Asking a girl out

This is not a puzzle. So, for those of you who follow this puzzle blog, please bear with me for just one post. Interesting Math in this article though :P

Most of my friends already read an article that I wrote more than an year back - "Speak Up"

Here, inspired by the movie, The Beautiful Mind, I give a mathematical analysis of asking a girl out. Nice time it is. Feb 10. No plans for Feb 14 and I am sure this article makes me look even more geekier and all the more reason for me to believe that I will be alone, yet again. But what the hell, lets do it!

Note: This is not an independent analysis. There are many "mathematics sites" which does "similar" analysis.

@Consultants, correct me if I am wrong in my estimates. :P

Why is there a need to be selective?

From the age of 15, I guess there are approximately 3,600 girls I have liked (On average days, I don't see new girls. But going outside, I like about 30 girls. Saying that I go out once every week right now and once every month earlier, on an average I go out once every 15 days. So, I like approximately 60 girls every month. That means I have liked approximately 3,600 girls in 5 yrs.)

Going ahead with this number, slow as I am in developing human relationships, I need at least 3 dates to "test" whether I like this girl or not. So, If I am to date all 3600 girls, I need 11000 dates. Even if I am "seeing" multiple girls together, I need 30 years to date all of them. So, clearly problem reduces to selecting a smaller subset of girls.

Which girl should I ask?


Lets remind you of the scene from the movie: The Beautiful Mind. Suppose all the guys are equally smart and intelligent. Suppose you are there in a bar with a few friends and there is a group of beautiful girls all of whom are brunettes, except one blonde. Most people would like to approach blonde first, however this is not a good strategy as Nash points out:

If we all go for the blonde, we block each other and not a single one of us is going to get her. So then we go for her friends, but they will all give us the cold shoulder because nobody likes to be second choice. But what if no one goes to the blonde? We don’t get in each other’s way and we don’ t insult the other girls. That’s the only way we win“.

This means that the prettiest girl in the group would always be there to be asked. No one would ask her out as everyone would be too afraid. Consider a guy who decides to talk to the blonde.

There are three possibilities:
1) He talks to the blonde and gets accepted. (Gets x points)
2) He talks to the blonde and gets rejected. He cannot go to the brunette now. (Gets 0 points)
3) He does not talk to the blonde and goes to the brunette directly. (Gets y points)

Note that x>y>0

Assume there are N guys and N girls (I am not talking about an IIT situation)
Each guy (since none of them is gay) has 2 possible actions (talk to blonde or talk to brunette). So, the sample space has size 2^n.

However, a particular guy gets x points if the guy approaches blonde while all others do not. Let us assume that the probability that a guy approaches blonde girl is p. So, for me to approach blonde, the award associated with it is x(1-p)^(n-1). While in the other case, the reward I get is y. So, the pareto optimal equilibrium point is the point when x(1-p)^(n-1) = y

So, p = 1 - (y/x)^(1/N-1)

Implications:
1) At N approaches infinity, p tends to zero. That is people are more afraid to ask the most beautiful girl out.
2) If you are a beautiful girl and you know that N is large, don't be choosie. Just go out with one of those N guys (I am one :P)
3) If you are a guy and y value for you is very small, you don't have a lot to lose. Go for the prettiest girl.
4) Whatever it is, I know the math behind this article is flawed. Read it and forget about it. You are a fool if you argue with me and a gentleman/gentlewoman if you leave nice comments!! :)

Update(11/02/10): Had a lot of small mistakes earlier. Improved it. :)