Friday, March 25, 2011

Family Blog

We have a family blog now, over at The following is my first post over there. I figured I would also post it here, because, why not?

While my wife has been thinking about the scriptures, I've been considering the mathematics of competition. In America, this subject is also called March Madness.

1. My office does a March Madness pool every year. I decided to enter (with no money, so I'm not gambling) in order to perform an experiment. Instead of basing my selections on research or any understanding of basketball, I made most of my selections by flipping a coin.

Most of them.

I gave the #1 and #2 seeds byes for the first round, meaning that they were picked without a coin being tossed. Anytime that two seeds played each other who were within 2 seeds (like a #7 playing a #9, for instance) I would flip a coin. Heads, the higher seed wins (#7). Tails, the low seed.

For everything else, I gave the higher seed a 5/8 chance of winning (which involved rigging a gimmicky coin-flip combination scheme, but never took more than 3 flips per prediction.)

It wasn't nearly enough.

My bracket is demolished. Washington (a 7 seed) made it all the way to the championship game in my bracket, and they've been gone for a while. I only have 1 team left in my Final Four and only 2 of my Elite Eight.

What can we learn here? (Other than the fact that I probably should have given the higher seeds a 3/4 chance to win instead of 5/8.) People who know almost nothing about basketball (i.e., my coworkers) are destroying me in this competition based on knowing about basketball. Because I relied on numbers and probabilities instead. And it turns out that probability doesn't know that much about basketball, either.

2. If someone were to enter a rock-paper-scissors tournament that had a $20 entry fee, would that count as gambling?

3. I read about a computer programming competition that took place at one of those computer programming colleges. (Funny venue, I know.) Each contestant had to create a program that would play Mancala. The programs would face off in a single-elimination bracket, producing one winning program. Two programs made it to the finals.

Program A was designed such that every turn, it calculated every possible move that it could make and would make the move that gave it the most stones, every time. The program had enough data and was smart enough about its analysis that it absolutely destroyed every program it went up against by enormous margins.

Program B also made it to the finals, but it seemed to just barely scrape its wins together. It never blew out any opponents, often winning with only a differential of a stone or two. Nobody thought it had a chance against Program A.

But Program B won--by merely a few stones. How did it eke out a victory against its incredibly dominant competition? While Program A was designed to get the most stones per turn, Program B was designed to get at least 1 more stone per cycle of turns than its opponent. It didn't just optimize the number of stones it could get, but also ran that against what its opponent would then be able to do based on that move, and made sure that whatever move it decided to do, its opponent would not be able to match it--even if the difference were just a stone or two.

Much like David from Survivor, all Program B cared about was winning. Program A looked at the symptoms of winning and mistook them for winning itself.

In short, Program A was winning, but Program B was bi-winning.

4. I play Starcraft 2 online. The game is so competitive at its higher levels that someone has created a program, called Evolution Chamber, that optimizes the decisions you make in-game so as to produce a certain result at a benchmark time. It's supposed to turn you into a robot programmed to, basically, get the most number of stones per turn (although instead of stones we're talking about mutant alien beasts). It's led to a number of creative, optimized build orders that produce surprising results when your opponent isn't ready.

And no professional Starcraft 2 player uses any of those builds, because there's a lot more to winning than having a build perfectly optimized for only one moment of the game. Again, you can use numbers and mathematics to produce the symptoms of winning, but the actual act of winning requires something extra. Tiger blood, perhaps? (Maybe simple human blood is sufficient.)

5. Ken Jennings and some other smarties battled in the bloodied colliseum of Jeapordy against mankind's most hated rival: a personal computer. But this computer was programmed specifically to win at Jeapordy. After the first day of competition, this computer and Ken Jennings were tied. After a week, the computer was ridiculously ahead. Why? Because the silly humans couldn't hit the darn button fast enough. Not because of any actual lack of knowledge.

In our future dystopia, we won't need to fear computers knowing more than us. We'll just have to worry about how fast they hit buttons. Computers don't have to make decisions, because they have no choices of their own. Drastic decisions for them aren't drastic, or even decisions--just a couple lines of code being carried out. Does that make them subservient to us, or simply terrifying? At the very least, it apparently makes them way good at Jeapordy.

6. Sports, and other competitions, are exciting precisely because you cannot know the outcome ahead of time. If I begin a mathematical exercise, like 2+2, the result (SPOILER ALERT) is oftentimes 4. Easy peasy lemon squeezy. If I try to guess who is better between two teams, the only way to really know is for them to play each other. That exercise doesn't happen in our heads or on paper, but in real life.

There's a lot in life that is probably unfair. Good competitions with solid rulesets can make some things fair, at least fair enough for people to throw their all into doing their best. I think that's noble. I think that may be why I like games in general.

Baseball metrics, Hollinger PER, and David Stern are all in place to determine the winners, but the best proof of all is, as they say, in the pudding. And who doesn't like pudding?

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