Tobold's Blog
Monday, November 22, 2021
Board games and math problems

I am reasonably good at math, because both my natural science degree and my day job required it, so I get to practice math more than the average person. And one of the skills you pick up if you are comfortable with mathematics is to know whether something is a math problem or not.

Imagine you want to know what "A + B" equals to in a given situation. If you have precise information about both A and B, or a sufficient number of equations linking the two together, this is a math problem, and you can solve it. For example if you know that "A - B = 1" and "A * B = 6" you can calculate that A must be 3 and B must be 2, so A + B = 5. But if you know that there is randomness involved, for example both A and B are numbers determined by throwing a 6-sided dice, that isn't a math problem that can be solved. You can still apply some math, for example stating that A + B is "most likely" to be 7, but can't know what A + B is for sure until you throw those dice.

One old classification still being used about board games is to divide them into Eurogames and Ameritrash games. Obviously there is much wrong with that classification: Eurogames aren't necessarily made in Europe, and Ameritrash games aren't necessarily trash. But quite often the difference comes down to this: Euro style games are math problems, American style games aren't.

American style games are quite often thematic games that have a lot of randomness and narrative elements to them. If a game allows you to make a decision, and that decision determines which page to read in the storybook, or which story card to read, that isn't a math problem, unless you know the content of the whole storybook or the whole deck of story cards (which you shouldn't). And the randomness makes it so that you math skills can be used to make reasonable decisions ("If I do this, I need to roll 5 or higher on those two 6-sided dice, and that is likely to work"), but still leaves open the excitement of not knowing what will happen, and everybody at the table laughing or groaning when you end up rolling a 2 with those two dice.

Euro style games often have little or no randomness, no storybook or cards with unknown content, and little or no player interaction. Terms like "worker placement" or "tableau building" are used to describe a game in which players choose an action, and know exactly what the outcome of that action will be. You place your worker on this field, and you *will* get 2 grain. Now the trick of these games is to create math problems that most people can't solve in their heads. You place workers to get resources, use those resources to get buildings, those buildings produce other resources or new workers, and certain actions are worth a certain number of victory points. In some cases there is absolutely no randomness nor player interaction, so gameplay basically consists of people making a series of moves based on gut feeling or experience more than math, and somebody at the end has the most victory points and wins. Obviously, if in the next game you would do the exact same sequence of moves, and there is no randomness or player interaction messing up the result, your victory points will be exactly the same as before. The outcome is deterministic.

Now a computer is much better than a human regarding math problems. If you play such a deterministic Euro style game, a computer could either solve the equations and determine the best sequence of moves, or it could with some machine learning algorithm quickly learn how to optimize. A human wouldn't be able to beat a computer in such a game. While people rarely play Euro style games against computers, it does happen that people play such a game against somebody who has played the game before more often than they do. And if a machine can learn the optimum sequence of moves, so can a human. Usually a more experienced player at least knows which first move(s) in the game are better than others, even if he hasn't learned the complete sequence of best moves yet.

I don't like Euro games much. I recognize them as a math problem, and I don't like to solve math problems for fun. The deterministic nature of the game combines with factors like "Joe brought the game to the table because it is his favorite game, while the other players don't know the game yet" to the predetermined outcome of "Joe wins". Also I find that the gameplay action of "I place a worker here to gain 2 grain" isn't inherently fun because there is no discovery or luck involved. I find rolling dice or reading page 127 of the storybook / card 127 of the story deck more fun, because I don't know what the outcome will be. Thus in the narrative, American style games I prefer, every move is an experience. Winning after X moves isn't necessary, and I actually prefer co-operative games.

Having said all that, most games are not 100% in one of these categories. A classic "Euro style" game like Settlers of Catan does have dice rolls to determine resource gains and direct player interaction via the robber, so it isn't totally deterministic. Still, my preference for American style / narrative / thematic games remains: I would much rather make a move that can be described as "I move my hero next to the orc and chuck some dice to see whether I hit him" rather than "I place my worker on the farm to gain 2 grain". However, I do like a bit of resource management and options to mitigate randomness in my games. I absolutely love Sleeping Gods, which my wife and me are currently playing, in spite of every move starting with me placing a worker on a section of the ship; I like that I don't know what will happen if I choose to go to a certain location. But I also like that if for example a combat happens and I have bad luck, I could use some of my command points to mitigate that, or that by carefully managing my wounds and fatigue I can make a win in the combat more likely. I don't want my games to be math problems in which I need to calculate 3 moves ahead, but I am fine with the bit of math needed to evaluate probabilities of dice rolls.


A German who doesn't like Settlers of Cataan and Eurogames? You have obviously been out of the country too long Tobold. Return before it is too late!
Seems a bit like the dichotomy in roguelike games. Are you carefully avoiding dangerous monsters while assembling your kit to run for the final boss... or are you frantically burning your resources escaping from one monster after another? The best roguelikes have a bit of both!
Since when Settlers of Catan is an Eurogame? Because it's german? It's a game which is completely random.....

For me the separation is different, I split games into two categories:
- games where when I lose I know what I did wrong and I can avoid doing it next time, if I win, I can tell the loser what he did wrong
- games where after the end of the game, if I lost, nor I nor the winner is able to tell me what I should have done differently, and if I won I usually explain that it's my superior card-drawing/dice-rolling skill :)

I don't care about the second group, because then we're just better off watching a good movie, the story is out of our control but it's usually way better than any random dice-rolling.

Most games fall in-between, and while there are some random games which are fun because in reality you just don't care about the result, many use randomness to hide a hollow game mechanics which would be ridiculous trivial.
Since when Settlers of Catan is an Eurogame? Because it's german? It's a game which is completely random.....

According to Wikipedia, "The Settlers of Catan became one of the first German-style board games to achieve popularity outside Europe.". So it is frequently cited as "the first Euro style game" coming to the USA, even if, as you correctly state, it isn't a pure Euro game by today's definition.
I often read about those two types, and I find it is missing a big part of the game genre : the one with no (or few) randomness, but mainly based on player interaction : Citadels, Times bomb, Linq, Dixit, Concept, Jungle speed, Kuhhandel (Boursicocotte in French) to list some examples from my game collection.
Traditionnal games ( Belote, scrabble, other classic card games,...) also fall out of the 'Ameritrash' definition - there is some random part, but does not play such a big role, and theme is very important - but clearly are not eurogame.
Duel game ( chess, GYmkhana, Pentago, Abalone, ...) are even another category.

I do not know if this a french bias, but this opposition seems always to miss the majority of the games I know and play with my friends. And I find them far more interesting than the strong randomness of ameritrash, or the non-interaction or 'eurogame'. Is it because those games does not succeed out of the french market, or is it because we do not call them board games ?
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