Number of variables to be selected?

[DlarehAtsok]

I am struggling with some of the Definitions in the 5th chapter. The definition of "Defined" games is " . . . the exact number of variables to be selected is fixed in the scenario or the rules". My understanding, using also your example, is that the number of variables to be selected refers to the size of the group(s). However, the definition of Balanced games is "the number of variables to be selected is equal to the overall number of available spaces". Doesn't the "variables to be selected" mean the same thing as "available spaces"? Furthermore, even your example "eight students are divided into two-four person study groups" implies a different thing, i.e. the number of variables to be selected (available spaces) is equal to the total number of given variables. I would have thought of it as a typo, but since it is also mentioned in "Unbalanced" definition, I am afraid I am missing something.

[Ladan Soleimani]

Hi Dlareh,

Those definitions can get a little bit confusing, but I think you are correct with your understanding of them. Your second description of a balanced game is pretty much correct. A balanced game means there are the same amount of variables given as slots. Think of it as the number of variables to be selected from, instead of just selected, equal the number of available slots. A defined game means you know exactly how many variables are in each group. So 8 people filling two groups of four would be balanced and defined.

An unbalanced game has more or less variables available to fill the slots. For example, choosing between 7 people to fill a four person committee would be an unbalanced game. It would also be defined, because we know we are picking exactly four people. Undefined games do not tell you how many variables are being selected. So a game where you are selecting an unknown number of courses offered at a university from a group of 8 would be undefined.

I hope this clears up any confusion with the definitions!
Ladan