Monday, October 31, 2011

Gaming Math: Problem 18 Answer and Problem 19

The answer to Problem 18, "Rating Trading", has been posted.

Problem 19: Rating Trading, Part 2

Consider the following generalization of the Math Trade Problem, which I came up with while thinking about how to use a similar "math trade" process to trade Magic cards. The difficulty with trading Magic cards using math trades is that Magic cards vary extremely widely in value, so the restriction of one-for-one trades is likely to be prohibitive. Therefore, suppose that we have the following Generalized Math Trade Problem:

Consider a group of N players, each of which has one or more cards to trade. Each player has a separate "subjective value" of each object - i.e. one player might value a given card at $12, while another might value it at only $8. The goal is to redistribute the cards among the players so as to maximize the sum of the amount each player values the cards he ends up with, subject to the constraint that each player ends up with cards that he values at least as much as the cards he started out with.

The "decision problem variation" of the Generalized Math Trade Problem is as follows: given an instance of the Generalized Math Trade Problem and a target value, determine if there is a solution such that the sum of the amount each player values the cards he ends up with is at least the target value (subject to all the other constraints of course).

Problem 19: Show that the decision problem variation of the Generalized Math Trade Problem is NP-complete.

Hints (ROT13 to read; you can read them one at a time)

1. Gur erqhpgvba vf gb gur fhofrg-fhz ceboyrz.
2. Gur fbyhgvba vaibyirf bayl gjb cnegvpvcnagf.
3. Bar bs gur cnegvpvcnagf unf bayl bar vgrz.

And the solution.

Sunday, October 30, 2011

Mini News Quiz #2

According to a recent article in the Wall Street Journal, a controversial new breed of iPhone apps claim to be able to do what?

1. Trick automated phone systems into connecting you with a human being faster.
2. Detect electromagnetic fields believed to indicate the presence of ghosts.
3. Display rapidly-changing images that hypnotize viewers into breaking bad habits.
4. Transmit voices across long distances using invisible waves of energy.

Saturday, October 29, 2011

Hints for Gaming Math Problem 18

ROT13 to read:

18A. Qba'g sbetrg gung pbfgf pna or artngvir.

18B. Fcyvg rnpu abqr vagb gjb.

18C. Guvf zvtug vaibyir nqqvat fbzr nqqvgvbany abqrf.

Gaming Math - Problem 18

Problem 18: Rating Trading

Consider the following problem, which we will refer to as the Math Trade Problem:

Consider a set of N players, each of which has one game that they want to trade. Assume that each player has a different game. Each person also has a list of games that he wants (You may assume that nobody lists a game they already have as a game they "want".) The goal is to determine how to distribute the games between players such that the number of trades (i.e. the number of people that end up with a game they want) is maximized subject to the constraint that everyone ends up with exactly one game, and each person ends up with either a game he wants or he keeps the game he already has.

The minimum-cost network flow problem with node capacities is as follows:

Consider a graph G with a set of vertices V (also known as "nodes") and (directed) edges E between these vertices. Each edge has a maximum capacity, which states how many units of flow can be sent along that edge, and a "cost", which gives the cost of sending each unit of flow along that edge. The goal is to find a way of sending flow such that the amount of flow going into each node is the same as the amount of flow going out, and the total cost of all the flow sent is minimized. Additionally, nodes may have "node capacities" which give the maximum amount of flow that can flow through that node. (In some versions of the network flow problem, there can be "source" nodes or "sink" nodes for which the amount of flow going in need not be the same as the amount going out, but these will not be necessary for our purposes.)


Problem 18A. Given an instance of the Math Trade Problem, show how to transform it into an instance of the Minimum-Cost Network Flow Problem with Node Capacities, such that a solution to the network flow problem will give a solution to the given Math Trade Problem.

Problem 18B. Given an instance of the Minimum-Cost Network Flow Problem with Node Capacities, show how to transform it into an instance of the Minimum-Cost Network Flow problem without node capacities. (There are several well-known algorithms that can be used to solve this problem.)

Problem 18C. Consider the following generalization of the problem. Suppose that each player owns multiple games, and we want to maximize the number of trades (i.e. total number of games that people want that they get) subject to the constraint that each player ends up with the same number of games he or she started out with, and each of those games is either one he already had or one that he wants. However, we also add the complication that several players may want to trade the same game, and nobody wants to end up with two or more copies of the same game.

I will put some hints up later tonight and I will put the solution up tomorrow.

Tuesday, October 25, 2011

More Gaming Math Problems Coming Soon!

As you probably have noticed, I haven't posted up many Gaming Math problems in a while though. However, that will soon change. Today at board game night I learned about a new big thing in board game related commerce called "Math Trades." These "Math Trades" are generally run on the web site Board Game Geek and the way they work is everyone posts what games they want and what games they want to trade. Then a computer program uses a mathematical algorithm to figure out how to maximize the number of beneficial trades, which often involves "trade circles" - i.e. if person A has a game that person B wants, person B has a game that person C wants, and person C has a game that person A wants, they can they can trade in a circle. Obviously there are a lot of interesting math problems in here, but I haven't posted any up today because I will have to think about the problem some more in order to figure out what the right way to formulate the problem is. (Of course, I could just read the web site for the software that explains how it works, but where's the fun in that?)

Sunday, October 23, 2011

Shipping Jobs Overseas?

One of the members of our local Belegarth group, John Degraffenreid, is running for Congress as an independent candidate. One of the planks of his platform (direct link won't work; click on "Platform" then "Trade") is that it is "time to hold corporations accountable for moving jobs overseas" and that American corporations should be required to pay overseas workers a "fair wage" to protect other countries from being "taken advantage of" and to eliminate the advantage of "moving jobs overseas."

Of course, most economists would say that most "moving jobs overseas" is actually a net benefit because each country can specialize in what it produces best, thus improving overall output - i.e., if a company saves money by "moving jobs overseas" and importing products rather than producing them in the U.S., that just creates jobs for the people in the U.S. that produce exports to exchange for the imports, and this analysis is not affected by whether the reduced costs are caused by the overseas workers being "taken advantage of". Of course, this argument has been discussed to death, and I don't really have anything new or interesting to say about it.

What I find more interesting is the implied moral claim that there is something blameworthy about a corporation "moving jobs overseas", such that the corporation needs to be held "accountable" for it. (Of course, I'm not picking on Degraffenreid here; lots of the public and politicians seem to have similar view, which is part of why I find this interesting.) Consider the following two cases:

A. Acme Corporation currently employs 100 American workers. It has an opportunity to expand into a new market and hire 50 more American workers, but instead decides to stay its current size.

B. Acme Corporation currently employs 100 American workers. It has an opportunity to expand into a new market and hire 50 more American workers, but instead it builds a factory in Pakistan and hires 200 Pakistani workers instead because it is cheaper.

I doubt very many people would say that in case (A) Acme Corporation did anything blameworthy, but in case (B) they would say that Acme Corporation was "shipping jobs overseas." But in either case, the change in number of American workers was exactly the same - zero. What principle could justify the difference? You can't just say that corporations have a responsibility to hire as many American workers as possible, because that would make (A) as blameworthy as (B). One possibility is to say that corporations have a responsibility NOT to hire foreign workers, but that seems hard to justify. Why is giving an American worker a job good but giving a Pakistani worker a job bad? I can understand why Americans value other Americans more than they do Pakistanis, but I don't understand why people would put a negative value on Pakistani jobs.

One possibility is that people think that Pakistani workers aren't actually being helped by the new jobs. But that doesn't make sense, because if the new jobs were really inferior to whatever they would be doing in the absence of the new jobs, then why would anyone take the new jobs? Another possibility is that people think that corporations have a responsibility to hire foreign workers AND pay them well, so that their lot would be improved by even more than before. But that doesn't explain attitudes like Degraffenreid's, since he says (probably correctly) that making American firms pay foreign workers more will induce them to hire fewer foreign workers. (Unless the idea is that it is better to help a few foreign workers a lot than to help a lot of foreign workers a little each.)

Possibly a better explanation might be to go back to the principle that "American companies have an obligation to hire as many American workers as possible", and explain the reluctance of people to assign blame in case (A) a different way. One possible explanation would be that my premise (that people don't assign blame in cases like A) is false. After all, people do sometimes consider companies blameworthy when they lay off workers, and Barack Obama did exhort companies to start investing and spending more if they had the money to do it. Another explanation might be that people think that (A) is theoretically blameworthy, it's just that "not expanding as much as you can" is much less visible than "opening up factories in foreign countries".

Here is another question: let's say that reforms designed to "bring jobs home" were implemented, and because of that, corporations pulled their investments out of Pakistan and brought them "back home" to the United States. In that situation, would Pakistanis be right to complain that the corporations are "sending jobs overseas" back to the United States? If so, then why does a corporation that operates in both the U.S. and Pakistan have greater obligations to American workers than to Pakistani workers? If not, then what is the relevant distinction?

Finally, consider the following third case:

(C) Acme Corporation currently employs 100 American workers. It sees room to expand and hire 50 more American workers. Instead, it buys more machinery to make each worker more productive, so that it doesn't need to hire any new workers.

I think most people would think there's nothing wrong with (C); or at least much less wrong with (C) than with (B). Sometimes people do lament the fact that technology puts people out of work, but certainly I have never heard any politician saying that we have to slow down progress on labor-saving technology in order to preserve jobs. But in both cases (B) and (C) you are choosing an option that allows you to hire fewer American workers in order to reduce costs. So a general principle that "it's wrong to hire fewer workers just so you can reduce costs" is not the driving force here.

A possibility is that there is some sort of (implicit) cost-benefit analysis going on. That is, people think that reducing costs is a legitimate benefit, but that it has to be balanced against the (perceived) costs of putting people out of work. With labor-saving technology, it's really obvious that the benefits are enormous: if we had never developed any labor-saving technology whatsoever, we would still be hunter-gatherers living in caves. But with international trade, the benefits are a lot less obvious, so it is easier for people to think that the costs exceed the benefits.

Of course, a lot of this is just speculation, and I don't know what the right answer is. I found an interesting web site called "Experimental Philosophy" that discusses research where they do surveys to ask people these types of questions in order to understand how people actually form judgements about these questions (like what makes someone morally responsible for something, or when it makes sense to say that someone "intended" for something to happen.) Reading that web site is part of what gave me the idea to think about this issue in this way, although I don't see any posts on that web site that discuss political/economic questions like this one. Also see here for a related discussion about "moving overseas" and moral responsibility (although I think that discusses a slightly different issue).

Wednesday, September 21, 2011

Saving Green By Going Green, Followup

Today, I sent the following letter to my congressman Cory Gardner:

I am writing to urge you to vote against the TRAIN Act, which will delay implementation of key environmental protections that could save thousands of lives. While proponents of the TRAIN Act claim that they are interested in ensuring that the benefits of regulation exceed the economic costs, their actual actions clearly show that this is not what they are concerned about. First of all, the EPA already does cost-benefit analyses of its regulations. If TRAIN Act proponents believe these analyses are flawed, why wouldn't they just fix them, rather than wasting time starting all over? Second, the latest version of the TRAIN Act explicitly blocks the Cross-State Air Pollution Rule and Mercury and Air Toxics standards. If proponents were really interested in making an honest inquiry as to the costs and benefits, why would they write into the bill what conclusions they want before even doing the analysis? Finally, the pro-pollution lobby's own words prove their dishonesty. The American Coalition for Clean Coal Electricity, a key pro-polluter lobbying group, on the front page of its website ( states that proposed EPA regulations would "eliminate more than a million American jobs". However, if you click through to their own analysis you will find that is not true - they actually claim it will eliminate 1.4 million "job-years", totaled over an 8-year period, which is not the same thing. If the pro-polluter lobby can't even get basic facts straight, why should we believe anything they say?

I'm not too hopeful as to what Gardner will think about this issue, given that he is a staunch conservative and as far as I can tell from his votes, has hasn't voted on the pro-environment side on any recent bills. I don't see anything on his web site where he supports "protecting the environment." However, one of the proposals he supports, the Business Cycle Balanced Budget Amendment, says it will "force government to budget itself in a countercyclical manner", which actually makes economic sense. However, the actual proposal says that the budget limit for each year is an (inflation-adjusted) average of revenues for the past three years, and I don't think that's what "countercyclical" means.

Tuesday, September 20, 2011

Saving Green by Going Green ... Or Is It?

Today, I received an email from the Environmental Defense Fund urging me to protect clean air by calling my congressman and urging him to vote against the TRAIN Act, a law that will create an independent committee do do cost-benefit analyses of new EPA regulations before implementation. Opponents of the bill argue that it is unnecessary because the EPA already does cost-benefit analyses of its regulations and the new law would just duplicate that effort and delay implementation of the regulations. On the other hand, proponents say that the EPA analyses may be biased (after all, they're not exactly a disinterested party) and that an independent analysis is necessary to make it unbiased. (Actually, the latest version of the act does a lot more than just call for cost-benefit analyses; it also explicitly blocks certain regulations, see here.)

What I was interested in is just what, in particular, proponents believed the flaws of the EPA studies were. The American Association for Clean Coal Electricity, (ACCCE), a power-company lobbying group, has a web page that discusses the issue from their point of view. They identify two perceived flaws: first, that the EPA considers only one proposed rule at a time and does not lump multiple proposed rules together in its analysis; and second, that the EPA does not consider other negative economic effects such as lost jobs. (Note that on the association's front page, they claim that the regulations the TRAIN Act will block will cost 1.4 million jobs. However, on the actual page that discusses the TRAIN Act, they say it will cost 1.4 million job-years, totalled over an 8-year period. These are very different.)

Anyway, the first criticism does not, at first, seem to make any sense. If regulation A has costs which exceed benefits, and regulation B has costs which exceed benefits, then added together, regulations A and B will collectively have costs which exceed benefits. The only way this will not be true is if either:

(a) The benefits of implementing both regulations A and B are less than the benefits of implementing A alone plus the benefits of implementing B alone.

(b) The costs of implementing both regulations A and B are greater than the costs of implementing A alone plus the costs of implementing B alone.

This, of course, raises the question of in what circumstances these can be true. For case (a), I can think of a simple example: suppose that both regulations will reduce exposure to the same pollutant, and the pollutant has a hormetic dose-response relationship. But for some reason I don't think that's the case that the ACCCE is thinking about. For case (b), I can think of a different case, that seems to be the case that the ACCCE is discussing. Suppose that both regulations reduce the production of electricity, and electricity (like most goods) has diminishing marginal value. Then just looking at each regulation individually, and estimating the cost by multiplying the current price by the amount of reduction (let's say), will understate the total costs. In the diagram below, the true cost is C+D but the "looking at each regulation individually) approach will give you something closer to C.
We can now estimate about how big this difference is. For the sake of argument, I will use the assumptions that are most favorable to the ACCCE's position. They mention that there will be a total reduction in coal power production of 30 to 100 gigawatts (GW) due to "these and other rules". 100 GW is equivalent to 876,000,000 MWh over the course of a year, or about 25 percent of the total U.S. electricity consumption 3,741,485,000 MWh per year. Of course this is not a good estimate of total electricity consumption lost because some of the capacity lost in coal gets replaced by other energy sources. If I am interpreting the chart labeled "2016 CATR+MACT impacts" of their own report correctly (it's on page 6 of the PDF, or page 5 going by the page numbers on the page), it looks like about 60 percent of capacity lost in coal gets made up in increased natural gas. So you end up with a total of about 10 percent reduced consumption. According to the review here, the short-run price elasticity of demand for electricity is about 0.2. So 10 percent reduced consumption corresponds to about a 50 percent increase in price. That means that the triangular area D is about 25 percent of the area C.

However, my understanding (at least based on what it says here) is that for most of these regulations the benefits exceed the costs by at least several times. So just a 25 percent error won't make a significant difference.


The comment about jobs, however, is more interesting conceptually, and I think they have it backwards. Here's how I am thinking about it. Let's say that electricity and labor are perfect complements, so a business can produce a "widget" by using one worker and one unit of electricity. Suppose that currently the business is producing X widgets, and so it is using X units of electricity, and the new regulation will increase the price by Y. Suppose you ignore the issue of jobs. Presumably that means you assume that the business will just produce the same number of widgets as before. Then the total cost is X times Y. But suppose you take jobs into account, and you take into account the fact that now the business will produce fewer widgets because the cost of producing them went up. But if they made this change, then that means the change was beneficial (compared to just absorbing the extra cost). In other words, the "reduction in jobs" is partially a benefit because it means that you are now using less of the more expensive electricity.


Of course, conservatives aren't the only ones who often use faulty economic reasoning when talking about environmental issues. During the 2008 presidential campaign, Barack Obama claimed that oil companies had 68 million acres of land they were "not using" and that we needed to make them "use it or lose it." Most importantly, this claim was false: most of the 67 million acres of "non-producing land" was actively being explored and prepared, it's just that no oil was coming out of it yet. But even if it was true that oil companies were deliberately ignoring large portions of their land, why is that necessarily a problem? There are only two reasons I can think of as to why they would do that. One reason is because they think that oil will become more expensive in the future and they would rather wait and sell the oil when it's more expensive rather than extract and sell the oil now. But if that's the case, then the oil companies' actions would raise the price now (when it's cheaper) and lower the price when they get around to extracting it (when it's more expensive), thus reducing the volatility of oil prices over time. Isn't that a good thing; to save it for when it's scarcer? Another possible reason is if they are colluding to reduce supply in order to raise the price now. But that theory doesn't seem to hold water because oil is traded on a world market, and the vast majority of world oil and gas reserves are controlled by companies outside the United States, so it doesn't seem like U.S. oil companies could reduce the world supply that much just by drilling a bit less. And in any case, if the problem is that we are using too much oil, isn't it good if the oil price goes up because that means that people will have an incentive to switch to renewable sources?

Saturday, September 10, 2011

Mini News Quiz

President Obama's proposed new "American Jobs Act" prohibits employers from discriminating against job applicants who are...

(a) politically active
(b) environmentally conscious
(c) recently divorced
(d) currently unemployed

Friday, August 26, 2011

My new home

So, I have finished up with everything for scvhool, I have deposited my thesis, and I am ready to start work on Monday. Here is what I have found so far:


Transportatoin will be slightly more difficult here than in Champaign. I live in Fort Collins, then about 10 miles south of Fort Collins is downtown Loveland, and about 4 miles east of downtown Loveland is where I work. There is a bus system (Transfort) in Fort Collins, which I don't need ot use much because I can just bike everywhere in Fort Collins that I want to go usually. In order to get to work, I need to take the "Flex Bus" down to Loveland, then get on a COLT (City of Loveland Transit) bus to get to where I work. The last Flex Bus northbound from Loveland leaves at 7:12 PM, so I have some time to do stuff thereafter work. One problem with the bus system is that none of the buses run on Sundays (see below to find out why that is a problem). I did try riding my bike down all the way from Fort Collins to Loveland once, but I don't think it's something I will want to do very often. There is also a taxicab company (Denver Yellow Cab) here. According to here, it gets horrible reviews for customer service, but I have used it three times and so far have no problems, except that sometimes I get put on hold for a few minutes while calling for the cab. It is about $30 to go all the way from Loveland to Fort Collins.


There is a major street (College Avenue) with all the usual chain stores like Target, Best Buy, Barnes + Noble, and so on. Another thing I have noticed here is that there seems to be a lot of outdoor stuff, camping, and hunting going around here, because I've seen several outdoor equipment stores including a dedicated archery store. Also I have seen lots of signs for gun shows - I wonder if those are geared toward hunters. Also, when I was in Loveland I saw the store Phoenix Nest, which sells Renaissance-style garb and they also do custom made leather products. I will probably be back there a few times to get stuff for live-action role playing (see below). Another store that is cool is in downtown Fort Collins, and it is called Science Toy Magic. It is a very small store but it is packed full of cool toys that demonstrate principles of science, and the guy who runs it does really fun demonstrations. A couple weeks ago I saw a sign indicating that they would get new toys in, so I went back to see the demonstration of the new toy, which was called the "Invisible High Bouncing Ball". The demonstration was okay, but it was a little hard to see what was going on. You can also watch this YouTube video here. Here's another thing which obviously won't affect me directly, because I am not going to use any illegal drugs, but might be interesting: I saw in the newspaper that Fort Collins is considering banning medical marijuana, and if you have been here you will understand why lots of Fort Collins residents complained that the ban would screw up their economy.


There are two main game stores in Fort Collins: the Haunted Game Cafe and Gryphon Games and Comics. They all have things going on almost every night, including role-playing games, miniatures games, and board games. The Haunted Game Cafe has a shelf full of games you can borrow to play in the store., and they sell drinks and snacks there. Each of these stores is a little bit bigger than the ones in Champaign. I haven't played any role-playing games yet here so I don't know what the scene there is like. As far as miniatures go, it seems like I may be in luck. I like miniatures games because of the strategy and tactics, but I don't really like haveing to paint and maintain all the miniatures. At the Haunted Game Cafe, I saw a game called Malifaux, which is a miniatures game where each side only has a few miniatures (a starter army has about 5 miniatures, compared with several dozen for a game like Warhammer). One of the factions in the game has the ability to summon new units during a battle, which adds clever new strategies and tricks you can do. Back in Champaign, I looked into Malifaux and they advised against that faction because you have to have the additional miniatures for the extra units in order to be able to summon the extra units. I asked about that here, and they said they don't play that way here. When we came here before on our house finding trip we saw a game store called Duelist Kingdom in Loveland, but that store is closed now. Fortunately, it turned out that the reason it was closed was because it was bought out by a bigger game store called Grand Slam Games and Comics, but I have only been there once so far.

Live Action Role Playing

There is an Amtgard group in Fort Collins, which meets on Sundays, and one in Denver, which meets on Saturdays. I went to the one in Denver just to check it out. It was sizable - about 20 people showed up - but it was not nearly spectiacular enough to be worth the trip all the way up there on a regular basis (I had to take an airport shuttle from Fort Collins to the Denver airport, then another airport shuttle from the airport to the park). During the battlegame there I aplayed an archer, and about halfway through the game the person running the game pulled me aide and said "we have to talk about your arrows." For a second I thought I was doing something wrong, but the real problem was that I was so effective with the arrows he thought it was unfair for the other team. (Part of the reason was that the scenario had the opposing team transporting a torch between two locations, and they are required to stay near the torch. This made it so they were all in one place and easy to hit, and they were unable to chase me down.) I went to the group in Fort Collins, and I was originally planning to take the bus there but I forgot that the buses don't run on Sundays, so I had to take a cab. When I got there the people there said I must be really dedicated to the game in order to be willing to take a cab. There weren't a lot of people here that day so we didn't do a whole lot exciting (apparently the previous week was a big tournament, so everyone was tired from that, plus it's the first week of school). Additionally, I learned that there is a Belegarth group in Loveland that also meets on Sundays. That group has a "small" practice with 20-25 people each Sunday, and then ion the first Sunday of each month they have a "big battle" with 50-75 people.

Wednesday, August 3, 2011


After lots of hard work, I finally submitted the approval form for my thesis this morning.

Actually, I'm not technically done yet. First of all, the form is submitted but there's still an electronic thesis deposit process I have to go through. Also, my advisor still thought that some of the citations weren't adequate, so I agreed not to do the electronic thesis deposit until after I had fixed those issues. Also, I have to make sure that all the documentation for the software is updated. But I can easily do all that from Colorado, and I have plenty of time between now and when my job starts.

Anyway, I'm off to GenCon now, and then on to Colorado! I'll make sure to keep you updated.

Tuesday, July 19, 2011

Origins 2011: Part 4 - "Rules of the Game"

First of all, today I learned that John, the owner of one of the local game stores, read my previous posts. He didn't agree with my contention that necromancers are environmentally friendly, because "rather than letting the corpses return to the earth, they're just going to send out [the undead] to do more harm" and "no necromancer is going to raise skeletons to clean your house or something."

Second of all, another thing I did at Origins is the following. Last time, I mentioned that I didn't get a chance to tell the author of the Hero System books about what I thought about the quality of his writing, but this time, I did. Of course, he said that he "disagreed completely" that the writing was too wordy, and said that the reason for the wordy writing was that his customers demand detailed rules. I am under the opinion that the same information could have been provided in a more concise way.

Rather then talk more about the details of the Hero System, the rest of this post will be about a more general topic - how the differences of opinion between me and some of the other people I play with about the rules of various games reflect fundamentally different ways of looking at game rules.

Consider the following conversation that I had with another Amtgard player. (This was a long time ago, so some of the details like the names of the spells are probably incorrect, but the general idea was the same.)

Him: "There's a gray area in the rules with the 'Dimensional Portal' spell. If two people are both under its effects, can they cast spells at each other?"

Me: "Why? What's unclear about it? The spell says that it takes a player out of game. Under the definition of out of game, it says you can't be affected by anything. So it seems obvious that they can't affect each other."

Him: "Yes, but it's the same out-of-game area."

Me: "What do you mean, out-of-game area? The rules don't say anything about out-of-game areas. You're either out-of-game, or you're not."

Him: "But in Dungeons & Dragons, the 'Dimensional Portal' spell does work that way."

Me: "This game is not Dungeons & Dragons. The rules of Dungeons & Dragons have no force in Amtgard."

The cause of our disagreement was that I was looking at the rules as a self-contained set of information, while he was thinking of the rules as codifying some pre-existing conception of how he thought the game should operate (if you're both transported to the same other dimension, you should both be able to affect each other).

A similar thing happened when the new 4th edition of Dungeons and Dragons came out a few years ago. I was reading some articles online discussing the new system and comparing it to the previous editions, and one of the most common complaints was that the new system "didn't make sense." For example, in the previous edition, fighters generally had only one or a few attacks that they had to keep using, while wizards had lots of spells that they could each use only a couple times per day and after those were done their powers were very weak. 4th edition balanced out the two classes by giving all classes some powers that they could use all the time, and some powers that were restricted to once per encounter or once per day. Lots of people didn't think this made sense because why would a fighter not be able to use a specific move once he had used it once earlier in the day? At first, I was really confused about why this would be a problem. I mean, true, maybe it isn't realistic. But I can't think of any criterion of realism that "I can magically throw a fireball, but only once per day" would pass, but "I can stab the dragon with a sword a certain way, but only once per day" would fail. And there are all sorts of physical phenomena that do happen in real life that are counterintuitive (have you ever watched MythBusters?) so I don't see why the fact that it doesn't fit with your intuitions about how fighting should work should be a problem. Again, this was a case where I understood what was going on because I just looked at the rules as a self-contained system, while others got bogged down because they tried to fit how the rules worked with their pre-existing conceptions of whoe combat should work.

Of course, sometimes things work out the other way around and my method of thinking is a hindrance. One example is some problems I was having with archery in Belegarth. There was a rule that you had to draw your bow back only half way when shooting at an opponent within 15 feet. (The issue is that if you shoot a target at full draw at close range, then the arrow will be going very fast, and is likely to hurt.) People were complaining that I was not following this rule, so I brought a tape measure so I could practice judging distance. This didn't completely help, so I came up with the idea like taking video and then going over it afterward so we can see what the distances were, and whether I was judging them correctly. They said that it wouldn't work because "there are too many variables." I was confused - I thought there was only one relevant variable: the distance to the target. At one point one of them tried to help me by asking me to stand in one place, then backing away and saying "okay, this is 15 feet." When I asked to measure to ensure that his judgement was accurate, he said that "it doesn't matter" whether it's accurate or not. This made me even more confused: how can it possibly not matter?

The problem here seemed to be that I was focusing on the particular rule about 15 feet, while what they probably had in mind was a more general concept about how to do Belegarth archery safely, which is why they thought there were "too many variables," and getting the distance right isn't the most important factor. It seems to me, though, that if the 15 foot rule isn't a good proxy for safety, then why is it in there at all? It would make more sense to say something like "The velocity at impact shouldn't be more than X feet per second," with X chosen appropriately. Then you could test to see what combination of draw distance and ranges given you that velocity (this would only need to be done once for each bow, before any battles).

Basically, I tend to interpret things based on what they say. If the game mentions 15 feet, I assume that they mean 15 feet. If they actually mean something else, then they should say something else.

Sunday, July 10, 2011

Origins 2011: Part 3 - "Learning From the Masters"

Another thing I did at Origins was go to some seminars. I did this because the seminars are one thing you can only really get at gaming conventions, and lots of them are interesting. At Gencon I went to a seminar on balance in games that I really liked, so at Origins I signed up for two seminars that sounded interesting: "Making Magic Real" and "Internal Consistency." When I got to the seminars I found out they were about books and literature rather than games, but they were still interesting. The seminar on "Making Magic Real" was given by fantasy authors R.T. Kaelin and Jean Cade, and they talked about how good stories need to have limitations on the magic. I mentioned that games are good sources of ideas because games are all about setting up limitations - for example, in "Magic: The Gathering" you have to draw a random set of cards at the beginning and can only cast what is in your hand. They said this would be a good idea for a story - a mage who doesn't know what spells he is going to get each day. The seminar on "Internal Consistency" was given by science fiction author Timothy Zahn. He had a list of a series of ten plots from different stories and asked us to describe what was inconsistent about them. For example:

PLOT: A small, ragtag resistance force tries to overthrow a universally hated dictator.

PROBLEM: If the dictator is universally hated, why is the resistance force so small? (Perhaps most people are too afraid to rise up, but in order to project his power the dictator would need a police force and army, and those people at least would have to support him.)

PLOT: The last two humans on Earth seek shelter from the vampires.

PROBLEM: If there are only two more humans on Earth, where are all the vampires getting their blood to feed?

Overall, both seminars were fun to go to. One thing that was funny was during the "Internal Consistency" seminar when Zahn was talking about how writers can make their stories more consistent. One example he gave was the "Jurassic Park" movies and television shows, where the security system that is used to keep the dinosaurs in was very poorly designed - "even zoos have better systems for keeping animals penned in." He suggested that one thing writers can do to make their stories better is to do more research. For example, Zahn suggested, if you were writing a story like that you could "call up your local zoo and ask them to explain how to design an impenetrable system to keep animals in = and how that system could be beaten." Of course everyone in the room laughed, because we all had exactly the same reaction - that the response you would get is similar to what would happen if you wore this "Personal Electronics Vest" when going through airport security.

Saturday, July 2, 2011

Origins 2011: Part 2: "Knights in Columbus"

As before, one of the fun things to do at Origins was the LARPs (Live Action Role Playing). The National Security Decision Making Game was running, although I didn't participate in it. Even though I liked it the first time because of the novelty, it seems like in order to get into it you have to be able to manipulate people, and that isn't a skill I am particularly good at. I did three different LARPs: “Nero”, which is a swordfighting game like the ones I've already talked about, “TerrorWerks”, a science-fiction adventure where you shoot enemies with Airsoft weapons (the enemies shoot back with Nerf guns), and “Rising Lash,” a game where you go through the dark, solving puzzles and fighting zombies. Nero was a three-part adventure where you were trying to rescue Lady Serenity, an adventurer who was kidnapped by an evil necromancer. (By the way, how come necromancers are almost always evil? I mean, all they're doing is recycling decomposed organic waste. It's environmentally friendly!) Anyway, in Part 1, we started out by going and fighting some orcs, who had a map saying where Lady Serenity was being held. The next two parts had us journey there, and in the third part we finally reached the evil lair. As you can see from the picture, the door was guarded by a magical Sudoku puzzle. Once we got in, our leader tried to negotiate for the prisoner's release by offering a magical item:

Leader: “I offer this magic ring worth 120 gold pieces for the girl!”
Boss: “There's no way that's worth that much.”
Leader: “Even if I were overstating its value by half, it would still be worth 60 gold pieces.”

I tried to point out the mathematical error but he didn't understand it. Anyway the boss tried to double-cross us but we got rid of the bad guys. Also, I volunteered as an NPC so I could see the adventure from the monster's eyes.

In TerrorWerks, we were soldiers trying to invade a robotics research facility where a bad guy has uploaded a virus to the central computer which reprogrammed the robots to be hostile. Our goal was to fight through the robots and get to the central computer to install the antivirus software. I played the engineer, and my special power was to unlock the doors – I had a kit with wires that I was supposed to connect between certain points on a grid to light up a bulb, and I also had a gun to defend myself. There were also computers that had information on them, such as that the big “super-robot” at the end has a control panel on the back that you could use to turn it off. When we got to the robot, one of the other players disabled it with a grenade while I ran around back to the control panel. The robot turned back on and no matter how many switches I flipped I couldn't turn it back off. When I tried to run back away from it I tripped over one of the poles holding up a wall and dropped my gun, but fortunately my teammates where there to back me up. Eventually we got rid of the evil robots, put the antivirus in, and got out.

Rising Lash was a relatively straightforward zombie game. We go through a series of rooms fighting zombies, and if you get hit you fall down. You can be healed by a doctor, but you get infected, reducing your combat capabilities. You can get rid of the infection with an antivirus (the biological kind this time, not the software kind) but there are a limited number of those. At the end of the scenario, if you survived without getting infected (or have an antivirus to heal you) then in the next scenario you level up and get extra powers. The scenario we did this time was pretty easy and pretty much we all got out alive.

By the way, if you are into video games you have probably heard about the so-called “freemium” business model. This is where the main game is free but you can spend real money for benefits in the game, such as in-game items. A lot of free-to-play MMORPGs use this model, and apparently some of the LARPs have caught on to the idea. For instance, in the zombie game if you buy one of their promotional T-shirts and wear it to the game you get extra armor. TerrorWerks also sells promotional “swag” and has a tiered reward system where one piece of swag gives you extra health, two pieces gives you a healing item, and so on.

Also, in keeping with the whole “being a hero and helping people” theme, there was a blood drive going on. There was an announcement on the PA systme that said they wanted as many people to donate as possible because there was a “critically fortunately I wasn't able to because I went to Vietnam last year.

Tuesday, June 28, 2011

Origins 2011: Part 1 - "A Hero's Journey"

Last week was the Origins gaming convention in Columbus, Ohio. I wrote about it last year on this blog, and I went again this year. The first interesting part of the adventure was getting there. I originally booked a combination flight/hotel deal on Travelocity. The flight was from Champaign, through Chicago, and then to Columbus. However, the day of the flight, I was informed that the flight from Champaign to Chicago had been cancelled, and they automatically rebooked me on a flight the next day. I looked online and found that if I took a Greyhound bus to Chicago, I could still make the flight from Chicago to Columbus, so I called Travelocity and asked them to book me back on the original flight. However they informed me that was impossible because the flight from Chicago to Columbus was also cancelled. I wasn't sure they understood what I wanted, because I looked online (if you put the airline and flight number into Google it will give you the status of the flight) and that flight was showing as on time. However, when I called American Airlines, they told me the same thing. Eventually I decided to just not use the outbound ticket and take a bus from Champaign to Columbus instead, and take the plane back. (I felt really stupid for booking the flight in the first place and not remembering that there was a bus, especially since I took the bus from Champaign to Columbus to get to my brother's graduation.) looked online to see if I could get a refund for the part of the ticket that I didn't use, and I actually found that for some airlines if you don't use the outbound portion of the ticket, they won't honor the return portion. So I had to call American Airlines to change the ticket. I called and was directed from phone number A to phone number B, then to number C, then back to A, then to B again, and finally after about half an hour of waiting they told me that they were able to change the ticket, and I wouldn't get a refund because it was booked through an external source, but it wouldn't cost me anything extra. (It would certainly have been annoying if they charged me extra for not using part of the ticket.) Anyway, it worked out and I ended up in Columbus the night I expected to. Also, it was a good thing I decided to take the bus because as it turned out, the flight the next day that they originally rebooked me on was also cancelled.

So here are a few things I learned. First of all, always check to see if there is a bus or train before booking a flight. Second, I wonder why sites like Travelocity don't also incorporate things like buses and trains into their tool - it seems like it would be useful to have a tool that figures out the best/cheapest way of getting from point A to point B whether that involves a bus, train, plane, or some combination. I guess it just doesn't come up that often. Third, always book directly through the airline if you can because it is easier to change your flight that way if necessary. Fourth, according to the Bureau of Transportation Statistics, the Champaign-Urbana airport has an average of 28% of its flights delayed and 6% cancelled, compared with the national average of 20% delayed and 3% cancelled. After I move to Colorado I will usually be using Denver International Airport, which is better at 18% delayed and 1.6% cancelled, which of course makes sense because the people who work at the secret underground base there wouldn't want their evil plans ruined by flight problems. Of course, if there really was an evil conspiracy going on there, information about it wouldn't stay posted on Wikipedia. Or maybe that's just what they want you to think, and it's a clever diversion. (Of course, I don't actually believe that there's a conspiracy or anything, I just thought it was funny.)

But that's just part of the adventure. Next time I will tell you about what happened after I got there!

Friday, June 17, 2011

Interesting Pictures: Gaming

Will you look into the world of gaming? Games show many things.

Things that are...

... things that were...

...and some things which have not yet come to pass.

I wonder what the "non-simplified" version of this game looks like?

Although gamers are not usually major consumers of personal hygiene products, this manufacturer has developed an innovative way to market to this under-served demographic.

A recent "Magic: The Gathering" card set focuses on the conflict between the artifact-based Mirrans (not shown) and the virulent Phyrexians (represented by the symbol on the box). Evidently, the City of Champaign public works department supports the Phyrexians.

Thursday, June 16, 2011

Debit Card Swipe Fees

In the news recently there is talk about legislation to reduce the fees that retailers pay to banks for debit card transactions. The fees currently average 44 cents per transaction, and the proposal is to cap them at 12 cents per transaction. Here are my thoughts:

- Clearly, the socially optimal amount to charge for swipe fees is equal to the marginal cost. And the marginal cost is probably very small; I imagine most of the costs of running the transaction system are fixed costs that don't depend that much on number of transactions.

- Of course, that only really matters if debit card transactions are at least somewhat price-elastic; i.e. number of transactions is affected by how much they cost. If the number of transactions is unaffected by cost, then changing the fee just redistributes money; it doesn't affect overall efficiency. (Of course, people do care about how the money is distributed.) And I would imagine that the price elasticity is very low: consumers don't care about swipe fees when they use their debit card (since they don't pay them) and most retailers don't choose not to accept debit cards just because of the fees (except sometimes for small transactions).

- The discussion from both sides seems to be centered on whether it will help or hurt consumers, which is reasonable. The pro-regulation side says that businesses will pass the savings on to consumers, while the anti-regulation side says that will not necessarily occur and banks will be forced to increase other fees or reduce perks like free checking to make up for the lost revenue.

- From the retailer's perspective, the swipe fee is like a tax on the transaction, so whether it's the consumer or the producer that ends up paying it depends on the relative elasticity of supply and demand for the goods, as described here. Of course, almost none of the coverage that expresses opinions about this questions even mentions price elasticity. (You could do a similar analysis to answer the question about whether banks will increase other fees; think of the reduction in swipe fees as like a tax on the banks based on how often their customers use debit cards).

- Of course, I don't have any data on the questions above, so I don't know who is correct. But one thing I did notice is that pro-regulation advocates say it will "help small businesses" and take money away from the "big banks", while anti-regulation advocates say that it "helps giant retailers" at the expense of "small credit unions." My question is: How did the whole "big business equals bad, small business equals good" thing start? I mean, isn't the theory behind capitalism that the way businesses become bigger is by improving efficiency to lower costs and responding to the needs of their customers to increase revenue? Maybe Joe Kernen is right that we are being indoctrinated with anti-capitalist values.

Monday, June 6, 2011

News Quiz

1. Which of the following is an actual reality show about to enter its second season?

(a) The Auditors, which features stories of taxpayers who have been audited by the IRS, from the initial contact through the final accounting of taxes owed.

(b) Extreme Couponing, in which shoppers save thousands of dollars through strategic use of coupons, store promotions, and similar deals.

(c) Health Care Hustle, which features a "behind-the-scenes" look at the business side of a doctor's office in Oakland, California.

(d) Wikipedia Wars, where contestants compete to use Wikipedia to find the answers to trivia questions while strategically editing it to confuse their opponents.

2. Which of the following is an actual recent scientific finding?

(a) The gene responsible for blonde hair also produces neurotoxins which lower intelligence.

(b) Using Twitter and Facebook immediately after studying for exams improves grades.

(c) The most important factor in determining how much students learn in college classes is how funny they think their professor is.

(d) Showing Apple fans images of Apple products activates the same areas of the brain as showing religious believers images of deities.

3. Sarah Palin recently made which of the following false claims about American history in an interview?

(a) Part of the purpose of Paul Revere's famous ride was to warn the British that they would face American resistance.

(b) Alexander Hamilton once gave a speech warning of the dangers of financial bailouts.

(c) Abraham Lincoln freed the slaves because he wanted to sabotage the Southern economy.

(d) President Kennedy ordered Predator drone strikes on Cuba during the Cuban missile crisis.

Saturday, June 4, 2011

Interesting Pictures: Politics

Here are pictures of Lyndon LaRouche supporters, from my previous post. Despite their kookery, they promote some sensible policies like increased investment in science and technology.

In order to do that, though, they'll first need to cut excessive spending. Unfortunately, nobody wants their own pet program cut.

Maybe the cause of the budget problems is that our children are being indoctrinated with anti-capitalist values in our schools. (He must have gone to a different school than I did, because I don't remember being indoctrinated with anything.)

Friday, June 3, 2011

Interesting Web Sites: Economics and Statistics

Another feature of this blog that I am going to start writing more often is web sites that I think are interesting. I already mentioned Cheap Talk,a blog written by economists that applies economic and game theory analysis to topics as diverse as crime and politics, and corruption, and has lots of interesting new ideas. While browsing some of the old posts I came across an article that mentions a company that I interviewed for a job at (but did not get an offer.) There are lots of very interesting blogs written by economists; probably the most well known one is Marginal Revolution, and if you scroll down you will see links to other blogs about economics, inclusing one about statistical analysis.

Wednesday, June 1, 2011

Interesting Pictures: Technology

With my new iPhone I have been taking lots of funny and interesting pictures, and I haven't gotten around to posting them on my blog .. until now! This is the first of a series of posts with pictures in them.
Apparently, this port replicator is not a Jedi Master yet. And what's that on top of it?

As it turns out, its just a little thing to change the "gender" of a VGA connection. (On many different types of connectors, the part that sticks out is referred to as the "male" side, and the socket you stick it into is referred to as the "female" side. The intended metaphor is left as an exercise for the reader. For the answer, see here.)

This pinball machine is in the ACM (Association of Computing Machinery) lounge. As you can see, not all computer science students are just into software; they like to do stuff with hardware too.

This computer is hooked up to a vending machine, and enables you to pay for caffeinated drinks using your university ID. It keeps track of the total amount of calories and milligrams of caffeine purchased.

Not all advancements in technology involve high-tech electronics. One example is the microwave popcorn bag. While versions of this technology date back to 1973, a recent breakthrough holds the promise to significantly reduce cleanup effort.

Tuesday, May 24, 2011

More Interesting Stuff

A couple days ago I started the Weight Watchers diet program. Weight Watchers is cool because it is based on a point system, where each food has a point value based on the amount of fat, carbs, protein, and fiber, and you can eat whatever food you want provided you stay under the target point value depending on your weight and activity level.

I just finished my classes, so no more tests or exams ever! But I still have plenty of work to do because I have to write a paper for a conference which is due on July 6, and then I have to expand that paper into a thesis which is due on August 8.

Today in the mall in Champaign I found a stall selling "Power Balance" bracelets which are similar to the bracelets I mentioned in the previous post in that they work by the placebo effect. They cost about $30, but you can save a lot of money and buy functionally equivalent "placebo bands" here.

Another thing I am planning to do more often on this blog is to post links to other web sites which I find interesting. One interesting web site I found is Cheap Talk, a blog written by two economists. They have lots of discussions of economic theory applied to a variety of topics including game theory and ticket scalping. (Under the "game theory" tag if you scroll down you will see a post called "how to get bumped" about how to score free airline tickets, and below that is one about ticket prices in restaurants which is also interesting.)

I just got an email asking me to support Illinois athletics by switching my energy provider to "Fighting Illini Energy." One of the options that they say they offer is the ability to choose a plan that provides 50% or 100% of your energy from renewable energy sources. (What does that even mean? I mean, isn't electricity fungible? All of it goes from the power plants, onto the grid, and then into your home. I didn't even think it was possible to track a particular "unit" of electricity from the power plant to your home.)

The gaming club on Saturdays at UIUC is still going on over the summer. Since it is summer the building we normally play in - the English Building - was locked so we ad to go into the student unoin. The only problem was that the area of the student union we played in had a TV tuned to MTV, so whenever a song came on that any of the other players had heard before, they would all start singing along and making lots of noise, and they kept doing that even after I asked them to stop several times. Apparently they thought it was funny. I think what I will do next time is say something like "Let's say you had a friend who was in a wheelchair, and you kept taking the wheelchair away so he couldn't get around. Now maybe you might think it was funny but probably he wouldn't think it was funny. So just like some people have a hard time getting around without wheelchairs, I have a hard time playing games when everyone is making lots of noise. Maybe you might think it's funny to make lots of noise so I can't concentrate, but I don't think it is funny."

Thursday, May 19, 2011

Weird Stuff

Today in the airport I saw a group of people handing out literature for the LaRouche movement. I've heard that the LaRouche movement is a bunch of kooks, but I was interested in learning more. Part of what they said made some sense, like how we should spend less money on the bailouts and more money on technology and infrastructure. But a lot of their literature descended into conspiratorial kookery, such as claiming that JFK was assassinated by "British Empire bank-connected assassins" for wanting to get us out of Vietnam, claims that White House science adviser John Holdren supports forced population control (no, he doesn't). But their literature also taught me something about science that I didn't already know: it talked about using electromagnetic fields to predict earthquakes, and I thought that didn't make any sense but I looked it up and it turns out there is scientific evidence for that.

Another thing sort of related - in the mall today I found a stall selling "negative ion bracelets" for $25. It is an ordinary rubber bracelet that (according to the person selling it) had a small amount of volcanic ash embedded in it to emit "negative ions" that supposedly improve your strength and balance. I asked for a demo and he gave me a "balance test" with and without the bracelet, but the bracelet didn't make much of a difference, which makes sense because there's no scientific evidence that the bracelets do anything. Also, it seems that the people who wrote the brochure about it didn't know much science either, because it said something like "negative ions are natural ... when water mist falls to earth, it loses an electron, which turns it into a negative ion." (Of course, electrons have a negative charge, so if the water "lost" an electron it would gain a positive charge.)


And also, something that might be interesting on the Internet - the web site I linked to above is part of a network of "Stack Exchange" web sites which allow you to ask questions and get and look up answers on a variety of topics - it started off with computer programming but on expanded into lots of other fields like math and statistics. It works a lot like Wikipedia in that it is entirely community driven where people post answers to and edit each others' questions.

Tuesday, May 10, 2011

Job Search Conclusion

So my long job search is finally over, and I got a job at Numerica Corporation. I had interviews at a couple interesting places. One was Two Sigma Investments, a financial company based in New York City. I got there a day before the interview, which gave me some time to explore the area. I tried to get a taxi to the Dave & Busters in Times Square, but I tried to get in a taxi and they said they didn't know where it was (even after I showed them the map on my iPhone.) I took a subway there but when I tried to go back, my phone was out of battery power so I couldn't use the GPS to find my way back. I again had no luck finding a cab, so eventually I had to go into a subway station and use the pay phone to call the hotel to get directions back. The next day I had my interview which ended early, so I got to use the extra time to go to a local game store. Then I got to the airport and the flight was delayed. The flight landed back in Chicago about two hours later, and I had assumed I had missed my connection so I used the rebooking phone to call for rebooking, and they said that the only flights they had were for two days from then. I decided instead to just stay in a hotel and take the train home the next morning, but while I was walking back to talk to the airline about reclaiming their backs I saw the departure board which saw the connecting flight was also delayed, so I was able to get on it and get home. Also, one of my professors was on that plane coming back from an NSF panel, and he took me home. Unfortunately I didn't end up getting the job.

Lots of interesting stuff happened on the interview for Numerica. My flight was originally scheduled to leave at 7:00 AM. I overslept and woke up at 6:30, and rushed out the door in the vain hope of getting to the airport in time. I got there at about 7:10 but fortunately the flight was delayed until that afternoon. I got rebooked on a 2:15 PM flight which gave me time to go back home, do some stuff at school that I needed to do, get the charge for my laptop (which I left at home), then go back to the airport. On the flight from Champaign to Chicago a different professor I know was also on this flight. I landed at the Denver airport and took a taxi out to Loveland. The hotel was next to a strip mall so I was able to go out to dinner and also finish up a presentation on my research, which I gave as part of the interview. The interview went vrey well. During lunch, I mentioned that I was interested in board games, and one of the people who worked there was also interested in board games and knew of some board game stores in the area, and offered to take me to them that evening. It was probably the best interview experience I have ever had.

So I decided to accept their offer, and I will be starting work by the end of August. I definitely think that stopping with a Masters degree rather than continuing with a Ph.D. was the right thing to do. I'll be able to continue doing what I love doing, and I'll also be making a lot more money than I am as a graduate student. I am not sure what I will do with all that money, but there are other people in this world who need the money a lot more than I do.

Monday, May 9, 2011

An unusual poster

For the past few weeks there has been a whole bunch of posters up in the Student Union that say "Rise Against Bad Religion." I assumed these were advertising some sort of protest march against religious extremism, but I was in the game store today and I heard people talking about it, and it turns out it was actually advertising a concert featuring the two bands "Rise Against" and "Bad Religion."

Monday, April 4, 2011

In an email from Maryland PIRG

Maryland PIRG (Public Interest Research Group) is a student advocacy organization that I somehow got on the mailing list of at Maryland and they still send me stuff. Their most recent email included the following:

"Some proposals in Congress would significantly cut student aid - the U.S. House voted to slash Pell Grant funding by $5.7 billion – cutting, on average, $785 in financial aid for over 9 million students."

"over 9 million" * $785 is over $7 billion, not $5.7 billion. (On the other hand, this may make sense if the $785 number is the median, and not the mean.)

Friday, April 1, 2011

New Blog Feature

As you may notice, I went back and added category tags to all my blog posts. This makes it easier to find previous posts. For instance, if you want to look at all my Gaming Math problems, you can click on "gaming-math" on the right hand side.

Monday, March 28, 2011

From USA Today

A recent article in USA Today discussed standardized testing in D.C. public schools. It mentioned that some high-performing schools have very high numbers of answers erased on tests (when you erase an answer on the Scantron sheet and put in a new one, the machine can detect the residue). The article claimed that this could be possible evidence that teachers tampered with the tests prior to submitting them for grading.

The following quote appeared:

"Noyes is one of 103 public schools here that have had erasure rates that surpassed D.C. averages at least once since 2008. That's more than half of D.C. schools."

This statement is not too surprising. If the distribution of erasure rates were symmetrical, then in any given year half of them will be above average. Since the schools above average will change from year to year (if only due to random variation), then over a 3-year period more than half of the schools will be above average in at least one of those years. (For instance, if the erasure rates are random and independent, then each year each school will have a 1/2 probability of being above average, so each school will have a 7/8 probability of being above average in at least one year.)

Aside from this sentence, the rest of the article was actually fairly good statistically. It mentioned that this particular school hasd erasure rates so far higher that it wasn't due to chance, and included a lengthy discussion of possible alternative explanations for the data.

Friday, March 18, 2011

Gaming Math - Problem 17

Recently, University of Illinois computer science professor Sheldon Jacobson has developed a mathematical model to predict the distribution of seeds in the Final Four of the NCAA basketball tournament. (The NCAA basketball tournament consists of 64 teams divided into 4 regions with 16 teams each. It is a single-elimination tournament, and within each region the teams are "seeded" from 1 to 16, with the teams in order from strongest to weakest. The team that wins in each region goes to the "Final Four".) There is a web site allowing you to explore the results of the model. A key finding, reported in media coverage about this web site, is that the most likely combination of seeds is not (1,1,1,1), but rather (1,1,2,3).

Problem 17: Seeds of Victory

According to the web site, the probability that all four 1-seeded teams will go to the Final Four is 1 in 31.82, while the probability that two 1-seeded teams, one 2-seeded teams, and one 3-seeded team will go to the Final Four is 1 in 14.05.

In the article, Jacobson made the following statement:

"But I can tell you that if you want to go purely with the odds, choose a Final Four with seeds 1, 1, 2, 3.”

For concreteness, suppose that you are asked to pick, for each region, which team is going to the Final Four, and you are only considered "successful" if you correctly pick all four regions. Assuming that the probabilities given by Jacobson's model are accurate, is it true that picking a (1,1,2,3) split is more likely to be successful than a (1,1,1,1) split?

The answer is here.

Wednesday, March 16, 2011

Job Search

So, last week I made my decision: I will be switching to a Masters degree program. This does mean that I won't get to do that internship at Lawrence Livermore, because the internship requires that you commit to staying in school through the Fall semester. This actually turns out to be okay because I will get to stay at school through August to finish up my thesis. There's a fair bit of work still left; I have to finish up all the remaining programming work, write documentation on all my code so that my replacement can figure out what's going on after I leave, and of course write the actual thesis. Also, I have started to look for full-time jobs for after school.

I went to the Engineering Career Services office and got my resume and cover letter looked at, and they basically had me rewrite the whole thing using the format described in the career guide, which made it look much better. I took the new resume and cover letter over to the Graduate College's career services office, and they told me that my resume and cover letter looked very good, and they only had a couple minor stylistic changes. I searched for jobs online and through job posting on bulletin boards in the Computer Science department. So far I have submitted resumes to 9 companies, and have gotten phone interview requests from 2 of them. One of them was MathWorks, which makes Matlab. Another was Palantir Technologies, which makes a data analysis and visualization platform (read the web site if you are interested). They wanted to interview me for a "Business Development" position, and I'm very interested in what that position entails. I'll report back when I see how the interviews go.

And one more thing. When I was in elementary school and people asked me what I wanted to be when I grew up, I would answer "math test-question editor", because I took lots of math tests like the Math Olympiad during that time and often I found the test questions ambiguous. During my online job search, I found an online job advertisement for a math test-question editor. But things have changed a lot in the past 15 years, and I decided not to apply for that job.

Thursday, March 3, 2011

The results are in

I have two pieces of good news to report:

First, I passed my qual! I haven't got the “official” announcement yet but Jeff told me that the qual has been graded and I passed it.

Second, all the votes are in and I am now going to be an official member of House Valdemar in Belegarth. They are in the process of making the special tunic for me and I will have an official “initiation ritual” next Saturday, March 12.

EDIT: I typed "not" instead of "now" before.

Monday, February 28, 2011

News Quiz!

Now it's time for a new feature on this blog: the News Quiz! These are some questions about local (and some not-so-local) news events - whatever I find interesting.

1. So-called "Castle Doctrine" laws give citizens the right to do what?

A. Participate in medieval re-enactment.
B. Use lethal force to defend their homes.
C. Engage in collective bargaining over rent payments.
D. Build moats around their property.

2. Which of the following companies have been recently praised by gay-rights advocates, and why?

A. Verizon, for canceling a planned ad campaign that featured two characters getting "stuck" in a same-sex relationship due to a competitor's poor cell-phone service.
B. Bioware, a video game company, for announcing that the highly anticipated space-adventure video game sequel "Mass Effect 3" will provide the option to have the player's character engage in same-sex relationships with aliens.
C. Facebook, for giving users the option to set their Facebook status to "in a civil union" or "in a domestic partnership."
D. Wizards of the Coast, for printing a series of "Magic: The Gathering" cards that feature pairs of same-sex characters that get bonuses if you have both of them on the field at the same time.

3. A new iPhone app is designed to make it easier for religious believers to do what?

A. Pray
B. Confess
C. Proselytize
D. Find churches

4. The University of Illinois computer science department took it as praise recently when a report came out showing that the department is number one in what?

A. Academic integrity violations
B. Nobel Prize winners
C. Percentage of students using alcohol
D. Average number of Facebook friends



Question 1
Question 2
Question 3
Question 4

Thursday, February 24, 2011

Gaming Math - Problem 16:

Problem 16: "Fall Out Pick Up"

The video game "Fallout 3", and its sequel, "Fallout: New Vegas", are set in a post-nuclear-war world where most civilization has been destroyed and the few people remaining alive must scavenge for supplies to stay alive. Each piece of loot that you can pick up has a weight and value. There is a limit to how much weight you can carry, and when you get to a town you can sell your loot for bottle caps (the game's currency) based on its value. The problem of maximizing the total value of items you can pick up while staying within your weight capacity is known as the "knapsack problem" and is a well-known NP-complete problem.

In the game, however, there is an additional complication. You only observe each item one at a time, and because of the dangers and rival scavengers it is impossible to go back and pick up an item that you dropped or left behind. So you have to make a decision about whether to pick up each item, as well as which items to drop in order to make room, as you see each item.

(a) Is there an algorithm that gives the optimal result in all situations? (There is no limit on the running time of the algorithm.)

(b) The "competitive ratio" of an algorithm is the worst-case ratio of the value of the solution found by the algorithm to the optimal solution. For instance, if an algorithm always gives you a set of items with value at least equal to half the value of the optimal solution, then its competitive ratio is 0.5. Does there exist an algorithm for this problem with competitive ratio greater than 0? If so, give one; if not, prove it is impossible.

(Hint: Imagine there was an "adversary" controlling the capacity and sequence of items, and it gets to observe which items the algorithm selects before deciding which new items to present.)

(c) Suppose that the capacity is C, and the highest weight of any one item is M. Give an algorithm for this problem with competitive ratio 1-(M/C).

The solution is here.

Wednesday, February 23, 2011

Breaking News: Solution To Illinois Budget Crisis!

As you may know, the State of Illinois has been facing a severe budget shortfall and has recently been forced into massive tax hikes. Also, in the 2008 election, then-candidate Mitt Romney accused then-candidate Rudy Giuliani of turning New York City into a "sanctuary city" for illegal immigrants in order to get more workers and tax revenue. Recently, it appears that Illinois is following this plan, becoming a "sanctuary state" for Democratic politicians who want to avoid voting on bills. Lawmakers have referred to themselves as "refugees", and have been stimulating the Illinois economy by purchasing essential items. There has been speculation about whether police would be able to arrest the rogue legislators and extradite them back to their home states to stand trial. As for me, I am just waiting to see what the Capitol Steps song about it will be like.

Tuesday, February 22, 2011

More on Echo360

Because I posted on my blog about Echo360, I have been contacted by a marketing person from Echo360 who is interested in what I have to say. Here is what I told her about my experiences so far.

I think Echo360 is a very useful tool, but there are some other features that would help. One thing I think would be useful is to integrate a discussion forum with the lecture capture. The way I would envision this working is that when a student is watching the lecture online, if he has a question he can click a button and type his question in, then the question would be tagged with a timestamp indicating what point in the lecture he asked that. And there would be a way to link to a particular timestamp in the lecture. Then the instructors/TAs can log on and look at the questions, and when you looked at a given question you would have a link to the associated point in the lecture. Or an instructor could answer by pointing the student toward a particular place in the lecture. This would be useful to me because oftentimes when I talk to students, they say the instructor told them something which doesn't sound right to me, but it's hard to clear up the confusion without the lecture in front of me.

Another problem, which is a little more technical, has to do with the sound. The way our setup works is that there are two microphones, one worn by the instructor and one "shotgun" microphone. The one the instructor wears has much better sound quality but only captures what the instructor says, while the shotgun microphone can capture everything in the room. So one of the things I have to do is when the instructor pauses for students to ask questions, switch to the shotgun microphone, and then switch back when the instructor starts talking. This often isn't very reliable and you don't get all the questions. So a useful tool would be to have two or more audio channels going into the system, and it would automatically switch between them depending on who is talking.

I'm also taking a TA training seminar where we are reading the book "Teaching At Its Best: A Research-Based Resource for College Instructors" by Linda B. Nilson. That book talks a lot about how traditional lectures aren't very good at promoting student understanding, and has lots of suggestions for how to improve lectures. For instance, one way of improving lectures is to periodically stop and give students a question to answer and discuss in order to keep them engaged. Something like this could be incorporated into Echo360 - if you had a system like the one I described in the first paragraph, then the instructor could put a question on the whiteboard and ask students to answer it by posting something. It might even be possible to set up a system where the instructor can set the lecture to automatically pause and ask the student a question, and not to continue until the student gives an answer.

Saturday, February 19, 2011

More Belegarth Action

Also this weekend I went to Wolfpack Opener, a large Belegarth event. We had to squish in the back seat of a truck because we were low on space in cars, but we got there fine. The battles were exciting, and especially since I am an archer it was fun because it's inside, so everyone bunches up and there are lots of easy targets. There are different types of battles including "line battles" wher everyone lines up in two lines and you fight each other, and also "four corners" battles where each player gets a different color wristband, each color has a corner associated with it, you are fighting against anyone who is not your color, and the referees will periodically call out a color and anyone who is dead with that color comes back alive.

Another thing is they're in the process of voting to see whether I get to become a full member of House Valdemar. So far the vote is going in my favor, but not all the votes are in and several of the key members who are supposed to vote haven't been out to practices in a while and we haven't been able to get ahold of them to get their votes. Maybe they're hiding in Wisconsin.

The qual is finally done!

I had my qual exams this Thursday and Friday. According to the qual web site, normally the qual has 8 questions on it, and a passing score requires "nearly perfect" answers to about 3 of the questions and partial answers to 3 more. This time there were 10 questions on the qual, and I was able to get complete answers to 5 of them and partial answers to 4 more of them. So I think I passed, though I won't know for sure until the results come in, probably next week.

One thing that this does mean for the blog is that you will get to see more of my "Gaming Math" problems. The main reason I haven't been able to put up more of those problems recently is not because I haven't played any games with interesting math or computer science problems in them, but rather because most of the time I can't actually solve the problems I come up with. But preparing for the qual has helped me get better at solving those kinds of problems so that means that you will see more of them.

Here is a problem:

Gaming Math - Problem 15: "For Science!"

In the board game "Battlestations," players control crew members aboard a spacecraft, and they are sent on dangerous missions. In one of the missions, the players are trapped in a region of space containing N wormholes, and the only way to get out is to go through the wormholes in a specified sequence. The only way of finding out what that sequence is is by using the ship's Science Bay, which allows the player to ask any yes-or-no question about the sequence.

1. In the scenario described in the game, N=4. What is the minimum number of questions required to guarantee figuring out the correct sequence?
2. For an arbitrary N, what is the minimum number of questions required? Find an algorithm that achieves this minimum number, and prove its optimality.

(Hint: Don't forget that you can ask any yes-or-no question about the sequence.)

The answer is here.

Monday, February 14, 2011

More school stuff

- I have just finished creating, assigning, collecting, and grading the first homework assignment of the year as a TA. This homeowrk was about formal logic, including propositional and first-order logic. (Propositional logic just has variables which can be either true or false, while first-order logic allows variables to be arbitrary objects, there are "predicates" that are basically functions which take objects as arguments and return a boolean variable, and there are "quantifiers" which allow you to say things like "for any X, P(X) is true" or "there exists an X such that Q(X) is true". We thought this part would just be review (these are Masters students in computer science, so we thought they would already know about logic) but some of them had trouble with simple things like the difference between validity (statement is true all the time regardless of the values of the variables) and satisfiability (statement is true for some assignment of values to the variables.) In fact one of the problems we had to "cancel" and make it an extra credit problem because it had to do with proofs in first-order logic, a topic we didn't cover (I didn't realize that we weren't going to cover it when I wrote the homework, and the professor didn't notice when he was looking at the homework before posting it)

- I have my Ph.D. qualifying examination this Thursday and Friday. I have looked at most of the previous quals and it seems like I pretty well prepared for it. Another thing is even if I do decide to only get a Masters degree, passing the qual is a good idea because if I pass the qual I am exempt from the distributional requirements for a Masters (there are still two distributional requirements, hardware and systems, that I haven't taken courses in so I would need to do that if I were to go that route).