# Decision Making Matrix

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Ken
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Joined: 12/31/1969

OK, I'll run the risk of proving my lack of knowledge.

In another thread reviewing an excellent game, Chris mentioned a "decision making matrix". He even went so far as to say that it involved math (shudder :wink: ) and used a formula like "6X4". I have a vague and unsettling idea that I should know what this means.

What does this mean?

What do you use it for? How does it help? (Besides making you sound cool) How do you figure it out for any given game?

Thanks

PS If anyone else has any embarassing questions they would like asked, I'd be happy to set myself up as the "Ask a silly question guy" (IE "KEN was wondering ...what are dice?" "KEN just wanted to know about getting a patent for my ... er his ... totally cool monopoly variant?")

jwarrend
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Joined: 08/03/2008
Decision Making Matrix

I'm not sure "decision making matrix" is a well defined term, although it might be. I think what they meant in the context of the discussion you're referencing is probably that you have 6 choices and 4 allowed actions, meaning that each turn there are 6^4 = big number possible ways you could take actions. I think this is what they were referring to.

Anonymous
Decision Making Matrix

jwarrend has it right... although I would add that for a proper decision-making matrix, all 4 items must effect all six categories. So, a 6X4 leaves 24-factorial (because of combinations of effects) possible effects to any given player input. Gheos isn't a perfect decision-making matrix (not every input can result in all possibilities) but it is mathematically close.
XXOOCC

sedjtroll
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Joined: 07/21/2008
Decision Making Matrix

XXOOCC wrote:
So, a 6X4 decision making matrix leaves 24-factorial (because of combinations of effects) possible effects to any given player input.

zaiga
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Joined: 12/31/1969
Decision Making Matrix

sedjtroll wrote:
XXOOCC wrote:
So, a 6X4 decision making matrix leaves 24-factorial (because of combinations of effects) possible effects to any given player input.

What? You mean you can't process a 6x4 decision making matrix in a split second? :roll:

Actually, I don't think Gheos is that complicated. You can cut off a lot of decision points quite early in the decision making process because it will be obvious that those will not result in good moves for you.

- Rene Wiersma

Ken
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Joined: 12/31/1969
Decision Making Matrix

Thanks for the posts so far ... I think it is starting to sink through this thick skull of mine.

One more question: What sorts of things could you look at to "beef up" such a matrix? It seems to me that some form of Action Points are implied in one of the posts but are there other ways of doing this?

Could you work me through an example from one or two "common" games?

zaiga
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Joined: 12/31/1969
Decision Making Matrix

Ken wrote:
Could you work me through an example from one or two "common" games?

A good example of maybe not so much of a decision matrix, but more of a "decision tree" is Chess.

On the first move of Chess you have twenty possible moves (each pawn has two possible moves and there are two possible moves for each of your rooks). The opponent on his first turn can respond with any of 20 moves. This means that after one move by white and one move by black there are already (20x20=) 400 possible board positions.

As the game progresses the number of possible moves a player can do may increase or decrease, depending on the position of his pieces. However, if the average number of legal moves per turn is around 10 in Chess, that still means you have to work through a lot of permutations of possible board positions if you want to think ahead even a few number of turns.

Now, you can greatly reduce the number of permutations by "cutting off" certain decision points that you know or suspect will not pay off. For example, you know that making a move that will trade your Queen against your opponent's rook will not often be a profitable one, so you will not think through all the possible repercussions of that move.

A large decision matrix or a very deep and wide decision tree is not necessarily a good thing as it may induce analysis paralysis. I personally like to have a small random factor or some hidden information in my games so that not everything is perfectly calculatable.

I hope this makes things a bit clearer.

- Rene Wiersma

Ken
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Joined: 12/31/1969
Decision Making Matrix

Thanks Rene!

So if I'm following correctly, in a hypothetical game of cards such a decision Tree or Matrix would be dependent upon how many cards you hold, how many you are alowed to play in any one turn, who and where you could play them? It all adds up pretty quickly!

I was mostly concerned there wasn't some magical mathematical equation I'd been missing.

One final question (or series thereof), If you would all indulge me ... Has anyone (Chris maybe?) compared the D.M.Matrix of some of the more popular games on the market? How do they compare? Is there an inherent "magic formula" for the different game types? Should you be aiming for something in the 6X4 for a german-style strategy game ... something less for a typical Beer and Pretzels affair? When does the matrix become so small that it loses the "fun" factor, or too big and becomes "paralyzing".

(I realize this is all rather subjective, but I'd like to hear what you all think. -- i.e. I play chess from time to time, but I don't find a game with a Decision tree that big any fun...)

Ken

zaiga
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Joined: 12/31/1969
Decision Making Matrix

Ken, it is a subjective thing of course, but I think that in most German-style games you want a decision tree that is not wide, but you do want a decision tree that is deep.

What I mean is that you only have a handful of options (somewhere between 2 and 7) at each decision point, so that the decision tree is not very wide. This will circumvent analysis paralysis somewhat. However, I do think that a deep decision tree is a good thing, so that the outcome of a single choice is not immediately obvious, which leads to an agonizing decision.

A good example would be Puerto Rico where on average you can choose between 5 roles. You can probably narrow it down to 2 or 3 choices quickly, but deciding which one you will eventually choose can be hard, because you have to factor in with what role choice your opponents will respond. Typical line of thinking during a game of PR is: "If I chose role X, then he will chose role Y and she will chose role Z, which is bad for me, so maybe it is better if I chose role Y, so that he will chose role Z and then she will take role A. However, if I take role A, then he will take role Y and she will take role X, which is much better! Unless she takes roll B instead, of course... Oh, what to do?!".

I think there is a fine distinction between analysis paralysis because of a player trying to calculate too many permutations (=bad) and indecision because of posing an agonizing decision to a player (=good).

Quote:

So if I'm following correctly, in a hypothetical game of cards such a decision Tree or Matrix would be dependent upon how many cards you hold, how many you are alowed to play in any one turn, who and where you could play them? It all adds up pretty quickly!

It does add up quickly and that is why I like to keep things as simple as possible, both rulewise and strategywise. Give a player freedom of choice and 3 or 4 things to consider and you already have a basis for an interesting game. There's no need to complicate things, simply for the sake of making them complex.

Scurra
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Joined: 09/11/2008
Decision Making Matrix

zaiga wrote:

It does add up quickly and that is why I like to keep things as simple as possible, both rulewise and strategywise. Give a player freedom of choice and 3 or 4 things to consider and you already have a basis for an interesting game. There's no need to complicate things, simply for the sake of making them complex.

Yes, that seems like a decent "philosophy" for design.

I take your point about "deepness" in the decision tree - but it's worth noting that sometimes it can radically affect the feel of the game too, and you can end up getting so attached to one aspect that you can't see that it is distorting your game. Or sometimes that the reverse is true!

For instance, in one of my current designs, All For One, a player may choose to move any of six different characters, which could in theory lead to a lot of indecision.
However, their choice is largely dictated by the secret mission cards the players hold which collapses the matrix, although typically without making the player's choice instantly obvious which would make for a dull game!

But if the missions were open (rather than secret) then the decision matrix would grow enormously. This wouldn't necessarily make the game worse, but would change its dynamics and result in a game too complex for a reasonable playing time, even though it would almost certainly be a deeoer game (without guaranteeing a "better" game!)

IOW I think that sometimes you need to look at the "intent" of the game as well as the matrix of decisions.

Anonymous
Decision Making Matrix

...and the best "deep decision-making matrix" is the one that has the fewest rules in order that it be so.

This is one of the principle strengths of Gheos... few rules, but in-depth strategy.

This is also produces a game wherein the tactics/strategy of game play is both an extended learning curve and 'different each time you play'.

...again, and deservedly... Kudos Rene.
XXOOCC

Anonymous
Decision Making Matrix

Okay, I've been waiting for the "It's getting published!" post for too long now. XXOOCC has my curiosity peaked almost beyond control... soo... can I get a copy?

Tyler

Anonymous
Decision Making Matrix

Thats the best chuckle I had all day...

No, you can't get a copy from me. The game still belongs, part and parcel, to Rene (zaiga). I'm thinking that publishing it under contract from Rene is not a bad idea... but its a bit more complex than that. I do think zaiga sells 'net copies' if you'd like to drop a private e-mail that direction.

I need a business plan that tells me :
1) how much the game will cost in quantities that match what our research indicates is its one-year sales/market quantity.
2) I need to be sure that we have the investment money for same.
3) I need to have the logistics worked out as well... how many units am I storing, do I have the space for that, and how much will it cost to ship... and 'are there better answers than storing the product here'... such as 'flooring it' at one of our distributors.
4) Gheos can and should not be done 'on-the-cheap' and so greater planning is required than for a game like "Lemmings In Space!"

...and frankly, I'm still struggling through getting our release schedule put together OVER ALL... and getting it off to distribution. Right now, they think that we're making absolutely NO new product for the year.. because I'm not sure 'what and when' we'll release as far as new stuff for '04.

So... sorry to say... keep waiting for now.

GeminiWeb
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Joined: 07/31/2008
Decision Making Matrix

XXOOCC wrote:

Quote:
3) I need to have the logistics worked out as well... how many units am I storing, do I have the space for that, and how much will it cost to ship... and 'are there better answers than storing the product here'... such as 'flooring it' at one of our distributors.

Okay, don't let it be said that I wasn't willing to help this game become the widespread success it seemingly deserves to be. I'll happily store copies of the game at my house down in Oz ... think of me as your Australian warehouse ... :)

Try to keep the number of copies below 100,000 or it might become to hard to hide them from my wife :wink: