216: Romantic Drama Equation

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Romantic Drama Equation
Real-life prospective-pairing curves over things like age can get depressing.
Title text: Real-life prospective-pairing curves over things like age can get depressing.

Explanation

The equations in the comic and the graph show how many different love pairs can be made if you know number of females and males in a group. The text explains that it was inspired by TV Romantic Drama, but of course the formula is valid for any group of people. There are two graphs and equations - gay option is the case when we are looking for pairs with same gender, straight option in for heterosexual equations. The interesting/funny part about the results is that in most cases there are more possibilities when we consider the homosexual option. Also it is interesting to observe what is kind of obvious - in the heterosexual case the "best" case is if both genders are present equally and the possibilities drop very fast if there is substantial difference between genders.

Transcript

TV Romantic Drama Equation (Derived during a series of "Queer as Folk" episodes)
[A table shows equations for possible romantic pairings in a TV show. The equation under "gay" is n(n-1) = 2+x(x-n); the equation under "straight" is x(n-x).]
x: Number of male (or female) cast members.
n: total number of cast members.
[A graph plots pairings (for large casts) against cast makeup. Each of the above equations forms a curve. "Gay cast" starts high for an all male cast, dips down at 50/50 cast makeup, and then rises again for all female. "Straight cast" starts at zero for an all male cast, peaks at 50/50 cast makeup, and then drops to zero again for an all female cast. The two curves intersect at two points close to the middle.]
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Discussion

This can't be right, even at 50/50, the number of gay pairings far outnumbers the number of straight pairings.80.235.105.134 20:10, 28 February 2013 (UTC) Moved from article page

Not quite. Consider a cast of 4 with 2 male (A, B) and 2 female (C, D). Possible gay pairings - 2 (A-B and C-D). Possible straight pairings - 4 (A-C, A-D, B-C, B-D) 122.200.61.203 (talk) (please sign your comments with ~~~~)
He says for large casts. For 2000 cast members, with 1000 of each gender, the gay couplings comes out at 999,000 and straight at 1,000,000. Presumably this is the small cross over the diagram alludes to. If you substitute x = n/2 into the equations, then you get (n^2-2n)/4 for the gay combinations and n^2/4 for the straight combinations, so for gender balanced cast size of n, the straight combinations outnumber the gay by n/2 141.101.98.229 (talk) (please sign your comments with ~~~~)

There is a typo in his formula for gay casts. The + should be a -. 199.27.128.159 (talk) (please sign your comments with ~~~~) No, he's right. Notice the x-n term. x<n, so x-n is negative.108.162.215.61 03:14, 2 March 2014 (UTC)

This also the small implication that "Queer as Folk" was so dull that Randall produced this equation to occupy his mind during it. I often find my mind wandering while sat watching soaps with my other half. Drmouse (talk) 14:20, 3 January 2014 (UTC)
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