certain buildings available.

Again, there's nothing "wrong" with your way... just stating why we switched from playing your way to the system we invented.

Kind regards,
David
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Tibs
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dbergan wrote:
Again, there's nothing "wrong" with your way... just stating why we switched from playing your way to the system we invented.


OK. Well then, it seems kind of like your idea is the kind of thing that is playtested a bunch with different numbers of players, and then you record what prices the buildings hover around most often.

Then you can report the new "corrected" prices of the buildings, since those new prices more accurately represent what the building is worth. That could be the entire variant—the price-corrections of buildings based on opportunity cost.

Didn't someone try this 0-1-2 for -1/+0/+1 before? Certainly we could have some results for that. Plus, tracking the prices such that they're different than what's printed on the building could be a pain each game. I've taken heat from modifying my buildings between games before. Players don't want a change of rules from game to game—they want a change of tactic.

I guess my best advice is to wait for the new buildings to come out. That'll surely breathe new life into the game.
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Steve Bachman
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Nice work and interesting ideas. I think "perfected" is a misnomer, though, as many players do not find the "flaws" you "corrected" to be problems at all.

This would be a great thing to use in a stable game group that played PR a lot. If played infrequently, or with a varying group of players, it seems unnecessary as the variety will already be there.

It would be neat to see this implemented in one of the online versions.
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Devon Harmon
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David,

I think that your variant sounds like an excellent idea. If I ever find myself regularly playing this game with the same group of people again, I'm sure to give it a try.

I have always enjoyed games that had economies that carried over from game to game, ever since I played scorched earth for the computer. I've ofter advocated a similar economy for Heroscape, altering the prices of the units based on how frequently they are selected. Sadly, I believe I lack the necessary knowledge and skill to implement such a program. Thank you for the time that you and your group have spend on this. I am eager to see it in action.
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David Bergan
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Ward wrote:
Nice work and interesting ideas. I think "perfected" is a misnomer, though, as many players do not find the "flaws" you "corrected" to be problems at all.


What can I say... I have a tendency to use hyperbole. Plus you have to admit that using this title does draw people into looking.

I'd love to see this in an online version, too. It would be awesome to keep track of large population statistics like how likely a University is purchased at price 5/6/7/8. Or a small market at 1/2/3/4.

Kind regards,
David
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David Bergan
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kungfro wrote:
Then you can report the new "corrected" prices of the buildings, since those new prices more accurately represent what the building is worth. That could be the entire variant—the price-corrections of buildings based on opportunity cost.


You can find our data here. When I started, I thought (like you do) that the prices would "settle out" to certain values and then remain fixed. But as we have continued playing over the course of 2 years, it seems that things go in more of a cycle. The aqueduct, for example, has gone games without being purchased at 2 dubloons, and yet is still regularly purchased at 3 dubloons. That's because the factors for buying an aqueduct are more complicated than just its own price. (Like what planations do I have, is the Specialty Factory going cheap, etc.)

So yeah, I was thinking the prices would settle out, and you can certainly just take our latest prices and use them (for 3-player anyway... we've only played one 5-player game with this system, so those aren't settled at all). But we find it fun to see prices go up and down, and even at the end of one game, we plug in the numbers, see the new prices, and start speculating on how we would strategize in the next game.

Again, my goal was to make things less stagnant... and I think even "corrected" prices (if fixed and not variable) could lead to stagnation.


kungfro wrote:
Didn't someone try this 0-1-2 for -1/+0/+1 before? Certainly we could have some results for that. Plus, tracking the prices such that they're different than what's printed on the building could be a pain each game.


Yes, there have been other attempts at this, but to my knowledge, none of them adequately accounted for the "inflation" and "deflation" I discuss in the detailed FAQ... and so they didn't really pan out.


kungfro wrote:
I guess my best advice is to wait for the new buildings to come out. That'll surely breathe new life into the game.


When they come out, I'll revise my sheets, and start the prices over again. Looking forward to it!

Kind regards,
David
 
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dbergan wrote:
You can find our data here.

Um. Neat! Strange that many things have increased in price, but few have decreased. One that decreased a lot was the Trading Post. That strikes me as odd. But then again if you're using both Small and Large Markets in the same game, every game, of course the incentive to get the Office is higher than the Trading Post.

Quote:
So yeah, I was thinking the prices would settle out, and you can certainly just take our latest prices and use them (for 3-player anyway... we've only played one 5-player game with this system, so those aren't settled at all).

Right. Keep at it
I didn't expect them to "settle" permanently, but to oscillate around a certain price. That would be the fruit of your labor.

Quote:
Again, my goal was to make things less stagnant... and I think even "corrected" prices (if fixed and not variable) could lead to stagnation.

Can't argue there. That more more so that you would share them with other players who don't mind not changing them all the time.

Quote:
There have been other attempts at this, but to my knowledge, none of them adequately accounted for the "inflation" and "deflation" I mentioned in the FAQ... and so they didn't really pan out.

Thought so. The one where the price just goes up 1 or down 1 if both or neither were built seemed most comprehensive, though. Plus it didn't require a spreadsheet with near-calculus formulas to account for an "inflation."

Quote:
When [the new buildings] come out, I'll revise my sheets, and start the prices over again. Looking forward to it!

No, don't reset the prices for all the buildings you've used so far. That seems kind of like a waste of effort. Just allow the new ones to slowly grow/shrink as they interact with the revised old buildings. Of course, you might not have meant that at all in your comment.
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David Bergan
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kungfro wrote:
Um. Neat! Strange that many things have increased in price, but few have decreased. One that decreased a lot was the Trading Post. That strikes me as odd. But then again if you're using both Small and Large Markets in the same game, every game, of course the incentive to get the Office is higher than the Trading Post.


Well, mathematically speaking, for every (fraction of a) dubloon that is added to a building the same is taken away from another building. What I'm sure you're noticing is that the cheap buildings (the 1 quarry column) all tend to go up. We found that nothing stays at a price of 1 because if you have 1 quarry you can get those for free and someone always does. So even the worst buildings will get taken at a price of 1 because there are times when you want to save money, but still take a free building for the VP.

The buildings that went down in price (in 3-player) are mostly the column 2 ones... Guesthouse (-1), Trading Post (-2), Church (-1), Small Wharf (-1), Office (-1), Large Market (-1).

Column 2 has a hard time because the players are poorer due to the increase in Column 1 prices. And once players get a little cash flow going, they tend to save up for the more powerful column 3 buildings (harbor, lighthouse, factory, wharf).

Also, if you haven't played a lot of 3-player, you'll notice that trading is harder to do because it has to be taken twice to fill the trading house. Thus the trading-based buildings tend to be taken less.


That said, some really interesting strategies have arisen. For example, hardly anyone likes the Small Wharf and eventually it had dipped down to a cost of 4. The first game it did, I had 2 quarries and worked out a combo getting a quick Lighthouse for 7 (for my income), then a Harbor for 8, and then picked up the cheap Small Wharf instead of a warehouse. Afterward, during each Captain phase, I put 1 good on the Small Wharf... which normally is worth 0 VPs, but worth 1 VP and 1 Dubloon with the other two buildings in effect. So instead of shipping 4 corn on one of the main boats, I split it into 1 (or 2) corn on my Small Wharf and 3 (or 2) on the main boat... either way nets one 1db. Also I have the advantage of shipping goods even if the main boats don't carry my product. And I can be really tricky in some situations and keep 1 barrel after a captain phase (small wharf doesn't require you to ship everything), where I plan to pick captain myself right away (before they craft) putting that one barrel on a main ship for 1db 1db + 1vp 1vp 1vp or on my small wharf for 1db 1db + 1vp 1vp.

It's a strategy I would never attempt with the regular prices... but that's precisely what makes the fluctuating economy so much fun.


kungfro wrote:
No, don't reset the prices for all the buildings you've used so far. That seems kind of like a waste of effort. Just allow the new ones to slowly grow/shrink as they interact with the revised old buildings. Of course, you might not have meant that at all in your comment.


That's a good point... I was thinking about "starting over" with the printed prices, but I guess there really isn't any advantage to that.

Kind regards,
David
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Key Locks
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Jambo wrote:
I believe the only required change is as the game creator has already stated - University to 7 and Factory to 8.

When did the designer say this? Can you provide a link for the curious?
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Miguel de la Casa
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And, can you say you happily build an University for 7?
(Other than an end game buy for the VP)

I lowered it to 6 and still never buy it.
 
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Steve Bachman
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aristarco wrote:
And, can you say you happily build an University for 7?
(Other than an end game buy for the VP)

I lowered it to 6 and still never buy it.

I buy it at 8 quite often.
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Maciej Welc
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Ward wrote:
I buy it at 8 quite often.

So do I. I've also seen it leading to a victory.
 
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