A few years ago, the Levy & Campaign Series burst on the scene with Nevsky: Teutons and Rus in Collision, 1240-1242 from the gifted and beautiful mind of Volko Ruhnke. A series focused on medieval logistics and the feudal system where the arts of war and careful building of alliances were so important to the fabric of society all boiled down into a very playable game was like catnip to the wargame masses. Since that time, there have been several new designs in the series come about including Almoravid: Reconquista and Riposte in Spain, 1085-1086 from Volko as well as from other designers including Inferno: Guelphs and Ghibellines Vie for Tuscany, 1259-1261 from Enrico Acerbi and now Plantagenet: Cousin’s War for England 1459-1485 from Francisco Gradaille. Francisco has agreed to write a series of posts for our blog on his designs and way of thinking through issues a bit non-conventionally.
I’m a mathematician and a wargame designer. Over the years, I’ve worked in financial modelling but also in close relation with software developers. I’ve been an RPG GM for the last 30+ years. That combination makes me focus on history simulation and narrative flow when I’m designing a wargame. But it also opens the door to use all the strength of mathematical modelling and software development processes to help me while designing a game.
I’ll be writing a series of articles appearing here on The Players’ Aid Blog about how this can be used in the game design field. Its strengths and its weaknesses. What kind of results can we expect from this approach and how you can start learning about this subject, so that you’ll be able to have more tools available when you are working on your own designs.
This first article titled Game Design, Software Development and Math will talk about the basics and show some real game examples.
The first concept that we need to understand is that math is just a language. It’s not a science. Learning math is learning how to write using a different code. A universal code that can be translated to any other language and it’s a lot more efficient to work with. Simpler, faster and workable in any situation. So, when we use math to study a model, we are just translating it from standard language to a series of notations and formulas that will let us work on it and understand it.
Mathematicians have a certain way of seeing the world. They teach us to start building our theories and models from a small group of axioms that will be the foundation of all that comes later. Each step must be solidly anchored on the previous one.
They also train us to search for the simplest elements that define a model or a process. If you could simplify a system to its most essential elements, which ones would they be? What is their effect in the structure? What is their relation to the rest of the elements?
Finally, we are also taught to become obsessed by the second derivative. Not the first level consequences but also the second and third one. If I change this, how will it affect the system? Not the obvious effect, but are there ripples that will extend through all the system and are invisible on a first look?
When a mathematician arrives in a new field, they tend to extrapolate that process. This is the way we think and we work. And it’s a very standard thing to do, as this is how the human brain works. So even if we aren’t aware of it, all of us do the same: we look for the fundamental principles of a system and we study it first trying to learn the simplest elements and then the more complex ones. So, no math-magic at work here, just the same “monkeys in suits” everywhere doing the same thing.
Let’s examine a pair of examples showing how these tools and processes can be used, and we’ll make a more detailed analysis in the next upcoming articles.
Plantagenet: Cousins’ war for England, 1459-1485 is an operational wargame about the Wars of the Roses that is the fourth entry to the Levy & Campaign Series that the great Volko Ruhnke created for GMT Games. As of now, it can be pre-ordered on GMT’s P500 program, as well as the third game in the series Inferno: Guelphs and Ghibellines Vie for Tuscany, 1259-1261.
For Plantagenet we needed to develop a Battle system that, following the structure of the previous games of the series, was a good simulation of the actual battles of the Wars of the Roses. So, we had to get a coherent outcome and have a historical Sequence of Battle. We developed those changes and, when finished, we had to test them to see if they were giving the desired outcomes.
We had two options here. Get two or three friends together and start doing battles. Playing 40-50 battles in an afternoon and try to get a good number of them (200-300?) in order to gather the data.
Or we could program a Battle Simulator to do this tedious work for us.
And that’s what we did. We have developed a Battle Simulator that does battles on its own following the parameters we want for battle time decisions. So, we press a button and we can simulate 10,000 battles in less than one minute.
What is this giving us? It takes away the need to spend countless hours testing a battle system on a table to see if the numbers fit. If there is any broken strategy or undesired effect. And then testing again when we change a number. Just one number can totally change the outcome of the battle.
What is this not giving us? We don’t know if the battle system is fun. For that, we need to play it with friends. And this part of the testing is not going away. But now we don’t need to study it to see if it’s balanced. We know it is…or isn’t as the case may be. Now we need to see if people enjoy playing it, and if not, why and how can we fix it.
So, the designer’s and developer’s time is spent more efficiently. Focusing in on the truly important aspect of the game: are people enjoying playing it?
Another example, and this will be it for today.
We have a system of victory points in Plantagenet and we want to include a sudden death victory condition. When players reach a certain threshold, it’s not necessary to keep playing the game. One of the sides will win with a 99% probability or more.
So, we can play dozens of games and see how they develop, and try to establish a number of victory points that will be the barrier.
Or we can calculate in each of the turns what are the maximum number of victory points a side can get and with what probability (dice rolls, other random effects in consideration here). And go backwards, from the last turn to the first, and see at what point one side has lost the game in each of the turns.
Just calculations, no games played here.
And with that, we know what number should be the threshold in each turn.
As in the example before, we can use the testing time to see if the players are enjoying the game. If the mechanics fit well together and if the flow of it is coherent with the historical period we are trying to simulate. These are the most important aspects of the game, not if the victory conditions must be 31 points or 27. Let’s leave that to math, and let’s spend our time playing.
Well, these were a pair of examples of when using calculations, modelling, programming and math in the process is useful for designers. In our next articles, we will explain more details on that and some extra tools that we can use to make our time as designers more efficient.
Who is Francisco Gradaille –
Francisco Gradaille, Paco, is a mathematician from Barcelona that works as the CIO for an investment firm. He played chess in his young age, with moderate success. In the little spare time that his cats, kids, wife and ultra-running training leaves him nowadays, he plays wargames. He also is the DM of a role playing group that has been together for most of the last 25 years (wife included).
Regarding wargames and rules, he is always tinkering with the system trying to make them more soloable or fixing their shortcomings if there are any. He prefers games from before the 20th century and, with the American Civil War being one of his favorite conflicts, his most recent project involves testing a rules variant for the old American Civil War Series from Clash of Arms. He also has embarked upon his first design with GMT Games called Plantagenet: Cousins’ War for England, 1459-1485, which is currently on P500 and for which we posted an interview on the blog in December 2021.
We also posted a guest post from Paco in September 2020 showcasing a variant for the Men of Iron Series that was quite interesting.
If you are interested in Platagenet: Cousin’s War for England 1459-1485, you can pre-order a copy on the game page from the GMT Games website at the following link: https://www.gmtgames.com/p-960-plantagenet-cousins-war-for-england-1459-1485.aspx
Interesting article! I look forward to reading the rest of the series by Francisco. I get the main idea – get the computer model to do the hard work, and focus the human play-testing on the human factors. But back to basics – how does the battle simulator make decisions (especially, how does it select and balance an overall strategy versus calculating individual playing piece opportunities that might arise), and what sort of parameters might you use to constrain it? How far does it simulate the way humans approach a game?
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