Perfected Puerto Rico

From Summa Bergania

• Requires the Puerto Rico expansion (find links to buy the expansion here... should be around $5.00)

• All my files that I refer to below are in MS Excel format

Contents 1 Abstract 2 Rules 3 Results 4 FAQ

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

Is this method of playing discussed anywhere?

A healthy forum discussion can be found here.

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?

I know when you look at the formulas they are rather intimidating... so I'll try to simplify it here. Consider playing Puerto Rico where every time a small violet building was purchased, the next game the price for that building would go up 1 dubloon. That does create the incentive effect we want, but if that's all there is to it, then all the prices would be constantly rising throughout a series of games (inflation).

To counteract this, the buildings that were not purchased must simultaneously decrease in price. So do the unpurchased buildings then all go down 1 dubloon? No. Because in a 3-player game, you might have 13 small violet buildings purchased and 35 left unpurchased... and this means that altogether the next game's prices would be 22 dubloons lower than the last game's (deflation).

So the solution is to find out how much we are increasing prices on the purchased buildings and then simultaneously decrease prices on the unpurchased buildings by the same amount. So if purchased buildings increase 13 dubloons, as a whole, then the unpurchased buildings must decrease 13 dubloons, as a whole. The purchased buildings all get +1 dubloon, and the unpurchased buildings all get -13/35 dubloons. Check the math:

+1 (increase per bought building) * 13 (number of bought buildings) = +13

and

-13/35 (decrease per un-bought building) * 35 (number of un-bought buildings) = -13

Result: no inflation or deflation

So essentially, we have to keep track of all actual prices of the buildings and then round them off to the nearest integer (because our group doesn't play with fractions of a dubloon). So you will notice on the price sheet that there is a hidden column between each "# Left" and "New Price" that keeps track of a fraction-based "Actual Price". True to its name, this is the actual price of the building before rounding.

And with rounding we added a small wrinkle, too... Everything rounds normally, except when the "Actual Price" ends in .5 dubloons. Normal rounding of 0.5 always goes up, but we decided that if a price landed exactly on a half of a dubloon it would round in the direction of the original price. For example... if the Hospice's actual price was "5.5", then it will round down toward the original price ("4") and the new price would be "5". But if it's actual price was "2.5", then it would round up toward the original price, and the new price would be "3". And by doing this, we removed the possibility of having inflated prices based on rounding.

Now everything above hopefully helps clarify the concepts we used. In actuality, though, we don't increase the price of the purchased buildings a whole dubloon after each game. The increase is calculated based on the total number of purchased buildings. If there were a lot of building purchases, then the amount of increase is fairly small. If there were fewer purchases, then the amount of increase is larger. Again this ties into the supply/demand concept... if only 5 small violet buildings were purchased, then those five are perceived as quite valuable. But if the next game has 20 small violet buildings purchased, those buildings are only a quarter as valuable as those taken in the earlier game... so their price increase is only a quarter as much.

Then we have the more recent, updated price sheet which in addition to everything above, weighs a player's performance into the price change... where the winner's building choices influence new prices the most, and the loser influences less. The amount of influence a player has is proportional to how close he or she was to winning. If there is a tie in VPs, then 1st and 2nd influence prices the same amount. But if 1st wins by a margin of 15 VPs, then he will have a dominating effect on the new prices.