Setup and Rule Diagrams

[Administrator]

Setup and Rule Diagram Explanation

This is an Advanced Linear Game: Balanced.

This game has only six variables and three rules, and so creating the diagram is not an especially lengthy process.

From the game scenario, we know that there are two purchasers: a private collector and a museum. There are three different periods (periods 1, 2, and 3, from earliest to latest) and that suggests a linear setup with two stacks, one for the private collector and one for the museum:

pt43_j04_g3_1.png

The first rule can be diagrammed as:

pt43_j04_g3_2.png

This rule indicates that Z cannot be from the first period (and thus must be from the second or third period), and that S cannot be from the third period (and thus must be from the first or second period). The rule also indicates that S cannot be sold to the museum and that Z cannot be sold to the private collector:

pt43_j04_g3_3.png

Because there are only three periods, if S is from the second period, then Z must be from the third period. Conversely, if Z is from the second period, then S must be from the first period:

pt43_j04_g3_4.png

The second rule can be a bit tricky to diagram. The rule states that Q is not from an earlier period than T. Many students interpret this rule to mean that T must be from an earlier period than Q; that is not correct. Although Q cannot be from an earlier period than T, Q could be from the same period as T (remember, always read the rules closely!). Consequently, this rule is best diagrammed as:

pt43_j04_g3_5.png

Because T and Q could be from the same period, no Not Laws can be drawn from this rule. However, if T is from the third period, then Q must also be from the third period, and if Q is from the first period, T must also be from the first period.

The third rule indicates that V is from the second period, and that consequently V cannot be from the first or third periods:

pt43_j04_g3_6.png

The actions of V clearly impact the first rule. If V is sold to the private collector, then S must be from the first period; if V is sold to the museum, then Z must be from the third period:

pt43_j04_g3_7.png

Combining all the rules and inferences together, we arrive at the following diagram for the game:

pt43_j04_g3_8.png

Given the amount of information in the diagram, some students ask if it would be wise to make four templates based on the position of S, V, and Z (when V is sold to the private collector, S must be from the first period and Z can be from the second or third period; when V is sold to the museum, Z must be from the third period and S can be from the first or second period). Although at first glance this may seem like a powerful strategy, it only places S, V, and Z in four arrangements, and none of those arrangements definitively place Q, R, or T. Hence, the templates provide little additional insight into the placement of the variables, and it is better to attack the game with a straightforward setup.

[mp1224]

Hello,

What would be the best way to diagram the second rule of this game set: "Quarterion is not from an earlier period than Tesseract"?

I represented it as a not Q -- T, but this would make sense only if Q and T were sold to the same collector. How can I depict the rule to account for the possibility that Q and T could be from the same time period?

Thank you!

[Administrator]

Hi,

We've just posted the game setup above, so check out our explanation and diagram for rule #2!

[T.B.Justin]

Hence, the templates provide little additional insight into the placement of the variables, and it is better to attack the game with a straightforward setup.

I dont know if most students would agree but I found it to be more efficient identifying two templates:

V2P S1

In this template, since, Z is purchased by the museum in either the 2nd or 3rd period, Q cannot be in the 1st period, and the remaining variables (R, T=Q)


V2M Z3

In this template, since, S is purchased by the private collector either in the 1st or 2nd period, T cannot be in the 3rd period, and the remaining variables (R, T=Q)

[Adam Tyson]

As described in the setup at the top of the thread, Justin, there can be a real temptation to do templates with this game, but as you saw they really don't provide much info. In your first template, for example, we only know where V and S are to be placed, and then the other spaces all have multiple options. When you try a template approach like that and it yields so little info, that's a good sign that templates are probably not that useful and should be quickly abandoned in the interest of good time management. Especially when you consider that there are only 5 questions, a template approach with so much variation just isn't that wise a way to spend your time (and I tell you this as a confessed template junkie - I do way more templates than most of my colleagues recommend).