Decision Making Matrix

Man, talk about Analysis Paralysis!

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

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, 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).

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.

- René Wiersma