Solving the 'math' of popular Euros like Agricola

Hello boy-o's,

I saw that a popular idea that keeps popping up on this site is that many of the top Eurogames like Agricola, Puerto Rico and Caylus are 'solvable' via math. I understand that concept but does anyone know of any place where someone has gone through the trouble of 'proving' this? I've seen some very mathy proving being done to solve Puerto Rico's first turn but beyond that, not really.

Since Agricola is so new, I'd be very interested to see any math being done to solve that game. I haven't heard of this yet and I frequent BGG and stuff (where this stuff usually crops up).

Can someone direct me to this?


In case I get trashed for discussing Euros, I should mention that I used to own a copy of Fortress America so that should make me immune to all flaming (*crosses fingers*)

Immune to flaming? But you're already such a flamer!





When I hear the term "mathy" I don't think of it in terms of something being solved but rather in terms of 'number crunching' as part of playing the game. Where things boil down to "bid 5 for this, trade 3 for that, spend 4 to get this, which will give me an extra that..."

What that tends to do is bare the bones of a game thematically. You're "out of the moment" because you're running a bunch of algebra in your head.


What you're referring to is "solvability", which is totally seperate. And plenty of "solvable" games (mostly abstract) are capable of being solved without math--like Connect Four as a very, very simple example.

I guess when I hear mathy, I think the same way as Ken B. "Well if I do this, I will get X victory points but if I do this I will get Y victory points". If Y is more victory points, you will pick that. Or you might say, "I want to end the game with X victory points. In order to get there, I will need this and this and this". I think Puerto Rico is the perfect example of this. Agricola is less so because many times the short term needs (feeding your family) outweigh your long term goals (getting a balanced farm). Although in attempting to satisfy the short term needs you don't sacrifice much on the long term goals (Unless you use an action to grab the food). But both in essence amount to maximization problems...how do I maximize my victory points.

Yeah, I'm not sure I would use the word 'solvable.'

But in my experience, where the more egregiously dry and boring Euros have fallen down is when they fall victim to the mental algebra Ken mentioned. There is obviously appeal in this kind of exercise in some circles (Excited Man?).

I would use the term 'formulaic,' because a game like this can get a TON of play in the initial excitement period--e.g., maybe it shows up on BSW (you might guess I'm thinking of Caylus here). Through lots of community repetition certain moves or transactions within the game are determined to be superior due to their efficiency. In short, the game may advertise the ol' chestnut "multiple paths to victory," but the avid players are going to figure out--and likely publicize--the particular choices which "ought" to be made in a given situation. Here's the Caylus thread I remembered that prompted all of the above.

With the right (or wrong?) group of players, I'm sure you can see it's a slippery slope from this kind of analysis permeating the gaming community and becoming the accepted conventional wisdom to...


That worker I just placed had almost no opportunity cost!

This game uses a factorization algorithm that models binomial expansion when stripped of coefficients!

My problem with games like Puerto Rico and similar Euros is that they become purely mechanical once you get playing them and the whole point of the game turns into how you can most effectively manipulate the game system. Puerto Rico isn't about growing crops and shipping stuff, but it's about turn order, timing your role selections well, and squeezing more points out of the game than your opponents. The games may be balanced, but the good strategies are unintuitive in relation to the theme and are "gamey" and mechanical. I like abstracts, but when I play a game like Puerto Rico, I feel like I've been tricked when the theme doesn't connect with the mechanics or the strategy.

Puerto Rico and Agricola probably do have some solvable aspects--but not THAT many.

Agricola strategies do revolve around the cards you are dealt. That pretty much kills detailed analysis.

Both games do have basic paths (Agricola has Harvest, Gathering, and Animal Husbandry paths) (Puerto Rico has more closely defined paths, because it is a mostly zero luck game.)

These are good games and to me do not really feel solvable. The last couple of turns in both can be analyzed in a fairly detailed manner...leading to some point counting.

Some games strike me as having only one particular path. Instead of the kind of path jumping and planning Agricola and Puerto Rico have.


There are some Action Point games based around the school of Tikal, Java, and Torres that feel much more solvable. The entire structure revolves around...Receive X Action Points, Spend on Y Actions, Gain Z VP. These get old spectacularly quickly, as that kind of end of game math happens every freaking turn. The game generally has almost no paths--you are pretty much working out the best choice.

In the Wolfgang Kramer games, the tricky bits come from majority ownership. You can commit action points to get a bucket of points later. This adds interaction, but it is a very dry painful and obvious kind of thing. For a recent painful example of this kind of game, take a look at the curiously highly rated Age of Empire III. Actually, don't bother.

Solvable was the wrong word--what you're talking about is optimization. That's what all the work on PUERTO RICO's first turn Settler --> Quarry* was about. Games with a lot of open information like PUERTO RICO lend themselves mightily to easy optimization strategies--you know almost everything about every player, so you can really grind the numbers. In fact, I'm willing to bet Victory Points are hidden in that game only because making them visible would make everyone's turn take forever. The more hidden information added to the game, the fewer the opportunities for optimization. Now you have to optimize within probabilities, and as we've all experienced--sometimes that doesn't work -at all-. The game TITAN is a good example here. E. g., "More than likely, that 2-stack is two Trolls, so my Cyc, Cyc, Unicorn should handle it easily--oops, it's two Warlocks. That's a shame."

From what I know of AGRICOLA, it's got randomness in the card draw--that's hidden information that would make PUERTO RICO- or CAYLUS-style optimization difficult. I'm surprised we haven't heard squeals from players about getting totally stuffed by someone drawing the juice. Maybe there has been, I don't pay much attention to the AGRICOLA threads.

*Opening move of the 2008 WBC PUERTO RICO game? Builder --> Construction Hut.

jeb wrote:

Solvable was the wrong word--what you're talking about is optimization. That's what all the work on PUERTO RICO's first turn Settler --> Quarry* was about. Games with a lot of open information like PUERTO RICO lend themselves mightily to easy optimization strategies--you know almost everything about every player, so you can really grind the numbers. In fact, I'm willing to bet Victory Points are hidden in that game only because making them visible would make everyone's turn take forever. The more hidden information added to the game, the fewer the opportunities for optimization. Now you have to optimize within probabilities, and as we've all experienced--sometimes that doesn't work -at all-. The game TITAN is a good example here. E. g., "More than likely, that 2-stack is two Trolls, so my Cyc, Cyc, Unicorn should handle it easily--oops, it's two Warlocks. That's a shame."

From what I know of AGRICOLA, it's got randomness in the card draw--that's hidden information that would make PUERTO RICO- or CAYLUS-style optimization difficult. I'm surprised we haven't heard squeals from players about getting totally stuffed by someone drawing the juice. Maybe there has been, I don't pay much attention to the AGRICOLA threads.

*Opening move of the 2008 WBC PUERTO RICO game? Builder --> Construction Hut.

There is some whining about certain cards in Agricola (the Wet nurse comes to mind) but not that much. I think the cards and the variable action sequence add enough variability to make the game a little more interesting. the food thing sometimes makes the immediate needs take the front seat to long term goals.

This thread ties in very nicely with the simplicity article from the front page.

jeb wrote:

Solvable was the wrong word--what you're talking about is optimization. That's what all the work on PUERTO RICO's first turn Settler --> Quarry* was about. Games with a lot of open information like PUERTO RICO lend themselves mightily to easy optimization strategies--you know almost everything about every player, so you can really grind the numbers. In fact, I'm willing to bet Victory Points are hidden in that game only because making them visible would make everyone's turn take forever. The more hidden information added to the game, the fewer the opportunities for optimization. Now you have to optimize within probabilities, and as we've all experienced--sometimes that doesn't work -at all-. The game TITAN is a good example here. E. g., "More than likely, that 2-stack is two Trolls, so my Cyc, Cyc, Unicorn should handle it easily--oops, it's two Warlocks. That's a shame."

From what I know of AGRICOLA, it's got randomness in the card draw--that's hidden information that would make PUERTO RICO- or CAYLUS-style optimization difficult. I'm surprised we haven't heard squeals from players about getting totally stuffed by someone drawing the juice. Maybe there has been, I don't pay much attention to the AGRICOLA threads.

*Opening move of the 2008 WBC PUERTO RICO game? Builder --> Construction Hut.

Exactly. As one moves from Euros to AT, we kind of slide down the optimization to applied statistics (i.e., risk management) scale. Pure open information games leave themselves open to optimization, while a game like Last Night on Earth is ridiculous. Each addition of an AT element reduces the optimization ability of a regular human.

A couple of things that reduce the optimization of a turn:

1. Die Rolls/Card Draws -- this adds a probability distribution to the equation and it gets tough quickly.

2. Player Interaction -- this is the big one. Without player interaction, a game like Race to the Galaxy is just a big optimization problem. However, try optimizing Diplomacy, Risk, or Twilight Struggle. Without Player Interaction, Twilight Struggle would be a breeze to optimize; however, most turns you have a plan in the headline phase. By the turn 7 you are off in a different part of the world doing something entirely different. This speaks to adaptability/randomization/theme.

In my opinion, a well themed game hinges on the fact that there cannot be an explicit optimization on a given turn. I am working on a post that ties this all together as it is something I have been thinking about for awhile -- maybe as a user submission.

Jeez...where's Steve Avery when you need him?

i liek gamez w/boob & bomb

ubarose wrote:

It's really the glut of second tier Euros that suffer from this type of math bloat, rather than the most popular ones. All the "Caylus Lite" and "PR Lite" games that strip out the interesting, complex parts of the game and just leave the dry mathy parts. Not to mention the "Knizia sneezed into a Kleenex, slapped a theme on it and called it a game" games.

Math bloat is a good term for this phenomenon. I think that it's a result of the current infatuation with games in which the objective is to score VPs or "siegpunkten." The problem doesn't arise when players are trying to actually achieve a qualitative goal, like crossing the finish line first or eradicating the enemy army.

Wow, awesome replies. I see now that I've simply misunderstood the adjective "mathy" in how it's used on this site. I assumed it meant solvable but I see now it is optimization I was thinking of. That's okay too, since I was curious as to how ANY turn in Agricola (other than the last turn) can be optimized given the huge hand of cards you have.

But yeah, some games like Power Grid, I find myself grinding my gears trying to mathmatically come up with the best profit move for that turn. Not that much fun at all times.

Puerto Rico, Caylus and Agricola all have me trying to make moves that slightly better than everyone else hoping that will pay dividends by the end of the game (and it often does). But these Ameritrash games seem to have me simply rolling better than everyone else and if I keep that up, I should be good.

Like Battlelore has me performing probability calculations at various points in the game when I'm trying to think of if I should be attacking this turn or going on the defensive, etc.

But yeah, Twilight Struggle seems the ultimate in 'keeping me in the moment' in terms of theme-connection. I optimize my first turn (influence placement) based on my hand and after that anything goes. It's a total blast and I react to my opponent much more often than I react to the cards or die-rolls. Very cool game.


Someone called Last Night on Earth a ridiculous game. I was curious about that one cuz I had heard it was the best Zombie boardgame out there (I've tried Zombies and wanted to pull my eyes out after the 2nd hour). Do people here like Last Night on Earth?


anyway, dammit.. i was half-hoping Agricola was sorta-solved in the way the Settler-Quarry thing was solved. Although someone above said that the Builder-Construction Hut was the first turn in a big tournament?! Must have been a 5-player game no?