# My Article on Structural Numbers

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larienna
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Joined: 07/28/2008

I have just finished writing my article on structural numbers which is probably one of my primary obsession in game design. Here is the link:

http://bgd.lariennalibrary.com/index.php?n=DesignArticle.Article-Stuctur...

Enjoy and have fun!

X3M
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Joined: 10/28/2013
Nice article. But it seems

Nice article.
But it seems rather short. But after looking a bit further, I found the link. Perhaps making a sub menu of all the articles about numbers once you add more pages?

I too am fixated on numbers within games.
Just so happens, the number 3 is used a lot together with 6 in my game as well :).

Where your favourites are the numbers of fibonnaci.
Mine would be the triangular and the square numbers.

This because they are the most common used in wargames. With or without people knowing.
These 2 row of numbers are also the reason why wargames with different unit strengths are harder to balance then other games. Designers balance with the help of square numbers. While the first battles often follow the triangular numbers.

The main factors in balancing these games are the maximum number of units. And the build up during the battle. For the math of this, I could fill in pages. But only if someone is interested.

larienna
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Joined: 07/28/2008
I do love fibonacci, and 3 +

I do love fibonacci, and 3 + 6. But still it depends on the game.

For example, in an adventure game, I wanted to have physical and mental stat for the characters which forced me to use the number 4. Starting from this, It made the game progress differently.

When I was younger I love the number 4 because of the 4 elements (earth, Fire, Water, Wind) but when I found that a 5 element relationship offers much more possibilities, I somewhat abandonned the number for and used 3 and 5.

lewpuls
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Joined: 04/04/2009
No fixation here

If your game is intended to be "about math", as opposed to a people or story game, then I can see a fixation on numbers. I don't have that fixation at all.

Yes, "You want a cohesion between all the elements of your game", but this fixation on numbers contributes nothing to that cohesion, as far as I can see. However, if you feel it helps, then it helps you as a designer whether it actually improves the design or not.

*Shrug*

X3M
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Joined: 10/28/2013
It isn't a game about math, it is the math behind a game

Actually, having a clear view on the numbers does help designing a game. It greatly helps balancing. And all the numbers do interact with each other.

Finding this interaction between the numbers was the only way. (well, in my game the least)

So I do understand where Larienna comes from.

questccg
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Joined: 04/16/2011
Interesting article

The article was very informative especially for the size (it was an easy read - because it wasn't too long). Attention spans is a subject for another thread! ;)

What I really liked in the article was the 60% rule... That was very informative.

I don't think I intend to make my games match with numbers but in "Tradewars - Homeworld", I wanted resources to be values between 1 and 5 ONLY. Part of the reasoning was because in EXPANSIONS, I could add cards with values of 6 to 9! Again because of card design, I would like to have numbers LESS than 10.

I often like to do that: limit statistics to under 10. Like I said in some ways it's because of design (graphics), 10 and above means that single digit numbers will appear smaller using the 10 Font size. And just generally, I like to keep statistic below 10.

So I think my designs also have a *mathematical* component: namely all stats should be less than 10!

But I think "Tradewars - Homeworld" is more than just pure stats and strategy. There is dice rolling and Tactic cards which can lead to *game stories*...

What I mean by this is players will talk about a game EVEN AFTER it is done. Those two (2) aspects of my game, I believe yield unpredictable results altering the outcome of the game.

lewpuls
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Joined: 04/04/2009
X3M, watch/listen to this

X3M, watch/listen to this video: "Math, People, Story: three kinds of games" https://www.youtube.com/watch?v=8680nw61VWM That's the "about math" I was talking about.

rene.shible
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Joined: 01/30/2014
Interesting article, worth

Interesting article, worth reading and thinking about. Although I don't agree with all of the assertions made here, one specific paragraph describes very well the importance of structured elements in game design - copied and pasted from the op article;

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.

Very noteworthy!

tuism
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Joined: 01/14/2013
Very interesting concept! I

Very interesting concept!

I can see the advantages of using numbers that lock with each other to arrive at mechanically interesting interactions, but I don't understand how picking a bunch of numbers, whether random or "two of the previous ones add up to the next" would strictly equate to "ensuring balance"...

Maybe it's cos I'm not mathematically inclined myself, but I find the above two concepts to be a big stretch?

In Magic, there's a certain power/cost ratio that's often obeyed (and disobeyed). In Netrunner, certain numbers come up again and again (8 is the cost of most ice oncisdered big, for example), but I wouldn't be able to say that a certain set "ensures balance". How do you practically demonstrate that it does?

X3M
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Joined: 10/28/2013
What numbers mean to me

@ Lewpuls
I have seen your video. Will watch the rest. Although english is not my first language.
Further, board game design is not my profesion. I only have 1 design as a hobby.

You mean there is a distinct difference between "just" numbers (value's) and numbers with a meaning?
And I agree to that.

I think that numbers, visible or not to players:
Always should have a meaning in the design, a positive "and" negative one.
Always have interaction with each other.
And always have a meaning to the players.

Well, my game is entirely based on those 3.
A number on itself has no meaning.
And I reached my list of numbers after gathering data and creating formula's for a balanced game.
The only reason that I do play testing with my friends is to make sure they understand how to play. (Thankgoodness they do)

It was later on that I discovered that I was simply using the triangle and square numbers.

--------------------------

@Tuism

A set of numbers doesn't help balance. Unless you know how to use the set of numbers in a balance.

I have explained some stuff about my balance in this old thread:
http://www.bgdf.com/forum/game-creation/mechanics/wargame-based-rts-mech...

Search for the part about Armor and Damage.

lewpuls
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Joined: 04/04/2009
Just to stir the pot

Just to stir the pot ;-) What is the difference between this fixation on numbers behind the game, and numerology? (I'm assuming that you recognize that numerology is balderdash, just as astrology is.)

X3M
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Joined: 10/28/2013
Yes it is balderdash if it is

Yes it is balderdash if it is numerology.
If it is fixation on numbers, it might have good reasons.

***

http://en.wikipedia.org/wiki/Numerology
See: "Numerology" in science
Scientific theories are sometimes labeled "numerology" if their primary inspiration appears to be a set of patterns rather than scientific observations.

Numerology in gaming
Some players apply methods that are sometimes called numerological in games which involve numbers but no skill, such as bingo, roulette, keno, or lotteries. Although no strategy can be applied to increase odds in such games, players may employ "lucky numbers" to find what they think will help them.

***

If designing a board is considered to be a science. Then there are indeed designers who aply numerology. Simply choosing numbers they like. But there are also who search for the best numbers and have gathered data for a reason why to use those numbers.

It is up to Larienna to show us why she used the fabinaci numbers. Is there a strategic design reason?

------------------------------

The numbers I use and come from testing, after the test they where chosen. Thus I have strategic design reasons:

3600: easy dividable by a whole set of numbers. If an unit costs X then there is Y allowed on the map. X * Y = 3600. No more, no less. If Y is not a round number, then X is simply not allowed as price.

3: balance reasons. This is the Health/Damage ratio that I use for each unit. If an unit has +1 range, then the price for the damage side is +33%, or 10 compared to 30. Since 30 is a default. This results in 40. The same goes for the speed of an unit. The Rifle Infantry has 2 speed and 2 range, thus + 67% for each the damage and armor side. Both 50, a total of 100. That is a really nice starting number for players to focus on. It is also widely used in all kind of games. Thus there you could say, the science that I used had as goal, the chosen number 100.

8: Also a Health/Damage ratio that I could use with ease. Here the default is 40 and each range or speed adds 12,5% or 5 compared to 40. So if I use this set, the default is 40. Here a Rifle Infantry would still cost 100 with 2 speed and 2 range. Simply having 8 Health instead of 3.

3 and 8, are chosen from a list ranging from 2 to 15. 15 is usable too. But the game would take 5 times longer then using 3.

6: Dice, only reason. There was a time I used this number for Health, a lot of known RTS have this ratio. Dividable by 1, 2, 3 and 6. But for my board game it had imbalance. Now I use this number to determine Agility, Accuracy and Miss/Hit/Critical Hit. Still a good number to use. Hexagons have 6 sides. And the regions that we play on have 6 parts as well.

9: Maximum Range. More would require a bigger board.

50: True default, no matter what Health/Damage ratio I choose. All is based on 50. People like 50. It also gives design freedom.

The Armor and Damage value's compared to the Costs:
Since I wanted 1 RPS system that could be expanded infinetaly with only numbers and the effects would be lineair. I thought of taking the cost value of either Armor or Damage. Dividing it by 50. Then taking the square number. Since the effects are exponential but costs are lineair. The positive effects are lineair and the negative effects are lineair. Thus having twice the costs. Might mean the unit is twice as effective in combat. Or has only half the effect in combat.

Not just chosen numbers. They have a strategic design reason.

larienna
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Joined: 07/28/2008
Quote: I wanted resources to

Quote:
I wanted resources to be values between 1 and 5 ONLY

I also like using numbers between 1 ad 5 but for another reason. Makes it easy to modify and use D6 for rule modifications or optional variants.

Quote:
watch/listen to this video: "Math, People, Story: three kinds of games"

I'll Check it out when I get home

Quote:
In Magic, there's a certain power/cost ratio that's often obeyed (and disobeyed). In Netrunner, certain numbers come up again and again (8 is the cost of most ice oncisdered big, for example), but I wouldn't be able to say that a certain set "ensures balance". How do you practically demonstrate that it does?

Numbers sequences does not magically balance your game. It creates a structure to your game that makes it easier to balance. It also impose certain restrictions on which value is allowed making it easier to make a choice. Else sky is the limit.

Quote:
I think that numbers, visible or not to players:
Always should have a meaning in the design, a positive "and" negative one.
Always have interaction with each other.
And always have a meaning to the players.

I like the idea that a number have a meaning. It is the chosen one! (^_^)