Balanced, Unbalanced and Numerical Distributions

[hunterama1]

I am a bit confused on this distinction between Grouping- Underfunded/Overloaded/and Balanced combined with the concept of Numerical Distributions- the allocated set vs. the reciever set.

Pg 333 states "When you set up a game, always consider the dominant terms first. Thus, first consider the numerical aspect of the game, then the grouping aspect...the Hierarchy provides a logical order of analysis for an Logic Game."

However, immediately after this directive, the first LG June 2005 does the opposite - the grouping is analyzed first followed by the comment that "With six committee members filling nine spaces...you should be on the lookout for rules that reveal a specific Numerical Distribution." and through further analysis of Grouping set up arriving at the conclusion, "Thus, the game is controlled by a 3-2-1-1-1-1 distribution."

I took away from this that in fact one should use the grouping to figure out the ND and the ND to figure out the grouping but where possible try to get the ND first. So that worked out ok.

Then in the Hitchcock game, as taught I considered the ND first - got it right except for one recurring problem in my head - being able to distinguish clearly and immediately when a game is Overfunded vs. Unbalanced as that seems to be one of the first things LGB declares as determined each and every game analysis should be mimicked in our approach. But I am not always spotting the Grouping classifications as correctly right out of the gate on my own.

I understand the easy basics - that overfunded is more variables than available spaces (slots) and that underfunded is less variables than available slots, balanced is balanced but the somewhat confusing point is the meeting of the ND concept with this Grouping classification.

LGB regarding Numerical Distribution, p 329 says "The set being allocated will have an equal or greater number of variables than the receiver set" and that the purpose of the Distribution is to bring a balance to available spaces from the shortage or overage of allocated variables to the receiver set.

In the June '05 Subcommittee set that is pretty straight forward - 6 members for 9 subcommittee spaces is underfunded 6 into 9 with minimums of 1 per subcommittee by the scenario "each of whom serve at least one subcommittee" thus 3 spaces "extra"; the requirement to to have those three spaces filled by tripling up one subcommittee and doubling up another by the Rule 'one committee member serves on all three submcommittees". This results in a 3:2:1:1:1: ND or 9 members for 9 subcommittee and now balanced.

But then in Hitchock we have 7 Film Buffs for 3 Films with the same minimum "each of the film buffs sees exactly one of the three films" leaving an initial minimum of 1:1:1 (four 'extra' FB's) and then applying the rule of "Exactly twice as many film buffs see the Hitchcock film as see the Fellini film" a fixed minimum of 2:1:1 (three 'extra' film buffs). Examining the distribution first the game appears to me to be Unbalanced Overloaded - (7 FB's for 3 Films) and then becomes balanced by distributing the allocated variables to this receiver set leaving zero 'extra'.

In that game, I understand that it's Defined-Moving because we don't know what Film Buffs are seeing which films and the Buffs (allocated variables) can move around in the base. I guess my problem is immediately and conceptually distinguishing the receiver set from the base (available spaces). But I did see afterwards why you classified this game as Balanced by virtue of the fact that - after the Numerical Distribution was determined from the initial (unbalanced receiver set of 1:1:1 for 7 Buffs) to be 1:2:4 and 2:4:1 there were now 7 Films for 7 Film Buffs.

How did you spot conceptually from the scenario and rules that this was a balanced game right off the bat as stated in the Game Analysis when the Allocated Set was 7 and the scenario's initially stated Receiver Set was 3?

The same Balanced vs. ND quandary arose again in the June 2000 game although I got all of these questions correct with no peeking! I attacked this game a little different from your explanation by accounting for the three stated variables: Tours (T) (subscripted 1-5 though they turned out not having the need to be tracked individually so this became just a T in my diagrams), Days (M-F) and Division Tours (Sales, Ops, Prd). Examinng first per pg 333 (supra) the Numerical Distribution, I observed 3 Divisions for 5 tours - thus Underfunded with 2 Tours 'extra' but this was 'brought up to balance' by the Rule: 'Sales division is toured on two consecutive days and no other days" resulting in a 2:2:1 (S O P) distribution and a 2:1:2 (S O P) distribution as a little different from your analyses' Partially Fixed Distribution - the distribution can be fully fixed in these two distributions as I saw it and this worked throughout the game (although I ended up with 7 full Possibilities which one could argue was less efficient.) (The 'extra' part of the ND determination system almost implies that the allocated set will always be overfunded relative to the receiver set unless equal.)


But once again in this game I was initially confused with Allocated Set - Tours to Reciever Set (Divisions) as in this game, the receiver set is not also the available spaces (slots) and I was at first thinking the game was Balanced with the Allocated Set Tours (5) being equal to the number of Days (5). The only thing that saved me from Stumpedom was the principal stated above that the Allocated set will always be equal or greater than the receiver set.

So in short, do you have any suggestions to help streamline the convergence of these two principles - 'allocated set to receiver set' with 'overloaded/underfunded/ balanced?"

Overall I'm making great progress so thanks as always.

[Dave Killoran]

Hi Hunter,

I'm going to respond in two parts. The first part will be a general response today, and tomorrow I'll respond in more detail about specific distributions when I have time to pull up the various games you reference and review the connection between the points you are making.

First, the good news is that you are progressing! The second piece of good news is that you are now actively thinking about the numbers present in each game, and tracking that element and considering each time. This will bear significant fruit over time

When I talk about Numbers being dominant, it means that they typically control the outcomes in a game, and that all other elements must fall into line behind the numbers and conform to them. Thus, you have to be constantly watching them, and I'm always looking at that element as a top priority when I attack a game. At virtually that same instant, I'm also trying to identify the type of game--Linear, Grouping, etc. As I've mentioned elsewhere, the process should be like a cascade of water: it happens so fast that it almost appears to be a single event.

In the explanations, often the first thing you see explained is the type of game. This is because when explaining what is going on, I often find that is a useful starting point because the game type is often revealed earlier than the distribution in the scenario. Later, I'll move on to the Numerical Distribution, but that doesn't mean that the classification somehow overpowers the ND (especially because the rules in the game typically have a great impact on the ND, meaning I can't introduce the ND until I've talked about elements deeper into the game). Essentially, I may not even now there is a ND of note until later in the game (by which time I already know what the game type is).

So, numbers still rule the day, but it's like a one-two punch--I'm trying to identify the numbers and the game type as quickly as possible, but sometimes one jumps out first.

Please let me know if that makes sense, and I'll also be commenting on the greater portion of your message a bit later.

Thanks!

[hunterama1]

Hi,

Thanks for the prompt reply.

I hear you on 'cascade of water' and one two punches because it all happens so fast for you but one must understand the two concepts slow but correctly before he can begin to get fast.

I'm basically trying to find a 'method of spotting' that's consistent to spot the ND phrasing and the grouping quickly among the hai-kou wordings.

Seems to me that the "each and exactly one's" tie to something and the object of the verb ties to the base.

Don't beat your head against the wall - I should probably grapple with it some more and I may get through the fog.

Let me get back to you...

[Dave Killoran]

Alright, that sounds good. I'll be here

Thanks!