One of the most common problem involving Markov chains goes like this: If it has rained for the past two days, the probability that it will rain tomorrow is 0.7; if it rained today but not yesterday, the probability that it will rain tomorrow is 0.5; if it rained yesterday, but not today, the probability for tomorrow is 0.4; and if it didn't rain either day, the probability is 0.2. If it rained on Monday and Tuesday, what is the probability that it will rain on Friday?
To solve it, you have to set up a matrix. Once you do that, it's pretty straightforward algebra to find that the odds are a little better than half that it will rain on Friday.
I'm telling you about Markov chains for two reasons. First, after having been recently subjected to vegan recipes, there is a strong need to return to treating Weekly readers with the respect for their intelligence that they deserve. And second, I'm trying to help you win some mad cash in the office pool on the NCAA Basketball Tournament.
We all know that the three main truths about filling out a bracket are:
1. If your spouse knows less about basketball than you do, he/she will invariably do better on the bracket.
2. A trained chimpanzee will do worse on the bracket than will an untrained chimpanzee.
3. The UA will break your freakin' heart.
Most people who enter office pools usually buy two chances: the one they fill out with their head and the one they fill out with their heart (otherwise known as the "UA all the way, Baby!" bracket). Obviously, the winning bracket needs to be filled out by the spleen or the Isles of Langerhans or something.
But now, using a Markov chain, you may have a better chance. In fact, if you've never used a Markov chain before, but you're using one now, the chances that you'll do better this year are .500000001. The reason for this improvement is that simply knowing about Markov chains makes you smarter and therefore less likely to pick against Duke simply because you don't like the way Dick Vitale takes up residence in the hind pocket of Mike Krzyzewski's Dockers.
Plus, if you're reading this, that means that another week has passed since that vegan recipe disaster, and your damaged brain cells might be regenerating.
Anyway, the key to using a Markov chain is that you can't rely on the past, and you can't go backwards. It's like if you're on a small island, and you want to cross a body of water to another island. In the water, about a meter apart, are several outcroppings. Some of these outcroppings are rocks, while others are the heads of hungry crocodiles. If you're standing on a crocodile, the probability that you'll jump to another crocodile is .4. If you're on a rock, the probability that you'll jump to another rock is .5. You'll probably make it to the other side, but don't bet your house on it.
If fact, don't bet your house on anything, except the real estate market, which apparently has gone completely haywire. My wife and I bought our house about 15 years ago. All this time, she thought I was too lazy to move. Instead, it turns out that I'm a wily speculator.
As for the Cats, they're not going to win it, and the reason they're not going to win it is that they actually have a chance of winning it. The only year that they did win it was the one season in which they had absolutely no chance of winning it. If you understand that, then the Markov chain will be a breeze.
The UA women snuck into the NCAA Tournament after a maddeningly inconsistent season that ended with a home loss on Senior Day and then a first-round exit in the Pac-10 Tournament. If anybody asks you to take part in a women's pool, you should politely decline, because it'll probably just be the two of you. Women's basketball is catching on big in many parts of the country, but we're probably a generation away from the women's bracket office pool.
There's actually a chance that both the UA men's and women's team will play LSU in the second round of their respective tournaments. The odds that both UA teams will reach the Sweet Sixteen are astronomically high.
To help you along, I wrote this column like a Markov chain. There's a .4 probability that each paragraph will have anything to do with the paragraph that follows it. Now get out there and play. There's only one small problem. By the time you read this, the tournament will probably be underway, so you'll have to wait until next year to try out the system.
In the meantime, don't take the UA. A heart can only break so many times.