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Subject: Role of mathematics in boardgame design rss

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Marcus Kielly
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I've seen several reviewers/commentators state that mathematics plays a prominent role in boardgame design. I'd like to get some feedback from the designers on the BGG on this matter. Is a good understanding of maths required, preferable or optional? How has maths helped you to design a game? What fields of mathematics have you used in your design process (I'm guessing probability is an obvious one...).
Any feedback is greatly appreciated!
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Kai Bettzieche
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Most of my games are dicegames, so, yes, probability is the field I used.
(There is one exception: Generic Racing Game is all about vector movement)
Whack & Slaughter e.g. is a miniature skirmish game. You may move your fighter according to a strategy you have thought up. The attacks as well as defending is resolved by rolling a number of dice.
To give a player a better understanding of his chances, I included a table with the according probabilities in the core rules.

Understanding probability surely helps a lot, but you can as well compensate that knowledge with experience as well as lots of playtesting ..
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Asger Harding Granerud
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I've designed a Football/Soccer game called [Mental]-Football (under consideration by a publisher) and probabilities have played a part in the design, but not a prominent one.
At one point I switched from to d6/d8, without it really affecting the game play.

The one place where I have used very simple probability calculations is to ensure that the chances of a random long shot scoring a goal, are suitably low. This was done to ensure that the dominant strategy didn't become simply shooting as soon as you had a chance, which would be rather boring and bland...
Now a well played offence (difficult!) probably has a 5 times larger chance of scoring a goal, and hence the odds are heavily in favour of the person that takes advantage of gaining ball possession, rather than squandering it.

But none of this has involved heavy spread sheet calculations, it is simple head maths

Asger

 
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Thomas Rushing
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In ARC you play a character called an Aeon who has 4 abilities. The 4 abilities are as follows:

1 - Rift
2 - Draw a card
4 - A special ability different on each character.

3 - Attack

These abilities require you to have X amount of "ARC" before you can use them.
In order to make the game fair we had to make sure that the first 3 abilities listed had the same cost basis for each character.
Reason: If your character had a lower cost basis for these abilities you had a higher % of being able to use them which caused you to win more often.

The last ability was used mathematically to cause a character to be more or less aggressive. On characters we wanted to focus more on deck construction and craftier ways of winning we made it require more "ARC" to attack than those who we wanted to be more aggressive with the character itself.

We also put a cap on how many times per turn you can use the abilities. Allowing a player to only use 2 abilities per turn and never allowing the same ability to be used more than once per turn forces players to make tough decisions each turn. It also clamps down their ability to "Rift" (moving from one board space to another) and use 2 abilities per turn which gives your opponent a way to run away. Without this math cap aggressive characters would be much stronger.

This is just some of the math behind 1 of 7 card types in the game. We are not mathematicians and didn't sit down and go oh lets mathematically build this character like this, however, through trial and error we found there does need to be some strong symmetrical math as a foundation almost every game otherwise the game will be very unbalanced and unfair.
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Carl Nyberg
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I use math in game design. For example, if the chances of being attacked in the forest is 1/3, what are the chances of being attacked if one visits the forest 4 times? These sorts of things helps me figure out how much stuff should cost, how powerful things will be, etc. while keeping the game fair.
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Andrew Rowse
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I think it's essential to have a good grasp of maths, especially probability. I've seen quite a few Kickstarter games recently that demonstrate a complete lack of understanding regarding probability, and that almost always translates to a bad game.

EDIT - The alternative is relying on extra playtesting - finding problems without really understanding what causes them. I'm sure that would work for some people, and could result in a great game regardless. But it seems very inefficient to me!
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Tommy Occhipinti
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I'm a math professor and amateur game designer, and I'd say I don't use math very often. I certainly compute the occasional probability, and I'm more likely to use graphs like these to check for balancing and so forth:






but overall, if you can compute the numbers that you are balancing in game design, the design is probably too simple and solvable.

I think economics training has had a lot more impact. The ability to see what effect changes to rules will have on the choices players will make is the most important part of game design. A lot of games are designed with the implicit assumption that players will play it the way "it is supposed to be played." A few courses in economics will cure that idea quickly!
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Andrew Rowse
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delirimouse wrote:
I'm a math professor and amateur game designer, and I'd say I don't use math very often.

Do you think it's likely that, as a maths professor, you instinctively apply maths that other people would have to actively think about?
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Bobby Ramsey
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KAndrw wrote:
delirimouse wrote:
I'm a math professor and amateur game designer, and I'd say I don't use math very often.

Do you think it's likely that, as a maths professor, you instinctively apply maths that other people would have to actively think about?

Without a doubt.
 
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Tommy Occhipinti
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AnyMouse wrote:
KAndrw wrote:
delirimouse wrote:
I'm a math professor and amateur game designer, and I'd say I don't use math very often.

Do you think it's likely that, as a maths professor, you instinctively apply maths that other people would have to actively think about?

Without a doubt.

Yeah, I think in one draft of my post there was even a sentence to that effect. Logical thinking is a huge benefit to game design, to be sure. I was mostly trying to say that I have very rarely used specific technical knowledge.

Occasionally it is useful to solve questions like "What is the optimal ratio of Dukes and Duchys to buy in Dominion?" which is essentially a multivariable calculus problem, or "If I throw two 8 sided dice and three 6 sided dice, what is the probably the total of the 8 sided dice is higher than the total of the 6 sided dice?" which is an ugly probability problem.

Both of these problems, though, you could answer with some program like Excel rather than by finding an exact answer by hand. In this specific case, the first problem is not hard to do by hand, but an exact answer to the second is certainly not worth the effort, and I'd just do 1000 trials to find an approximation.
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Jason Fordham
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Perfect thread.

I am seeking a mathematician to test my relatively simple card game.

The game is currently being tested by fifteen testing groups (using prototype decks that I shipped out,) but I would very much like a numbers-only analysis.

If interested, GeekMail me, I will link you to the PNP file, and we'll talk about your offerings and fee, etc.

Thanks

 
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Dave Elliot
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Interestingly enough, I just saw this quote today from an interview Michael Mindes (Tasty Minstrel Games) did with Bruno Faidutti:

http://playtmg.com/blogs/designer-artist-interviews/4147492-...

Quote:
Do you think anything particular about your past helps you as a game designer?

I think that the fact that I’m a great reader, and like to analyze and dissect novels when I read them, was of a great help. Designing a game is very much like writing a novel – except that it needs far less time and actual work. The fact that I was not bad at maths in high school, even when I didn’t learn more maths afterwards, might be of some help here and there, for reckoning odds of dice or cards, but I think it’s far less useful.

Most people tend to think that designing games requires a logical and mathematical thought, I think they are wrong and a strong literary feel and culture is much more useful.


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Filip W.
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Math isn't required - you could create a good game without knowing any math at all. But as with all tools it makes game creation easier by letting you analyze your game instead of doing it the trial-and-error way. On the other hand, you could say that about any science and game design: you could use psychology to analyze player reactions, anthropology to analyze game types and their impact, geology to create maps and strata etc.

All knowledge you bring with you will make your job easier, not just math.
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Marcus Kielly
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Just want to say a quick thanks to everyone that has replied so far.
I used to work in video games (as an artist/designer) and one of the aspects I've found tricky to resolve is balancing mechanics that are either not directly related or easily modelled numerically.

For example, it's relatively straightforward to balance out ratios of speed, power, attack and defense since they equate to numeric values. If we take a realtime game like Mario, however, and throw in an effect like reversed controllers, it's hard to work out the impact of this numerically but it has a definite impact on the player's ability to "solve" the game.

Would you just iron this out through testing, or have you got any neat mathematical tricks you could use to model this type of effect?

 
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Tuomas Korppi
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I have a PhD in mathematics and little game designing experience as a hobby. My opinion is that anything that can be actually calculated can be resolved with solo play testing, so mathematics does not play a big role.

The difficult part in game design is to design games that allow rich development of strategies and hold together with strategically high level of play. Here the key in designing is simply to master the game well, so hands-on experience with the game is the most needed skill.

One application of "mathematics" is the design of two-player abstracts. When one designs an abstract, one must make sure that mathematical "stock strategies" such as mirroring the other player's moves are not efficient.
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Vince Lupo
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I think that some designers come at it very mathematically. Reiner Knizia for example.


And in my designs so far (no games public yet) I've had many concerns about which numbers to use for certain things. I think I determined later to try to just throw out some numbers that seemed right and playtest them.

I guess it's like cooking or something.
 
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Vince Lupo
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Punainen Nörtti wrote:
I have a PhD in mathematics and little game designing experience as a hobby. My opinion is that anything that can be actually calculated can be resolved with solo play testing, so mathematics does not play a big role.

The difficult part in game design is to design games that allow rich development of strategies and hold together with strategically high level of play. Here the key in designing is simply to master the game well, so hands-on experience with the game is the most needed skill.

One application of "mathematics" is the design of two-player abstracts. When one designs an abstract, one must make sure that mathematical "stock strategies" such as mirroring the other player's moves are not efficient.


My friend and I broke the small two player blokus one day by having him try mirroring my every play. We determined that unless you play a certain set of pieces that block a part of the middle of the board, the second player can just mirror. Very interesting.

In Dominion, players can try copying each other at the beginning but as soon as the first shuffle happens, things start to vary from player to player.
 
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B C Z
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I don't think that higher mathematics such as calculus and trig are required, but I think a solid understanding of the following really helps:
- Probability
- Combinations and Permutations
- Set Theory
- The basics: Addition / Subtraction / etc

These are by no means the only math you'd apply to game design (and playtesting/breaking a game), but are a great starting point.
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Vince Lupo
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byronczimmer wrote:
I don't think that higher mathematics such as calculus and trig are required, but I think a solid understanding of the following really helps:
- Probability
- Combinations and Permutations
- Set Theory
- The basics: Addition / Subtraction / etc

These are by no means the only math you'd apply to game design (and playtesting/breaking a game), but are a great starting point.

* Multiplication and Division are definitely present in 7 Wonders and others.
 
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Neo42 wrote:
* Multiplication and Division are definitely present in 7
Wonders and others.

Part of 'etc' in 'the basics'.
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Tuomas Korppi
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Neo42 wrote:

My friend and I broke the small two player blokus one day by having him try mirroring my every play. We determined that unless you play a certain set of pieces that block a part of the middle of the board, the second player can just mirror. Very interesting.

Fortunately, in Blokus Duo, the mirror can be easily prevented by house ruling. For example as follows:

First the second player chooses his start piece. Then the first player starts the game with some other piece than the second player's start piece. Then the second player plays his start piece. Then the game proceeds normally.

In the above variant, the second player chooses his start piece, because the game has a first-player advantage, and it's not good design to increase that advantage by letting the first player choose first.
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John "Omega" Williams
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Conversely you will find that approaching what sometimes feels like 75% of the BGGers have less than zero comprehension of how dice work.
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Ben Smith
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symbioid wrote:
Interestingly enough, I just saw this quote today from an interview Michael Mindes (Tasty Minstrel Games) did with Bruno Faidutti:

Fascinating viewpoint, thanks for sharing the quote!

I'd say it definitely depends on the thrust of your game and what the mechanics of it are. Games like Diplomacy, for instance, don't need any fancy math since the real mechanics are all in player discussion and deal-making. [edit: I'm sure someone will find ways to apply fancy to math to the game now that I have said this...]

I'd say that for balancing a card game like Race for the Galaxy, though, it's pretty important to calculate the effects of adding new cards in expansions, since adding new cards effects a lot. What does adding 20 new cards do to the player's chance of drawing a specific card? Do the new cards combine with previous cards in a way that could give surprising/unwanted bonuses? And if so, how often is that likely to happen?
I think some math could help a lot in balancing a game like that.
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B C Z
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bugeeker wrote:
I'd say it definitely depends on the thrust of your game and what the mechanics of it are. Games like Diplomacy, for instance, don't need any fancy math since the real mechanics are all in player discussion and deal-making. [edit: I'm sure someone will find ways to apply fancy to math to the game now that I have said this...]

The mechanics are only partially in the negotiation. You are negotiating about control of territories and movement of pieces, all of which functionally exist on a node/edge map with some specific rules about how the pieces move from node to node along the edges.

The map of Europe is not 100% accurate (it has various modifications from 1901 to 1913 or so), and was probably tweaked for game play reasons.
 
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Ben Pinchback
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Basic probability is easily what comes up the most for me. Usually it's in figuring out if a buff is too powerful based on the probability of card draws or dice rolls. Aka like "over x turns how much more money would draw 3 keep 2 make a player vs draw 2 keep 2"
I ran quite a bit of these problems/simulations when we were designing Fleet.

Math is certainly a tool, but I think the single greatest thing that helps me in game design is playing a crapton of games. The more you play, the more you understand what makes a game great.

Also to the point of expecting players to play optimally, we've been learning a lot about letting players make mistakes and even giving them more chances to do so.
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