Jack Bennett
United States Rougemont North Carolina
Play. Always.

As I've perused these forums for the past years, I've noticed quite a few questions that pop up when it comes to the math of someone's game. Probability calculations, usually, but other things come up.
I am very much NOT of the opinion that a good grasp of mathematics necessarily leads to a good game. You aren't missing some secret formula that will allow you to totally balance your game, if you were just smart enough to figure out the math. But I DO think math plays a role in most games, and that are simple concepts you can learn that might help.
To that end, then, I've been considering writing a series of columns about probability, statistics, and other mathy things as they relate specifically to the design of games.
There are a few topics I know I could talk about. And there are plenty of broader aspects that might be worth mentioning. But I first want to bring it to the designers.
So here are my questions:
1) Is this something you think would be helpful? Would you be interested in this?
2) What would want me to cover? What would be the most helpful for you when it comes to math and game design? What topics would you want discussed?

Justin R
United States New York

I am one of the guys that answers the probability questions, and wanted to congratulate you on your noble effort, but also perhaps respond to one of your questions on behalf of the people without a math background.
I think that something that explains the concepts will only be useful to the people that truly want to learn the underlying math. Not sure how many designers fit into that category.
One thing that might be helpful are sections after the subject matter that apply the information in certain readily adaptable ways. For example, you might end a probability discussion with a description of how different gaming mechanisms affect probability in different wayse.g., contrasting switching from a d10 to a d6 vs switching from d10 to 2d10. That way a designer can get hints at how to finetune his outcomes without having to reinvent the wheel.

Aaron Bohm
United States Appleton Wisconsin

Math is in most every game, whether you realize it or not. When designing a game, I feel you can either play test it many, many times to work it out so the actions and sides feel balanced or you can use math to skip a lot of that.
Also, the more complex the equations get, the more "hidden" the math seems. Take Trajan for example. I have no idea if Feld actually did the calculations but essentially there is X victory points or at least the probability of X victory points in any action you do and the probability of hitting those action points based on where your mancala dishes are at any given time. However, while playing it you think of it as "the shipping strategy" and not as a spreadsheet based, "if I take shipping I have 1 out of X chance to get this card, shipping means I would then get X points..." etc.
Personally, I like probability and predictability which, in both cases, I find an actually graph the most helpful. This tends to happen when multiple things are happening to effect the outcome, such as in a deck builder (EX. I have X total cards with Y # of Card A and Z # of card B, if so what is the probability of me getting a total of A and/or B, etc.)
At the very least, it's a nice fall back for working out card costs or which card to restrict etc.

Lucas Smith
Germany Munich

Cool idea, do that!!
Maybe it would be cool, to analyse the maths behind a common game to give people an example! And probably a style which is understandable using plenty examples is good!

Jack Bennett
United States Rougemont North Carolina
Play. Always.

Quote: I am one of the guys that answers the probability questions, and wanted to congratulate you on your noble effort, but also perhaps respond to one of your questions on behalf of the people without a math background.
I think that something that explains the concepts will only be useful to the people that truly want to learn the underlying math. Not sure how many designers fit into that category.
One thing that might be helpful are sections after the subject matter that apply the information in certain readily adaptable ways. For example, you might end a probability discussion with a description of how different gaming mechanisms affect probability in different wayse.g., contrasting switching from a d10 to a d6 vs switching from d10 to 2d10. That way a designer can get hints at how to finetune his outcomes without having to reinvent the wheel.
Most definitely!
The intent of these would be to give very lowlevel explanations. Just enough so that if people actually want to learn the math, there's something to learn, but also just to help people get a sense of how probability works in general, and how it affects games.
The idea would be to take a popular game or two, probably, and talk about different aspects. I agree that teaching through examples is the best way. And I don't really think it's always useful to sit there and calculate odds all the time. But humans are so bad at probability in general, that I hope I can help people see some overall aspects that would help them approach game design better.
I've just seen the answer to "What are your chances of rolling at least one six on two dice" be "2/6" enough that I want to see if I can give some general knowledge.
Also, if there are you or other people who would like to contribute, or proofread, I'm sure I'll need it!



That sounds fantastic, whether intentional or not, the math of a game will always be there. It's significant to keep track of it at the very least.



I would also find that useful. I have some background in math, but in game design it's difficult to know the math of every situation.
I try to use math to balance a game as much as possible between playtests.

Hector Garciduenas
Mexico

I would absolutely love something like this. If I can request something specific, I'd love to read about balancing games. As a crude example, how to balance point cost for Warhammerlike systems where you buy your roster and balancing ingame cost for resources.
I have a solid math background being an engineer and on probabilities and statistics having take several reliability engineer bing courses so maybe this topic wouldn't be too much if interest to others so if you could at least recommend some good books I could reference on these topics I would much appreciate it.

Steve Cates
United States Visalia California

Cool, I'd like to see this.
I'm a math guy but my background is more engineering and physics. I'm sort of self taught with probability and statistics. I'd like to see some examples of the binomial and hyper geometric distributions, fascinating stuff!

Jack Bennett
United States Rougemont North Carolina
Play. Always.

ironcates wrote: Cool, I'd like to see this.
I'm a math guy but my background is more engineering and physics. I'm sort of self taught with probability and statistics. I'd like to see some examples of the binomial and hyper geometric distributions, fascinating stuff!
Great! Definitely on the list.
Any other situations game designers have found themselves where they ran into a mathshaped wall? If there are common themes are problem areas, I can look at that as examples.

Steve Cates
United States Visalia California

One thing that I've figured out before that was quite a mathy challenge was determining strength of hands as in poker but with more 5 suits and 6 cards in hand adding in 3 pair and 23 of a kind 5 card straight/flush. Not sure it's a great game, but the idea could be useful for other designs doing that sort of calculation.

Rocco Privetera
United States New York

I love this concept. Here are things I'd love to see:
 regular columns of interest  discussions about specific games (how does the math work in game x)  guest columns  interviews with game creators  questions answered
Math to me is an important part of the underpinning in nearly all games.

Mark J
United States Monroe Michigan

I suspect people would be more interested if you replied to specific questions rather than gave rambling lectures. I usually find I get interested in a particular mathematical question when the subject comes up for some reason. Though I could certainly see room for level 101 rambling lectures to get people started, so they know what questions to ask.
Just rambling myself.

Mark J
United States Monroe Michigan

Never Knows Best wrote: However, while playing it you think of it as "the shipping strategy" and not as a spreadsheet based, "if I take shipping I have 1 out of X chance to get this card, shipping means I would then get X points..." etc.
If I like a game enough to play it many times, I usually DO end up calculating probabilities.
I recall one game, Freedom in the Galaxy, where instead of rolling dice to see if something you were trying to do  a "mission"  succeeded, you had to draw some number of cards from a deck, the number of cards being modified by all sorts of factors. Each card had a set of codes on it, with each code representing a type of mission. If your mission code came up, the mission succeeded, otherwise it failed. Like say you tried mission "Assassination". That was mission code "A". There'd be a bunch of factors to say how many cards you got to draw. Say it came to, whatever, 5. So you'd draw 5 cards, and if at least one of those was an "A", then the assassination attempt was successful.
Anyway, I ended up counting how many cards had each mission code, and making a big chart with a row for each mission code and a column for the number of cards, and then calculating the probability of success for each. It was a bunch of arithmetic in those prehomecomputer days.

Kristian JÃ¤rventaus
Finland Loviisa

I'd really like to read something about things beyond simple probabilities. By simple probabilities I mean calculations that you can do that tell you how probable a dice result is or a card hand, those are pretty easy if you know the maths or know some app... But beyond that, methods of figuring out what happens to those probabilities in a game. Like a card game where you choose what cards to keep and what to discard and replace with newly drawn cards: a poker hand is not a simple probability in this sense, it's the result of a strategy by the player (though you can still model all the possible spaces a poker hand can exist in). Basically, the problem the poster in this thread: http://boardgamegeek.com/thread/1063838/gameyahtzeewithca... has.

John "Omega" Williams
United States Kentwood Michigan

Id like to see designers and especially players better educated in how card and especially dice probabilities really work.
When you have someone arguing that a d10 (or any dice) is imbalanced/skewed because its average is 5.5. Something seriously needs to be done.

Kristian JÃ¤rventaus
Finland Loviisa

Well, we could always change it so that a d10 (with a 0) is 09 so we get... wait, damn, that has an average 4.5 D:

Mark J
United States Monroe Michigan

I had a math teacher many years ago who said that gamblers don't believe in probability: they believe in luck.

Mark J
United States Monroe Michigan

This brings to mind the story of the mathematician who was caught trying to smuggle a bomb onto a plane. Of course the security people dragged him off to question him. He protested that he was not trying to blow up the plane. In fact he was trying to protect the plane. "After all," he said, "Have you ever calculated what the odds are against there being someone on any given plane who is carrying a bomb? So imagine what the odds must be against there being TWO people on the plane with a bomb!"

Andreas Pelikan
Austria Vienna

saneperson wrote: ... So imagine what the odds must be against there being TWO people on the plane with a bomb!" Excellent topic for the OP: a priori (before the fact) versus a posteriori (after the fact) probabilities.



Naeddyr wrote: I'd really like to read something about things beyond simple probabilities. By simple probabilities I mean calculations that you can do that tell you how probable a dice result is or a card hand, those are pretty easy if you know the maths or know some app... But beyond that, methods of figuring out what happens to those probabilities in a game. Like a card game where you choose what cards to keep and what to discard and replace with newly drawn cards: a poker hand is not a simple probability in this sense, it's the result of a strategy by the player (though you can still model all the possible spaces a poker hand can exist in). Basically, the problem the poster in this thread: http://boardgamegeek.com/thread/1063838/gameyahtzeewithca... has.
Yes, i think it's more than simple probability. I like to: 1) learn basic probability related to design of game. 2) know how card distribution (numbers of cards, suits), board (spaces, positions..) is defined by math. Thanks you



pusherman42 wrote: (...) I've been considering writing a series of columns about probability, statistics, and other mathy things as they relate specifically to the design of games.
There are a few topics I know I could talk about. And there are plenty of broader aspects that might be worth mentioning. But I first want to bring it to the designers.
So here are my questions:
1) Is this something you think would be helpful? Would you be interested in this?
2) What would want me to cover? What would be the most helpful for you when it comes to math and game design? What topics would you want discussed?
Omega2064 wrote: Id like to see designers and especially players better educated in how card and especially dice probabilities really work. I agree.
In general, I think that having a single bgg repository to point people to for all things about probability and statistics, from the simplest formulas to any advanced topics Jack and others may include, maybe centered on dice / cards / chits / whatever randomising mechanic one can think of, would be of great benefit to many. (supposing there isn't already any such repository: I'm not aware of any)
Apart from that, I'd like to see some important concepts explained and "hammered home" once and for all, such as:
1)
Puschl wrote: a priori (before the fact) versus a posteriori (after the fact) probabilities.
1b) Somewhat related to the one above: the limitations of the expected value as a balancing tool for games, and alternative approaches (likely based on confidence levels or similar ideas).
1b) Again related: what the Law of Large Numbers say, and what it does not guarantee, especially in a game that has you rolling five dice for twelve turns or similar scenarios.
2) What random really means.
2b) What are the real differences between apparently different randomising mechanisms (for instance, the impact of "resetting" the odds periodically vs not resetting them).
3) Probably others that I can't think of at the moment.
In the more general logic / maths field, I'd like to see a discussion of how symmetry affects games positevely or negatively, but that's perhaps a bit too far from probability / statistics.

Mark J
United States Monroe Michigan

Puschl wrote: saneperson wrote: ... So imagine what the odds must be against there being TWO people on the plane with a bomb!" Excellent topic for the OP: a priori (before the fact) versus a posteriori (after the fact) probabilities.
In real life, there's a common misunderstanding about probability that goes like this: The chance of rolling a "1" four times in a row is very small. So if we've just seen a "1" come up three times, it's very unlikely that it will come up again. Gamblers often rely on this flawed idea, so, for example, if they see that the roulette wheel has come up black three times in a row, they'll bet on red.
The problem with this idea is that it confuses the probability of a given combination coming up BEFORE we have rolled any dice, with the probability that a given combination will come up AFTER we have already rolled part of that combination.
The probability that you will roll a 1 on a fair die is 1/6. So the probability that you will roll 2 1's in a row is 1/6 x 1/6 = 1/36. But the probability that you will roll 2 1's in a row, GIVEN that you have already rolled a 1, is just the probability that the next roll will be a 1, that is, 1/6. The previous rolls have nothing to do with future rolls. As one clever person put it, Lady Luck has a very bad memory.
If your intuition doesn't grasp this, consider this case: What is the probability that, if you roll two dice, both will come up 1? That's 1/36, right? Okay, now, given that you have just rolled one die, you are looking at it sitting there on the table and it is a 1, what is the probability that you will roll at least one 1? Clearly it is 100%. You already rolled it, you know that it's a 1.

Warren Adams
Australia Mt Lawley Western Australia

I like the idea, but then I am a numbers guy. Not a great one I assure you but I get them.
I have friends that can not do numbers. It is just not there thing. They can dance, I can't. It is not my thing.
The simplicity of the questions they ask me often bemuses me (like a basic percentage calculation) but I don't question them any more  they are asking a serious question because they just don't do numbers.
Just something to bear in mind. No matter how much trouble you take to explain some things to people, in this case numbers, some of them will never get it.
I know, I have tried.

Lucas Smith
Germany Munich

tallboy wrote: I like the idea, but then I am a numbers guy. Not a great one I assure you but I get them. I have friends that can not do numbers. It is just not there thing. They can dance, I can't. It is not my thing. The simplicity of the questions they ask me often bemuses me (like a basic percentage calculation) but I don't question them any more  they are asking a serious question because they just don't do numbers. Just something to bear in mind. No matter how much trouble you take to explain some things to people, in this case numbers, some of them will never get it. I know, I have tried.
I agree. However, nobody will have to read (and understand) the thread about maths. Whoever doesn't like it, doesn't read it.


