My Brush With The Lottery

Not long, a great many Americans went crazy attempting to buy a chance to win the largest lottery prize ever: the Mega Millions $656 million jackpot. And, despite my usual practice of avoiding such things with amused condescension, I was one of them. There was a pool of people buying tickets where I work, and, after considering the enormity of the prize, I put $5 (the minimum share) in. After considering the idea of actually winning, though, I began to regret my decision. After the initial thrill wore off, what would I do with all the money? Hedge funds? Charities? Investments? More importantly, who all would know that I had won and had just come into a large sum of cash? Family? Friends? Unsavory characters? People who have won the lottery in the past tend to have a record of losing both the money and their friends - sometimes even their lives. I determined the prize was like Radium; you either needed to keep it very well contained or just get rid of it.

Still, such financial quandaries aside, some of you may still be wondering why I bought the tickets in the first place. Don't I know math??? The answer is yes, I do know math. In this case, just enough to hang myself. Before I threw my money into the pot, I calculated the expected value of buying a ticket. Expected value is a simple statistical calculation that can give you a rough idea of how much each investment in some activity will gain you over the long run. If the expected value is positive, the investment is probably worth it; if not, you'll only come out ahead by being lucky. The expected value of gambling is usually negative (though there have been some instances of people cheating the system with math and coming out ahead consistently). To calculate it, you just take the reward at stake, multiply it by the probability of getting that reward, and subtract the cost.

Now, the chances of winning the jackpot were 1 in 175,711,536, the price of a ticket was $1, and, at the time, the jackpot was around $400 million. A quick calculation showed that the expected value for buying a ticket was $1.28; it was actually positive! Now, this didn't mean that I had any greater chance of winning the jackpot, but it did mean that the shear enormity of the reward was enough to outweigh the slim chance of getting it. So I bought 5 tickets.

Well, I didn't win, of course. If I had, this blog would be inexplicably gold-plated. But afterward I found myself somewhat troubled. Not because I hadn't won - I can't say I ever really expected to win - but because it looked like my calculations had somehow been wrong. Overall, Americans spent around $1.6 billion in tickets, with only a $656 million prize in return. How could the expected value have been positive and yet the overall result show a negative return on investment? After thinking about this a while, I realized that my error was that I hadn't taken into account the fact that other people were also buying tickets and that, in the case of multiple winners, the jackpot would be split. This meant that in my expected value formula, the reward would have to be divided by the number of people expected to win, including myself. This made the formula look like so:

(This holds true for either each person buying one ticket  or fewer people buy multiple tickets. The only case for which this wouldn't work is if someone were to buy the same ticket twice.)

Running the calculations again with 1.6 billion tickets purchased gave the much more reasonable expected value of -$0.63; buying a ticket wasn't worth it.

The above formula can be worked backwards, too. No prize less that $176 million is worth buying a ticket for, buying a ticket  for a $176 million jackpot would only be advisable if no one else were playing (highly unlikely), and a ticket for the recent Mega Millions would have only been worth it if no more than 480 million other tickets had been sold; less than one third the actual amount.

Now, there may still be a way to game the system. If the data were evenly distributed, the math predicts that there should have been nine winners, but there were only three. This is because people tend to pick some numbers more than others: birthdays, lucky numbers, etc. So, since multiple winners was the reason for the reduced expected value, if you were to pick numbers that other people have a lower chance of picking, you just might be able to get a positive expected value again. However, this would require more data-mining than I am capable of, and due to the large responsibilities associated with actually winning, I don't think I'm going to try.

While I Was Out...

Well, posting has been sparse recently, and there's a good reason for that: I've been on vacation.

My vacation started on August 19 when I went to a friend's wedding up in Oregon. I was there for the weekend, and it was a good time with lots of food, old friends, and, of course, the wedding. The ceremony was very simple yet elegant, and was followed by a massive reception (apparently the bride's family has a reputation of being very hungry, but not all of them were able to make it, so there ended up being a surplus of food). I helped some in the kitchen and with clean-up, but was mainly there to attend.

Non-ceremony highlights included creating a whirlpool and playing with slot cars. These happened after the wedding when it was just a bunch of guys hanging out. First we went to a small community pool and, wondering if we could actually make a whirlpool, all started running in a circle in the 4-ft. water. There were about 20 of us, and we were able to get a noticeable depression in the middle of the pool. At this point, we attempted to suddenly reverse direction, resulting in mass floundering and hilarity. We managed to repeat this three more times and were all very tired after doing so. Later that night, the father of the bride brought out an old slot car set, and Synk, Hopps, and I had far too much fun seeing just how crazy of a track we could make, with an ever-growing loop-the-loop and a vertical portion of track. Part of our excitement was dulled when we discovered that the cars were magnetic and would stay on the track just about no matter what, but it was still pretty cool.

Right after I got back from Oregon, I drove down to Texas to spend the week at my old dorm, 41, during the floor's "Expended Orientation" for the freshmen. A lot of people immediately think of this as some sort of hazing, but that implies that we're harming the freshmen or lording our seniority over them, when it really consists more of playing late-night games of Capture the Flag and traversing campus en masse to sing "500 Miles" to all the girls dorms. Rather than being some sort of price to join the floor, I found it was the most fun I had my freshman year. And it creates the kind of bond that has people like me using up my vacation days to visit the floor over a year after I graduated.

While the whole EO week was very fun, one thing that was very weird to me was that, except for two days when other alumni showed up, I was the oldest 41er present. There were even some guys who returned as alumni that I had seen come onto the floor as freshmen, making me feel kind of old. Aside from general aging, though, I think much of my disconcertion was caused by the fact that my older brother also stayed on 41. For a long time, I was "Fjord's younger brother," but now there isn't anyone left on the floor who has met Fjord, and I suddenly ended up in the position of being Grey, the eldest.

Weird.



At this point, some of the more astute of you may have realized from the dates given that my vacation ended over a week ago, yet I'm just now getting around to a post about it. This is because after I got back, I lost just about all motivation and my life became very much like this comic. Fortunately, with the long weekend, I'm starting to become bored with being bored, and my motivation cores are coming back online. This means that, with any luck, the Facebook-promised post detailing the construction and workings of my Archimedes Death Ray (oh, yes!) should be coming sometime this week.

Until then, have some steak. I know I will.

Corn Chips Are No Place For Me!

A little over a week ago, I was informed of the existence of the Warrior Dash. This is a 3.5 mile run with 12 obstacles, including an 8-ft. wall, barbed wire, and fire. There just happens to be one going on in Tulsa next month, and a lot of guys from work have been encouraging me to go with them. Aside from the fact that the partying atmosphere isn't really my thing, the race itself does seem pretty awesome and I've decided that it's something I want to do; I'll just decline the beer, enjoy my turkey leg and be on my way.

I have not, however, signed up yet.

This is because I started training last week, and to my disappointment I was unable to even run a mile. Now I know that this is something that my body is capable of (or at least used to be capable of); I was able to run 2 miles without much difficultly a year ago. I suppose I just need to get warmed up to that level of activity after almost a year of sedentary living. I'm just not entirely sure I can get warmed back up in time for the race.

So, I have been following the "I just want to finish" training schedule on their website, with the intent of signing up as soon as I'm able to complete the recommended running distance for that day (I have until the 28th before the price goes up). We'll see how I do tonight.


(I suppose even if I can't run the entire thing, I do know that I can keep up a 4.5 mph walking pace just about indefinitely, so there is that.)

Perils of Procrastination

I have learned an important lesson this week: NEVER put off booking a flight.

A good friend of mine is getting married toward the beginning of next month, and both Hopps and I were invited to the wedding. I eagerly responded that I would attend, and proceeded to get the necessary time off from work. I did not, however, book my flight. The reason I did this is because I wanted to coordinate my travel with Hopps, if possible. The actual location of the wedding is about an hour away from the airport, and if we both arrived at the same time it would save on a taxi or be more convenient if someone was picking us up. For his part, Hopps, having just started work, was trying to work out if he could get time off and then waiting for confirmation.

We checked ticket prices about a week ago, and while they were a bit pricey (the airport we would be flying into is not frequented by airlines as often as others) we decided that we could manage to fit them into our respective budgets. Some more time went by without Hopps knowing for sure if he had the day off, and eventually I decided to go ahead and book my flight anyway. So this last weekend I got on the internet to book my flight. I wasn't too concerned about the price; the wedding was still three weeks away, and prices couldn't have gone up that much, right?

WRONG.

In the several days since we had last checked, the price for a round trip had increased to almost 150% of its previous value, putting it way beyond what we had decided was pushing it for our wallets.

And now, I have just gotten of the phone with my friend after explaining to him why I won't be coming even though I had told him many times that I would. Uhhhg.


I have another friend getting married at the end of August. I will be booking that flight tomorrow.

A Benign Crazy

I don't think there are very many people in the world who would spend their Friday evenings/early Saturday mornings calculating the effects of a temporal wormhole on an RC circuit, but I am one of them.

I'll re-run my calculations and get a "project" post up about it soon, but for now I'll just say that I've always tended to think of time travel in terms of an op-amp feedback circuit, so it just felt natural to run some initial thought experiments with electrical components. Although the circuit just had two resistors and a charged capacitor, the complications introduced by the wormhole were enough that I had to review my old notes from Differential Equations to get a handle on it. I was also aided in my endeavors by Grimholt and Sam, the Homework Gremlins (two whiteboards that I inherited from the Powersuite), who were happy to have something to do.

In other news, Hopps has been moved in for about two weeks now, and things are going fine. We're both somewhat solitary, but it's nice to have another person around. Another one of my friends going to be visiting over the weekend, so we got a grill (and lighter fluid!) and hopefully we won't kill ourselves with it, any July 4 activities, or just the sheer heat outside.

Or rather, hopefully Hopps won't kill himself. I am invincible!

Exciting Times

Today is an interesting milestone: it is the last day (at least in the near future) that I will be living by myself. Starting tomorrow, this crazy guy will be moving in with me, and provided we don't kill each other, I think it will be a very good arrangement. Still, I can't help but feel a bit nervous about the change. Not that I have anything against him moving in -- it was I who raised the question of sharing the house in the first place -- and having another person under the roof will greatly reduce the rent, utilities, and boredom. Really, aside from me no longer being able to break into renditions of "Be Prepared" from The Lion King whenever I want, there isn't much reason behind my nervousness; just the issue of change.

A similar thing happened about a year ago after I graduated and got a job. Leaving the dorm of 50-ish people and my three roommates, I moved into an apartment with Hopps. He shared the apartment with me for the summer while he was interning, then he went back to college and I was left alone. It was really difficult adjusting from the crowded dorm to the empty apartment and it took a while, but I eventually got used to it. And now, after a year of living on my own, I'm going to switch back to sharing my residence with another. The change won't be nearly as great as before, but it's still there, and while it's not unsettling in the sense of disturbing, it is a bit of a jolt.

I know that this feeling is temporary and I'm actually looking forward to having a house-mate (is that what you call it?), it's just a change, and I tend to be a creature of habit.

Layout Difficulties

I'm somewhat annoyed at Blogger. I had hoped to set up this blog dividing my posts between three distinct tabs: Life, Projects, and Philosophy. This way I could go into great detail in the latter two pages without clogging things up for people who just want to check in and see how I'm doing. Very neat and clean. Unfortunately, while Blogger does have the option for multiple tabs, I haven't found a way to submit multiple posts for anything other than the Home tab. The only way I know of to completely separate posts of different styles is by creating completely separate blogs, which I don't want to do.

So right now it looks like if you want read about my personal happenings, you'll have to wade through posts detailing exactly how I make my chainmaille armor -- both the internet tutorials I learned from and my improvements on them -- should I ever feel like posting that. The only division will be the labels at the bottom.

If you know how to make Blogger sort posts into separate pages under the same blog, please let me know.