Saturday, April 9, 2011

The Price is Right (Part 1)

I've been watching a lot of the Price is Right over spring break.  Some people really take this game seriously and study in order to really perform well on the show.
I'm looking at yoooou Barney!

Now, if you do seriously study for the Price is Right, there are two places where your game can loose clout.  First is getting George to tell you to come on down.  Second is the Big Wheel, because no matter how hard you study, it's a completely random process and there's no way to "guarantee" a win.  However, you can maximize your chances of winning.

Assume you don't spin first.  Then there is a bid that your spin must beat, and there is little choice on the contestant's part.  Thus, we assume that you spin first.  Now we need to figure out what number you should try to get above in order to maximize your chances of winning.

Since the wheel has values from 5 to 100, there are 20 spots for the wheel to stop.  The goal is to get closest to 100 from one or two spins without going over.  If your final total is a 50, then either person spinning after you can beat that score to knock you out (to simplify things, let's ignore ties for now).  For each person, they can either spin above a 50 (10/20) OR they can spin below a 50 and then spin a number which will not put them over.  I will consider each individual spin in order to correctly get the probabilities: if your first spin is a 5, then you have to get at least a 50, but not 100 (or 1/20*10/20).  If your first spin is a 10, you have to get between a 45 and a 90 (or 1/20*10/20).  If your first spin is a 45, then you have to spin between a 10 and a 55 (or 1/20*10/20).

This means that if you stay at a 50, then your chances of the first person beating you is (10/20+9*1/20*10/20=29/40), or almost 3/4.  The chances of either person beating you (roughly speaking) is 3/4+1/4*3/4, or 15/16.  We need a better number if want to get into the Showcase Showdown.

Continued in Paaaaaaart twwwwwwwo....

Tuesday, April 5, 2011

The Social Sciences

I was playing on Wikipedia the other day (basically looking up dropout ages for different states) and I stumbled across a certain philosophy (coined by one John Holt) which struck my interest: the unschooling movement. Basically, this guy wanted to completely do away with compulsory schooling. He said that students should be able to learn what they wanted to learn, when they wanted to learn it. Moreover, he says that it should be the responsibility of the parents to make sure that their kids are being successful, inquisitive learners.

Now here's my problem with the social sciences, and philosophy in particular. It seems that whenever a theory is presented, it's always presented in a perfect world model, and they never address why it might actually be a bad idea.
I bet you can guess which side I am on.

Here's the first issue that I have; he expects that parents give a shit about their spawn. Talk to any teacher about things they wish they could change about their school system, and I guarantee you that "I wish parents gave a shit about their spawn" would be in the top five. It's not a realistic assumption unless the government can somehow regulate it (which would require major changes in our constitution in order for it to be even legal, much less enforce it, etc.).

The second thing that is glaringly wrong with his argument is that we have already tried non-compulsory education. And it sucks. It created a rift in society where those who were educated had a huge advantage over those who weren't (granted, education was also a mark of wealth, and so part of it was that the rich were educated, not that the educated were rich). I mean, just think for a second about how much money casinos make because of their mathematicians. The mathematics of calculating probabilities is certainly within the grasp of most high schoolers, and yet these people still go to casinos to play losing strategies.



Lastly, schooling provides some students the opportunity to rise up out of their current social situation, and they grow up to be extremely successful.  My grandfather grew up in rural Nebraska and was recruited by West Point out of high school and afterwards was very successful (in the American Dream sort of way).  Had he been a product of the unschooling movement, I have little doubt that he would have continued working at his parents' gas station in Nebraska until he was old enough to take over.

 Now, that's not to say that our current system is better (in fact, it is far from perfect).  But in the end, this is, in my eyes, a distinct step backwards.