Game Theory

I think my last posted really touched on some interesting game-theory topics.

Then, coincidentally, I check Slashdot and see the following poll (I’ve modified it, removing a silly answer that’s included in every poll):



How’s that for a stumper?

Obviously, 0% can never be the right answer. If someone votes for it, it can’t be true. So we can immediately dismiss that one as the right answer.

100% COULD be true if everyone voted for it, but that assumes that everyone will be perfectly cooperative, which is unlikely. Note that if any single person deviates from that state of perfect cooperation and votes for 1%-25%, they would then be correct and everyone who voted for 100% would now be wrong. So it’s probably unlikely that 100% would win.

If the votes were randomly distributed across all choices, we should expect that 1%-25% would be correct, since 100% divided across 6 choices would mean each choice would get about 17% of the votes. But we can assume that everyone voting in the poll isn’t just a robot, but a rational human being, thinking along the same lines we do. If enough people thought that everyone ELSE would vote more or less randomly, then the 1%-25% choice would grow disproportionately large. But if enough people thought along those lines, they might vote for something else, which could make 1%-25% correct again.

I find stuff like this absolutely fascinating.

This led me to do some reading on game theory (thank you very much, Wikipedia!), and I came across an article describing the “Keynesian beauty contest”. The story is that there was a contest in a London newspaper where 100 female faces were shown, and entrants were asked to choose six faces that were the “most beautiful”. Entrants who chose the most popular choice would get entered into a raffle to win a prize.

If you were in this situation, what would you do? Voting for the six faces you find most attractive might work, but is a little naïve, since your tastes might be sort of individual. A more sophisticated approach might be to try to guess what the general perception of beauty is, and pick the six faces that match that. But, it’s probably safe to assume that others are thinking along the same lines, so maybe it’s better to try to guess what everyone else thinks everyone ELSE thinks of as the general view of beauty. And this can be carried on to the next order, and the next.

So what? “Keynes believed that similar behavior was at work within the stock market. This would have people pricing shares not based on what they thought their fundamental value was, but rather based on what they think everyone else thinks their value was, or what everybody else would predict the average assessment of value was.”

Simple games can reveal quite a lot. Exactly why is it that 100% is a bad choice in the above poll? What does that tell us about human nature? During rush hour, how do I choose the least populated route? Isn’t it possible that others might choose that same route, thereby making it the worst choice? When is the best time to go to the post office?

I think that’s why I enjoy certain board games so much. They are a tiny microcosm of some pretty vast social, biological, and economic ideas. Good, good stuff.

On Kingmaking…

A very interesting situation came up on Saturday night, as I was enjoying a game of “El Grande” (a board game) with Baditude, Iwan, Little Buhr, and Maja (pronounced “Maya”… those wacky Germans).

The specifics of the game are unimportant, but it involves scoring points. After a set amount of turns, the player with the most points at the end of the game wins. Points are good.

About two-thirds of the way through the game, I was in the lead, with Iwan not too far behind, and Little Buhr and Eryn mixing it up a little ways off behind him, and Maja trailing the pack. A specific card came up that would give me seven points, and give Maja four points. Maja had the option of veto’ing this play, or letting it stand.

Her options amount to this:

1) Let the play stand. In this case, I would get 7 points, she would get 4 points, and every other player gets 0 points. My lead would be extended, by 3 points relative to her, and by 7 points relative to everyone else. She would make up 4 points worth of ground on every other player. So while she decreases her (slim) chances of winning by extending my lead, she greatly increases her chances of not coming in last place. Those 4 points don’t get her out of last place, but they certainly let her get closer to the pack. It also makes me almost unbeatable.
2) Veto the play. She would remain in a relatively distant last place, but my lead wouldn’t be extended. Perhaps the next rounds of play could bring her better luck and she can make up ground, but her chances of winning remain the same – slim. I still hold the lead, but my victory is far from ensured.

The other thing, dear reader, you need to be familiar with is a term called “Kingmaking”. Kingmaking, as I understand it, is when a player that has no chance of winning a game is still able to affect who will win the game. Let’s say it’s Alice’s turn to play, with Bob going next and Charles going after that. Alice is presented with a choice that will prevent Bob from winning, but if she does that, Charles will win. Alice can effectively choose who she wants to win. The situation is compounded when Alice happens to be sleeping with Charles. (Not the case in this game, obviously).

I lobby for Maja to not veto the action. Clearly I want those 7 points, but I also know that Maja has been playfully whining about being in last place for most of the game. She’ll do what it takes to NOT finish in last, and I use that to my advantage.

So Maja makes her play, and decides NOT to veto the action. I take my 7 points, extending my lead and eventually winning the game (by less than 7 points). Maja gets her 4 points, and ends up still coming in last place by a single point.

After the game, Baditude is unable to contain his frustration at Maja’s choice, and grumbles something about “kingmaking”. I immediately get defensive. At the time, my impression of kingmaking is more like collusion, where a husband and wife team make poor plays to intentionally help the other person win. Clearly this is unfair to other players, and in my book, ranks a small step above cheating. Maja and I have no special relationship, and she has no vested interest in me winning, so at the time, I consider the “kingmaking” comment not only offensive but flat out wrong. (I understand now that kingmaking is more about a non-contender choosing an arbitrary winner, regardless of their relationship, so it makes a little more sense).

I’m reluctant to speak for Baditude, but my impression of his argument was that any play that reduces your chances of winning the game is a inexcusably “bad play”. Maja’s play clearly increased my lead relative to everyone else, including her.

I disagreed with Baditude, feeling a bit defensive that my hard-won victory was just going to be chalked up to an arbitrary choice by another player. I didn’t have a lot of time to think about it, but I was thinking that a play that reduces your chances of coming in last place can’t necessarily be a bad thing, can it? Baditude said that he respected my opinion, but disagreed. Well, that’s what his mouth said, at least. The actual message was a very clear “I hear your opinion, but you’re clearly wrong, and possibly insane.” I admit that made me bristle a little, too.

It was 1am, and I was getting up early the next morning, so I headed home, my head still spinning.

On the drive home, I thought a lot about that play. Was it “kingmaking”? Was she arbitrarily handing me a victory? Was it a “good play” – one that benefitted her position? Or was it a “bad play”, one that made it harder for her to win?

I thought about it mathematically. She gained +4 on three players, and -3 to me. If we were playing a two-person game, this would clearly be a bad play. If she did that move every time, she’d never catch up to me. However, in a multiplayer game, I became more and more convinced that this was a good play from a “long run” point of view. If she had somehow made the same play twice, but targeting two DIFFERENT players, she’d end up with two players up +7, and the other two players +0, and find herself in the lead at +8.

But in the short run? You can look at aggregate points scored. She went up +4 points relative to three players, for a total of +12, and -3 points to me, for a total of +9.

I will grant that her play made it harder for her to win. However, I don’t think that that, in itself, is enough to write it off as a bad play.

Baditude, as I knew he would, posted the topic to boardgamegeek.com, a hugely popular hangout for boardgame enthusiasts. I was hoping he’d post it, because after such a strong disagreement, I was curious to hear what others would think. It’s been a lively discussion and interesting reading. The majority opinion appears that Maya made a good play.

So, in the end, Maja’s play certainly helped me win the game. In that regard, I guess it could be considered kingmaking. However, I think it was kingmaking as a side effect. The motivation of her play was not to arbitrarily hand me a victory, but rather to increase her position to avoid coming in last place. And I think I’ve convinced myself that it was an outright good play mathematically, and it’s made me reconsider how I think about gaming strategy, and as a result, real life “strategy” as well. Good stuff.

Justification

As I mentioned previously, I’ve been coveting a Playstation 3 and Rock Band. I decided to sell a bunch of crap that’s been doing nothing but gathering dust, and turn it into something I’d use and enjoy and appreciate.

Here’s how the eBay sales worked out:

Roland TD7 drum module – $177.50
Roland KD7 Bass drum kick trigger – $102.50
2x Roland PD7 drum pad trigger – $56
1986 1/10 oz Gold Eagle coin -- $95
Birthday and Christmas Fry’s gift cards -- $50 + $50 + $50 + $25 = $175
TOTAL: $606

And the costs:

PS3 -- $400
Rock Band -- $170

Factor in taxes on the latter, and it’s pretty much an even trade.

I’m pretty impressed with the Playstation 3. Aside from being a gaming console, it’s also a BluRay player. The package came with a demo BluRay disc with some movie previews on it, and I was pretty blown away at the difference in quality. My understanding is that normal, standard definition TV is 240 lines of pixels. DVDs are 480 lines. BluRay is 1080 lines. The preview for “Casino Royale” looked spectacular. It also came with “Spiderman 3” on BluRay, and I’m almost tempted to crack that open just to see it in glorious high definition. But I strongly suspect that what I’ll get is a steaming pile of crap in glorious high definition, so it’s going straight to eBay, still sealed. And if I ever change my mind, I’ve enabled our Netflix account to get BluRay movies! Pretty sweet.

So not only is the PS3 a gaming console and BluRay player, but it also connects to our wireless network, and acts as a media sharing client. What this means is that I can share media (pictures, music, and video) from my desktop PC, and see it on the PS3. We pulled over some digital pictures, and they look really good. I tried streaming some home movies, but they were really choppy (presumably too big to stream in real time?) There might be ways around that, though. Music streamed through no problem, so with a little work, we could create some playlists and rip some CDs and have the music available out there.

And then there’s Rock Band. Previous Guitar Hero games allowed two players to play together, with one person playing a lead guitar and the other player either bass or rhythm guitar. Rock Band is the next generation of these games. You get two guitars like before, but also drums (via a nice little set of drum pads) and singer (via a microphone).

The first night I unpacked it, I left the drums in the box and just tried out the guitar. It feels a lot different than the Guitar Hero guitars, and takes some getting used to. It also took me a while to calibrate the timing for my particular TV. Soon enough, though, I was up and running, trying out a few songs. I even tried out an online battle, where you play against someone over the internet, playing the same song and trying to get the best score. The guy immediately jumped to the hardest song in the game and wiped the floor with me. That was funny. At the end of that song, I got a call from my boy Baditude. He also has a PS3 and Rock Band, and could see that I was online (since I’m on his buddy list), so we tried out the online cooperative play. That was a ton of fun. Not nearly a substitute for being in the same room, but it definitely would do in a pinch.

Later in the weekend I got the drums set up, and Diana and I jammed a little. Diana gave the drums a shot, and I’ll go ahead and say I was shocked. Diana is many, many things, but I wouldn’t list coordination and timing as some of her strongest attributes. But her first time sitting down behind the drums, she was busting out 90%’s or better on Medium difficulty. I was (and am) very proud of her.

Even later in the weekend, Diana’s parents came over to play, and Diana wanted to show them the game. We played, and Diana’s parents tried the drums (with less-than-stellar results). They tried singing, which was better. It was fun listening to Diana’s mom singing “Creep” in her classical choir voice. Diana’s dad belted out a half-decent “Should I Stay or Should I Go”, but it’s tough to sing songs without ever having heard them before.

I also started a Solo drum career on Medium difficulty, and am slowly working my way through the songs. I’ve played the game already a bit at Baditude’s, and have been a wanna-be drummer for a long time now, and so far Medium isn’t presenting a whole lot of difficulty. I tried one of the easiest songs on Expert as a lark, and it kicked my butt. So I look forward to the challenges.

Two other cool things about being the game being “connected” is that scores are uploaded to a server, which means that lists of high scores and stuff are all managed on a leaderboard.

Single player is fun and challenging. Online cooperative multiplayer is good. Online competitive multiplayer is really good. Local multiplayer is awesome. Local multiplayer with all four players after a couple of drinks is best ever. Rock Band party, anyone?

Threads

My dad just sent me a link to a video. It’s a slideshow played to the song “We Didn’t Start the Fire” by Billy Joel. “Have I seen this video before?” he asked. Funny he should ask.

Baditude and I have recently played a board game called "Twilight Struggle", whose theme is the Cold War. One player plays the USSR, and the other the US, and (among other things) players play card that represent actual historic events, and the result of these cards spread either US or USSR influence around the world. If you play the "Marshall Plan" card, for example, the US gets lots of influence in Western Europe... the "Nasser" card removes US influence from Egypt and adds USSR influence there. Stuff like that.

Playing this game got me really interested in the Cold War and I spent a while on Wikipedia reading about it. It’s really fascinating to know, in retrospect, just how crazy a place the world was when I was just a carefree lad, happily riding bikes and playing backyard soccer games. During my web searching, I came across a very similar video to the one he just emailed (another slideshow based on "We Didn't Start the Fire"). I've known that song for a long time. I specifically remember listening to it while driving up to Disneyland with Aileen, Sarah, Norm, and my brother in early high school. All this time, though, I never knew he was actually saying for the line "children of thalidomide". So I was pleased to fill in that little blank after all this time. Of course, I had to read about thalidomide and learn why it was included in the song.

Around the same time, an old college friend of Diana's came to visit with her family (husband and two children). One of the children was born missing her right forearm and hand. Her arm ends at the elbow. Shortly after that visit, I recounted this to my dad on the phone (this was weeks ago), and he mentioned something about thalidomide. I asked if he’d ever heard the song "We Didn't Start the Fire"... he hadn’t. But I guess he has now!

Weird how these multiple threads of my life have all joined together into a nice little package.

Vertigo

Yesterday afternoon, I was sitting at work concentrating pretty intently on what I was doing. My recollection is that I was sitting very still, reading whatever was on my monitor. I think I moved my head a bit to glance at something in my peripheral vision, and all of a sudden, I felt pretty dizzy. I decided to “walk it off”, and walked out to the break room, which is nearby. By the time I got there, the room was spinning around pretty good, and I decided that if I was going to pass out at work (hi Baditude!), I’d want to be near someone, so I walked back to my desk. At this point, I couldn’t walk straight. It was as if I’d spun around fast 50 times and tried to walk. The floor was tilting, and I could barely stay upright.

I made it back to my desk and lay on the floor and told my workboy that I wasn’t feeling well. I looked up at the ceiling and still felt like the whole room was rotating around me. My heart was pounding, and I broke a little sweat, but after just a minute or so, the feeling subsided. The room stopped spinning, and I was able to get off the floor. I decided to take the rest of the day off and drove home and went to bed.

Through the evening, I still felt a little unsteady, but better and better as the evening passed. This morning, I feel pretty normal, but a little scared to move my head around quickly.

The feeling of the room spinning was unlike anything I’ve ever encountered. It was crazy. I didn’t like it one bit. I talked to my dad about it last night, and read a little about vertigo, and it appears that it’s a pretty common occurrence.

Anyone else ever have any similar experiences?

Schooled 'em!

I get the magazine “Games for Windows” (until recently known as “Computer Gaming World”).

In the last issue, the editor wrote a column about New Year’s Resolutions for gaming companies in 2008. One resolution was to design game boxes that “won’t make people think I’m a pervert or moron if they see me with it.” Seeing a computer game box with big-breasted female character gracing the cover is not uncommon.

As it happened, earlier in that issue, they had a story with the headline “MoneyShot”. It was a story about the intersection of gambling and gaming, and how there are now some games that you can play and risk real money on your results. However, the article was printed SIDEWAYS, so that you had to turn the magazine vertically to read it, Playboy centerfold-style. Not only that, but there was a big picture of a nearly-naked female covering both pages.

I don’t particularly care one way or another about the issue of sexual objectification in games, but the hypocrisy was just too ripe. I wrote a letter to the editor calling them out on it.

I just got my most recent issue, and my letter was printed!

“In Greenspeak (GFW #14, pg. 96) Jeff writes: Design a game box that won’t make people think I’m a pervert or moron if they see me with it.” This is the same issue that has me turning the magazine sideways, centerfold-style, to read a story called ‘Money Shot’ (pg. 20), featuring a nearly-naked CG character. Try doing that in a public airport terminal and see what kind of looks you get.”

(I didn’t really read the magazine in an airport this time around, but I have before. I thought it painted a good picture).

They printed the letter with the heading “Touche”.

I’m pretty sure that means I schooled ‘em.

State of the Adman

Some quick hits…

Allison is still growing and going strong. Diana took her to the pediatrician for a second opinion after the whole ear infection thing, and they too pronounced her healthy and doing fine. She doesn’t appear to be eating as much as she used to, but she’s still going through diapers at a good clip, and that appears to be the de facto measure of performance. Perhaps she’s just gotten over a growth spurt. In any case, she’s still as cute as ever, and my favorite time of the day is getting home from work and seeing my girls. Her latest trick is making a new sound with her mouth: she kind of growls like she’s clearing phlegm from her throat. She thinks that’s pretty cool.

I’m starting to get a little warmed up to the presidential races. I haven’t done a whole lot of reading about the various candidates, but it’s fun to watch the horses race. I do, however, remember watching Barack Obama speak at the 2004 Democratic National Convention, and being totally impressed. I specifically remember thinking to myself that if he ran for president in 2008 that I would vote for him. At some level, though, I can’t help but think that no matter who is voted into office, they can’t possible do a worse job than Bush, right? (Here’s hoping, at least).

Which kind of leads me to a brief rant: Radio talk show hosts who complain about “the media”. I mean, come on.

In other news, how about those Chargers?! Diana and I had a bunch of people over for the game, and I was stoked to see them win their first playoff game in a long time. It’s going to be a big test this weekend, though, as they face the Colts. A winnable game, for sure, but definitely not a gimme. I hope they win. I have very little faith in their ability to beat the Pats, though it could happen. As they say, that’s why they play the games.

I’m still figuring out how to balance work, family, play, and sleep. Work has been busy lately, and I’ve continued to put in overtime, but things are starting to lighten up, and we have a meeting today where I’m hoping it will be decided that we can return to normal work hours. Those extra two hours in my day will go a long way.

My personal playtime, while important to me, has been prioritized behind work and family time (it sometimes ties with sleep). To that end, I haven’t been able to justify the cost of a new PS3 and Rock Band (in spite of the fact that we WANTS it, precious!). I already have a small stockpile of Fry’s gift cards from Christmas and my birthday, and I’ve decided that I’m going to earn the rest of the money. And by “earn”, I mean “eBay shit I don’t want any more”.

About 10 years ago, I decided I wanted to learn how to play the drums. Rather than going out and buying a full drum kit, I bought an electronic drum module and some pads and a kick drum trigger. You hook up the pads and kick drum to this module (a little computer), and plug in headphones or speakers, and you can do cool electronic drum stuff. Turns out that it was going to take a lot more money, time, and effort to get it set up in a decent way (I’d need to buy more pads, a rack, etc), and I never followed through. As I said, that was about 10 years ago. These things have been sitting in a box in my garage since then. About a year ago, a workboy sounded interested in playing the drums, so I loaned these things to him. And they sat in HIS garage for the last year.

So I’m selling ‘em on eBay, and they’re actually doing pretty well. In fact, I think they should do a pretty good job making up the difference.

http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=180203726508
http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=180203727313
http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=180203727935

The other factor involved here is the recent Blu-Ray vs HD-DVD news. I’ve been long lamenting the state of suck of the high definition DVD world. Different movie studios putting out movies in different formats pretty much paralyzes me from making any sort of decision for fear of making the WRONG decision. I briefly explained the situation recently to Diana, and after listening to and understanding the situation, she responded with “That’s dumb.” That’s dumb, indeed. However, with the recent news of Warner Home Video moving exclusively to Blu-Ray (and even more recent rumors of Universal and Paramount soon to follow suit), people are really saying that Blu-Ray is going to “win”. So that makes buying a PS3 (with built in Blu-Ray player) even more attractive.

So, there you go. The State of the Adman address. With that, I’m off to the dentist.

Allison Goes to the ER

On Friday night I came home from work to find a pretty cranky baby. Allison had just fed, which generally is my opportunity to play with her and give Diana a bit of a break. That night, however, I noticed that she seemed pretty uncomfortable, and was clutching and pawing very regularly at her right ear. Did she have an ear infection? Maybe she’d gotten water in her ear after a recent bath? I took her temperature by holding a thermometer in her armpit. The thermometer sucks, because it takes about two minutes to actually count up to the final temperature. And guess who doesn’t like having her arm pinned down for those two minutes? She didn’t appear to have any fever, but definitely seemed out of sorts. Her right ear actually felt warmer than her left, and Diana noted that she hadn’t been feeding very well that day.

This was hardly an emergency, but on a Friday night, we figured that if she needed to start taking antibiotics, it would be nice to start that as soon as possible. We weren’t panicked or stressed or anything, but just wanted to nip anything in the bud. We did some quick googling and found a local urgent care center that accepted our insurance.

Here’s an interesting point. I’m not sure the general public knows (or, at the very least, I don’t know) how to use the medical system outside or normal business hours. Do you even bother calling the pediatricians office after hours? Is it ok to call her at home? Is there a difference between “Urgent Care” and “Emergency Room”? My image of Emergency Rooms is gunshot wounds, heart attacks, and very serious things like that. Where do I go for different situations? (We’ll, of course, figure all this out at Allie’s upcoming monthly checkup).

Anyways, we drove to the local hospital, and went in the front door, where we were met by some sort of hospital liaison. We explained our problem, and she said we should go to the Emergency Room. So, we did.

Of COURSE by the time we got there and all checked in, little Allison was her usual angelic self, looking around wide-eyed at her new environment. Some woman was crying in the waiting room. I saw an old man wheeled by us, apparently unconscious. And we were there for a potential ear infection. I felt a little sheepish.

We were eventually seen by a triage nurse. She checked Allie’s blood oxygen by taping something to her big (this is a misnomer) toe. That was cute. I watched jealously as she took her temperature in about one second with a fancy ear thermometer. We need to get one of those. We then were seated in a little exam room, and eventually seen Dr. Smiley-Man. He listened to her breathing, and then looked in both her ears, and pronounced her healthy and fine. He even noted that there isn’t really any correlation with babies that young pawing at their ears and actual ear infections. Thanks for that, Doc. So we were dismissed with a clean bill of health.

In the waiting area, we checked out and paid the co-pay. $100. Ouch. Lesson learned? Check.

Sometime later, I looked behind her ear, and noticed that it looked a little dry and cracked, so we’ve been using a little hydrocortisone back there, and I think that’s helped a lot. She still itches a little at her ear, but I think she’s on the mend.

Happy 2008!

It was decided soon after the annual Baditude Holday Bash that he would also host our New Year’s festivities. Diana was unfortunately unable to attend, but I headed over (purposely avoiding beating everyone else over there by an hour! Yay! :) and met up with my peeps. Once we were all gathered (me, Baditude, Iwan and Sara, Gabe and Rhiannon, Little Buhr and Jen, Little Jay, and Speaks), we unloaded food and drinks (including about 50 gallons of booze), and headed over to the Blue Flame (or something like that) to meet up with Papa Roston for some drinks and appetizers. Papa Roston is always a fun guy to be around, and always knows exactly where the center of the party is – wherever HE is.

After appetizers, we headed back to Eryn’s pad for dinner. Steaks were on the grill, asparagus and smashed potatoes were being heated up, and Little Buhr and I found an opportunity to slip down into the garage to play the first of probably a dozen games of ping pong. I haven’t played any pong in forever, but man, what a fun game that is. Over the dozen games or so we played through the night, I’m sure I only won two of them. Say what you will about Little Buhr, the guy knows his way around a ping pong table. It was also fun to get in some one-on-one time with Little Buhr, as well. I think we both really enjoy those kinds of friendly competitions (I’m reminded of our 9-ball games when we went boarding at Mammoth recently). Good times.

Dinner was spectacular, with Speaks as official grill-master and doing a bang-up job. Rhiannon claimed to not like many vegetables, but I think his asparagus won her over. I realized later that I’d arrived with a salad (made by Diana), but totally forgot about it at dinner time. Oops.

After dinner, it was time for Rock Band. Let me tell you, that game was pretty much made for a room full of people in various states of inebriation. I started on drums, and S’Martin started on vocals, with Baditude and Little Jay on guitars. I have never seen S’Martin as fired up as I did that night. Between every song, she was bouncing all around pretty much screaming “I LOVE THIS GAME!” Songs were belted out, not only by the singer, but everyone else in the room. It was really, really fun.

As midnight rolled around, our rocking was interrupted briefly by watching the ball drop on TV and ringing in the New Year.

After midnight, though, the party had definitely turned a corner. Some folks were getting good and properly sauced, when people start stumbling around, that’s usually when I make myself scarce. I played a couple more games of pong with Little Buhr (hoping to take advantage of his drunkenness, but to no avail). Rhiannon and I rallied around a little, and it was nice to have some alone time with her.

I said my goodbyes around 1am. Eryn was washing dishes. S’Martin and Jen were having a suspicious heart-to-heart talk on the couch. The rest of the boys were smoking stogies on the porch.

They party continued the next morning, when Diana and Allison and I showed up for breakfast. Everyone was pretty bleary eyed, but up and watching college football. Leftovers were delicious, and it was nice to hang out with friends and Diana at the same time.

And now, it’s 2008! I can’t help but wonder what the year will bring. I’m not big on New Year’s Resolutions, and this year is no different. I do hope, though, that not a whole lot changes. Life isn’t perfect, but it’s humming along pretty well. It’s going to be exciting to see how much Allison changes in this upcoming year. Diana has done a great job of taking pictures and videos, and it is already fun to look back at her first month and see how much she’s changed.

Hope you, whoever is reading this, have a great year!