Your Mileage May Vary

sober andy is gonna be so mad at me.

Disclaimer: I don’t really believe in fortunes, astrology, palm readings, meteorology or the like, but I do enjoy basing my actions on other people’s random predictions about my life.

About a month ago I was eating some Chinese. After finishing my sesame chicken I promptly tore into my fortune cookie. It read, “You are next in line for a promotion at your job.” This was an unusually applicable fortune because I had just applied for a supervisor position at the clinic I work for, and was scheduled for an interview later that week.

But somebody else got the job.

A couple weeks later I once again found myself eating Chinese. This time my fortune wasn’t so applicable to anything directly going on in my life, but it was at least humorous in its bold assertion that Your wildest dream will come true. It seemed I had landed the mother of all fortunes.

I thought about it for a minute before busing my table and heading down the street to purchase a Powerball ticket, something I normally only do once a year on St. Patrick’s Day.

Nobody won the lottery that week.

Today I had some Chinese food with my coworkers. At the end of the meal I cracked open my cookie:

I love that this fortune attempts to predict my luck for the entire rest of my life.

Hmm, well I have had a crush on that one girl for a while. Perhaps today is the day I should ask her out. The slip of paper in my vanilla waffer said my luck was going to be good for a change.

So I asked her out, and lo, the cookie’s prophetic wisdom did not falter.

A possibility was later raised that perhaps my wildest dream did come true, I just didn’t know. So if you happen to see a pipe-smoking rhinoceros who speaks only in riddles and is really good at chess, let me know. Otherwise, I’ll assume the cookies are 1 for 3…so far.

Before leaving the grocery store today I realized that I needed some cash for beers tonight. So I used the ATM on the way out and requested $20 from checking. The machine whirrled as it instructed me to “Please Wait…” Then, right when I expected money to slide into the tray, the message changed to “Transaction Cancelled,” and the receipt printed informed me that it did not give me any money, and that my account reflected the amount dispensed.

These things happen. I stopped by the credit union on my way home and used their ATM. I pressed the $25 from checking button and the ATM immediately spit out two twenty’s and a fiver. I suppose that’s the $25 I requested plus the $20 I tried to get from the last ATM. The receipt did not indicate that it had given me $45.

I’ll have to wait for my next bank statement to be sure, but right now I feel like I’m up twenty bucks. And, in case you’re wondering, I did use the credit union’s ATM again and requested another $25 from checking. It gave me exactly twenty five dollars.

Over the holidays I house-sat for one of the doctors that I work with. As part of the arrangement I got full use of both of their vehicles. One snowy afternoon while living at the good doctor’s large, empty home, I picked up my friends in the minivan to go sledding. First we stopped off at Ace Hardware for sleds. I picked out the cheapest thing on the shelf: a blue plastic saucer.

By the time I moved out of the doctor’s home, I still hadn’t removed the saucer from the back of the minivan. I had totally forgot about it until today. The snow was piled high before I got to work, and continued to fall steadily throughout the morning. I thought I might like to go sledding again. Where did I put that blue disc?

Luckily the doctor was at work today, so I asked her if she drove her minivan. I told her my disc was in it.

“Is it blue?”

“Why yes, indeed it is.”

She then tells me about how she took her children sledding at a nearby school recently. When they got home and unloaded the van of it’s sleds, they found a blue saucer none of them owned. The doctor’s son was quite fond of the blue disc and asked if they could keep it.

“No, ” she explained, “some poor kid is probably missing his sled. We need to take this back to the school.”

As it turns out, her children were going sledding today at the same school, so she told them to be on the lookout for the blue disc. They didn’t find it, but her husband stopped by work today and dropped off my brand new, red SnowRacer® Disc.

A while back I had uploaded this picture of my friends bearded dragon to flickr. Like most of my photos, I gave it a creative commons license. I rarely use my flickr account so I never got the message from artslave that she was using it in a Wikipedia article.

So yesterday I was looking around the interwebs for info on bearded dragons and was just a little weirded out when I saw my picture of Ryuu at the foot of this Wikipedia article.

I told my friend about it and we speculate that Ryuu is probably the third most famous beardie in the world now. The first is the bearded dragon on that Dodge truck commercial, and the second most famous is the one featured at the top of the Wikipedia article.

Take a look at lottery ticket sales or the annual revenue of a Las Vegas casino and it becomes apparent that many people have a difficult time wrapping their heads around probability. But even someone like myself, who has a basic understanding of the law of large numbers, can be caught off gaurd.

This weekend I was reminded of a game called Penny-Ante. It took me an hour of thinking and experimenting to finally accept the results and understand the logic.

Penny-Ante

There are two players and one coin. Player one chooses a sequence of three flips (ie Heads-Tails-Heads) and then player two chooses a sequence. The penny is flipped and the results tracked until one of the players’ sequences shows up. That player wins.

There are eight possible sequences: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. Each sequence has a 1/8 chance of showing up.

So what’s the trick? Player two has an advantage over player one. He knows the sequence that player one chose before he chooses his own. Say player one chooses HTH. Player two can improve his chances if he takes the first two values chosen by player one (HT) and makes those his last two (?HT). His first value is going to be the opposite of his last. So player two chooses HHT. This formula can change player two’s odds from 1/8 to 2/3, 3/4 or 7/8 depending on which sequence player one chooses.

Don’t get it? Read this.

So I was thinking about Penny-Ante and remembering some other odd things that challenged my worldview.

Approximating Pi with Buffon’s Needle Method

A couple of years ago a friend of mine told me that you can approximate pi by randomly dropping a needle onto a piece of paper. I didn’t really believe him so I asked him to do it.

He requested a needle and a sheet of ruled notebook paper. He cut the needle so that it’s length was exactly the same as the distance between the lines on the notebook paper, then started dropping the needle on the paper. He kept track of how many times the needle landed on a blue line, and how many times it landed in white space.

After fifty needle drops he multiplied the number of needle drops by two and divided that number by how many times the needle landed on a line. He ended up with 3.134. I was shocked he could get so close. He said it would get closer to pi the more drops he made. He continued until he had 100 drops, multiplied the number of drops by two, and divided by the number of times the needle landed on a line. The result was 3.139.

How does randomly dropping a needle on paralell lines give you pi? My friend gave me detailed mathematical explaination that I couldn’t quite follow, but essentially the root of the problem involves calculating the probability that the needle will cross a line. This probability is dependant on the angle of the needle to the parallel lines. The equation for calculating this probabilty includes the constant pi because the needle can fall anywhere from 0-360 degrees. What you do when you drop the needle is work backwards from that equation. More detailed maths can be located here.

Let’s Make a Deal

Here’s one that I stumbled upon this weekend and still haven’t quite wrapped my head around.

You find yourself on a game show called “Let’s Make a Deal.” The host, Monty, has placed one million dollars behind one of three doors. The other two have gag prizes. You are asked to pick a door. You get to keep whatever is behind it.

You pick door number two. Monty then makes the game interesting. He opens one of the other two doors to show you a gag prize, say door number three. He asks if you would like to change which door you picked or stay with door number two. What should you do?

I assumed, like most people, that it does not matter if you keep door number two or change to door number one. The money has not moved so your chances are the same. I was wrong, you should change your pick to door number one.

Don’t ask me to explain, this guy already did and I’m still kind of confused.