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Numeric Clairvoyance and Structural Numbers

Page: DesignArticle.Article-StucturalNumbers - Last Modified : Sun, 23 Mar 14 - 2059 Visits

Author : Eric Pietrocupo

This is somewhat the sequel article of:

Playing with numbers

Numeric Clairvoyance

I have a tendency to see patterns in numbers. Which makes me want to make those pattern match when desiging game and when other games I play break those matching pattern, I find them not elegant. I'll give you for example 3 numbers:

2, 3, 6

What are the relations between those numbers? It's basically that 2 and 3 are part of 6 since 2 x 3 = 6 and 3 x 2 = 6. What about:

4 and 9

What is the relation between those 2 numbers? This one is much more complicated. Maybe I should give you a 3rd number:

4, 9 and 16

Do you see it:

4 = 22
9 = 32
16 = 42

I don't know for you, but when I see numbers 4 and 9 together, the relation between those numbers jumps directly into my face. I know there is a link between them. It is important to see links between numbers because this is how you are going to see them in action when playing a game.

I don't know if there is any way to train yourself seeing those relations. I think the more you play with numbers the more likely you should see those relation.

Structural Numbers

Now lets get to the main subject. Why all those numbers matters?

Let's diverge a little bit, I don't consider myself to be an artist. Yet if you give me paint and a canva, I will be able to pain you something. But one thing for sure, it will never be a masterpiece that will be exposed in a museum.

Board games are the same. Anybody can make a working game, but few of them are actually going to be masterpieces. My goal is to design masterpieces rather than making a popular game that will hit kick starter and be forgotten 2 years later. One of the ways to make a game looks like a masterpiece is through the use of structural numbers.

Structural numbers is a series of numbers that are recurrent through the design of a game. It can normally based on one or two numbers or on a part of a number sequence. For example, in my game fallen kingdoms, the number 3 is over used helped with the number 6. For another design in progress, I use the fibonnacci sequence everywhere (2-3-5-8-13).

The appearance of those numbers can be anywhere in the game. Basically, it could be numbers placed on components like unit strength, or it could be odds of dice or cards, or it could be event component distribution. Here are some example for a game in design where I wanted to use Fibonnaci all the way. As the design progressed, the relation with fibonnaci increased by itself.

  • Players will have heroes with strength rated with 2,3,5,8. The idea of using fibonnaci here is that each new hero is 60% stronger than the previous one. The other interesting aspect not currently used in my design is when combining strength. If you want players to combine units to arrive to ties, fibbonnaci is excellent since the sum of the current and previous number equals the next number ( 2+3=5, 3+5=8, 5+8=13)
  • It's a 6 players game, players need 3 VP to win, how many VP tokens to I need? 13, because in the worst case possible all 6 players will have 2 VP and when a 3rd one is given the game will end. So I need 2 x 6 + 1 = 13 VP tokens. So the fibonacci number used here are 2 and 5. Same thing for artifacts, I had 6 different types of 2 copies each + 1 dummy item for a total of 13. Since on the 6P board there are 8 territories where artifacts are going to be placed, there will be 5 unused artifacts.
  • The 6 player board used a fibonnaci distribution too. The board is made of various rings where the more you reach the center, lower the number of territories there is on the ring. So the first ring has 3 territories, the 2nd one had 5 and the 3rd one has 8 and the board has an octogonal shape.
  • The dices have special faces: 3 of them has hearts, 1 of them has a star, and 2 of them has either heart or stars (player choses). 1-2-3 is fibonacci so far. But also the maximum number of hearts a player can roll is 5 (3+2) while the maximum number of stars the player can roll is 3 ( 1+2) so again, fibonnaci repeat itself.
  • Each player had a set of cards, how many cards should each player have? I know that for poker size cards, 9 cards fit on a page. So I decided to use 8 cards made of 4 unique cards in 2 copies and use the 9th card as faction description cards. I could have used 5+3 cards, but I wanted more than 2 different types of cards. Another solution was to use 3+5+8 = 16 where smaller cards could fit on a page as a 4x4 grid for 16 cards. But again 8 copies of the same card was too big for no good reasons in my game. But for another game it could have worked fine.

Why put so much attention on details like that? First, it proves that a lot of thought has put into your game making it more "Designed" like a designer could design a room or a toothbrush. The second reason it to fix-up hidden interactions you cannot see. Structural numbers and number sequences are like security nets. Board games are very complex and there is a huge amount of interaction what you might not be able to see even after many playtests. But using the right numbers, you somewhat make sure that the interactions you cannot see are not broken. If makes your game feel like if those mechanics or numbers belonged together because they have a relation with each other. Which in the end makes your game less fragile.

You might often hear that certain things like rooms, toothbrush or clothes were made by a designer. What makes the distinction between regular creations and "designed" creations is the amount of thought put into the creation. Anymody could make a model for a plastic bucket or a shirt, but only the bucket or the shirt that was made by the designer will be the most optimal, convenient and beautiful solution due to the amount of thought placed into the creation.

Board games are the same, you don't want to only design a game that works. You want a cohesion between all the elements of your game and by putting more thoughts into your game, you are more likely to end up with a masterpiece.

The notion of cohesion could be related to the rule of "Echo" from Cristopher Alexander where each element of a design must have a relation with each other like if a thread was passing through each of them. For example, in interiors design, if you decide to use a swirl in your floor tiles of your kitchen, you'll want also to use a swirl on your backsplash and your door knobs. So the swirl pattern needs to reappear multiple times but most importantly no other pattern must be used. Structural numbers in games are like that swirl that you see repeat itself in the whole room.

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