Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Basic Linear: Balanced game.

The game scenario establishes that six monuments are constructed over the course of five years. At first, this scenario looks ominous because there is one more monument than years available, creating an unbalanced six-into-five situation. An “extra” variable can create a high degree of uncertainty in a game, and is cause for concern when encountered. Fortunately, the last rule establishes that two monuments were begun in 601, and that every other monument was begun in a different year. This fixes the “extra” variable in 601, and creates a balanced scenario:

PT58-Sept2009_LGE-G1_srd1.png

Rule #1. This rule establishes a simple sequence:

PT58-Sept2009_LGE-G1_srd6.png

As with any three variable sequence in a Basic Linear game, this sequence produces six Not Laws:

PT58-Sept2009_LGE-G1_srd2.png

Rule #2. This rule specifies that H was begun in 604 or 605, creating three Not Laws and a split-option of H in 604 or 605:

PT58-Sept2009_LGE-G1_srd3.png

Rule #3. This rule indicates that M was begun in 601, 602, or 603, creating two Not Laws:

PT58-Sept2009_LGE-G1_srd4.png

Given the common connection of 604 in the second and third rules, you should look to see if an inference follows. Because M was begun in 601, 602, or 603, and H was begun in 604 or 605, we can infer that M H. This same type of reasoning can also be used to draw two other inferences:

1.  M F. Because M was begun in the first three years and F was begun in the last three years (see the Not Laws from the first rule), M must have been begun earlier than F.

2.  G H. Because G was begun in the first three years and H was begun in the last two years, G must have been begun earlier than H.

The next inference of the game involves L. From the first rule, L was not begun in 601 or 605. L also was not begun in 604 because if L was begun in 604, then from the first rule F was begun in 605, leaving no options for H per the second rule. Thus, L was begun in 602 or 603.

The combination of all of the rules and the inferences thus far leads to an almost-final setup:

PT58-Sept2009_LGE-G1_srd5.png

In reviewing, this setup both 601 and 604 are restricted because each year has three Not Laws, accordingly, two of G, M, and S must be begun in 601, and one of F, H, and S must be begun in 605. That information, along with the insight that S is a random leads to the final setup for the game:

PT58-Sept2009_LGE-G1_srd7.png

[beeke]

Is this an identify the templates game? I noticed that the first and fourth rules are pretty restrictive.

[Adam Tyson]

Beeke, I am a total template junkie - I do them all the time, even when they aren't the best approach - and I don't think this one is a true template game. The last rule isn't all that restrictive, as it doesn't force certain variables into fixed relationships or certain spaces. All it does it establish that this a defined game, setting up a 2-1-1-1-1-1 numerical distribution. In fact, that actually suggests NOT doing templates - it would be much more interesting if the year for two monuments could be either 1st or 2nd, setting up two possible distributions, and perhaps templates based on those. With only one distribution, fixed firmly in place, templates may be going overboard and doing more work than is called for.

The first rule gives us a sequence of G-L-F, but that sequence, covering only 3 of 6 spaces, isn't that exciting. Add a fourth to that sequence and I would jump all over a template approach, but here it still leaves a lot of flexibility.

That said, once I diagrammed the rules, I did try out a couple "what if" ideas to see if it might be a template game and what other inferences I could make. For example, I like to push sequences to their extremes, so I started by putting G as far to the right as I thought I could get away with, the 4th position. That put L 5th and F 6th, and...wait a minute, there's no room for H! My not-laws for H under 1 through 3 helped me spot that quickly, and I added a not-law for G at 4th and another for L at 5th. Then I pushed the sequence the other direction and put F as early as I could, 3rd. That put L 2nd and G 1st. Not-laws for M under 4 and 5 meant that M had to join G at 1st, and H and S (the random variable) became interchangeable at 5 and 6.

At this point I could have pursued other "what-if" scenarios, but having gotten a good sense of the game I felt it was time to move on. Even I, a template junkie, didn't think it would be worth it to try G 2nd (if a question asks me to do so, I'll do it then), or G first and L 3rd (I'll go there later if I must). Why? Because the benefits didn't seem to be there. I could already see the overall shape of the game, the distribution was done, and the not-laws were doing great work for me. I felt well prepared for the questions, and that's all I want from my diagram. Anything more is overkill. I'm guilty of it much of the time, but not in this case.

I hope that helps! Don't get too addicted to templates!

[NR 2020]

Could you please post the setup and rule diagrams for this game?

[Jeremy Press]

Hi NR2020,

Sure, a diagram of the setup and rules is below! A couple notes on that diagram: as Adam mentioned in his excellent post above, the 2-1-1-1-1-1 distribution is reflected in the baseline, with two slots for 601 and one for each of the remaining years. In addition, the extra Not-Laws he mentioned (one for G underneath spot 3 and one for L underneath spot 4) are included, for the reasons he mentioned in that post. Other than that, it's a pretty straightforward Basic Linear-Balanced setup. Let us know if this triggers any additional questions!

Screen Shot 2020-11-04 at 12.16.22 PM.png

[atdale1980]

Out of habit, I connected M, F, and H like in a sequence game (see attached). Do you see an issue with continuing this?

[Robert Carroll]

atdale1980,

Nope, I like it! If the sequencing relationships can be extended and expanded that's always a good thing, as it makes certain inferences easier to see.

Robert Carroll

[SGD2021]

Hello, how do we know that all 6 monuments must appear from the introduction to this game? In a game like this that has more variables than slots, is it ever possible for a slot to have 0 variables in it?

Also, in a game where there are more slots than variables, we cannot assume all variables will appear in the game unless told, correct? Is it possible in those kinds of games (more slots than variables) to have more than one variable in a slot and if so, should we look out for that?

Finally, there seem to be certain things we have to make sure not to assume at the start of each game such as not assuming all variables will appear in the game unless we're told and not assuming that every slot will have a variable unless we're told. Is this correct and are there any other common things we should make sure not to assume/ ask ourselves to avoid assuming right at the start of a game?

[SGD2021]

One other question: in a game like this one about monuments, why can't G go twice, for example?

[Adam Tyson]

The scenario here tells us that these 6 monuments all began construction in this 5-year period, SGD, so we cannot leave one out and have an empty slot. And none of them can go twice because you cannot "begin" construction twice. In this case, those requirements and restrictions are inherent in the scenario itself, rather than explicitly stated in the rules. We have to give proper attention to the scenario as well as to the list of rules!

We do need to ask those kinds of questions all the time. Is there any way a variable could be left out? Could one or more of them go more than once? Can a single variable occupy multiple spaces? Can multiple variables share a space? Don't take anything for granted!