Which Abstract Games are Fun?

I recently read a great post from Nick Bentley, a connoisseur of abstract board games.  In it, he argues about concretely defining the properties that make a ruleset fun.

Unlike standard board games, abstract games are usually lacking in a tie-together theme.  This can be a barrier to enjoyment for some because players are not immersing themselves the role of a megalomaniac field general or a real-estate cartel in Atlantic City.

What, then, is so attractive about abstract games?  Nick references an article by J. Mark Thompson about what properties of good abstract games.  Nick then adds his own property, speciousness, a False Clarity about good strategies.  From Nick's post:

The greatest games pull this trick over and over – just when you think you’ve learned everything, the scales fall from your eyes yet again, and yet again you realize the game isn’t quite what you thought it was. And then, even after you know better, you’re sometimes tempted to make suboptimal moves because they just feel so right.

This goes beyond a standard of computational hardness and connects with a more psychological aspect. 

My inclination is that speciousness is more common with partisan games than impartial.  Hmmm.  Go enjoy Nick's full explanation to see some examples and follow his thoughts.

New Ruleset Table

I spent a bunch of time last semester starting a new web table for ruleset properties.

Here is the result: Ruleset Properties

I'm still missing lots of rulesets.  You can help me by suggesting some.  If you do some snooping around the page source, you'll see how I'm generating the table from some JS objects.

I would also like to get a glossary up of CGT terms.  That's not coming any time soon, though, sorry.

Integers 2013 Site

The Integers 2013 website is up.  It's been up for a little while, sorry about the delay!

The conference takes place at the University of West Georgia Oct 24-27.

Moving to Colby College

Today I finished teaching my final class at Wittenberg University.  Starting in the fall, I will be teaching Computer Science at Colby College, where I graduated from 10 years ago.

What's going to happen to this blog?

Nothing bad.  I plan to keep up with it.  Although I'll have new courses to learn, I'll have slightly less courses each semester.  With any luck I'll be able to update more regularly.  (I can't believe that I was doing this three times a week when I started here!)

When are you going to teach CGT next?

My course this semester went really well.  I don't know when I will get the chance to teach this again, but I would really like to make that happen.  I came up with lots of good ideas this semester and would like a fresh chance to try them out.  Colby's CS department is separate from the Math department, so that may make it a little less likely, but who knows what the future holds? :)

I have a few more things I'd like to post about before the year ends, but there's lots of finals and grading left to do.

Teaching with LaTeX

I've noticed a problem teaching Math to Computer Scientists.  (Aside from the fact that many don't seem to think they need it.)  When written assignments are handed in, they are often a mess and work is not properly shown or pointed out.

To be fair, this is exactly what I did as a student.  When not writing out a proof, my written assignments had a gaggle of work followed by an answer that I circled.  I hope my poor linear algebra grader will forgive me someday!  I ignored directions to: lay things out nicely; put only one problem on a page; and remove abandoned or incorrect calculations.

Oops.

My proof assignments came out a bit better (because the order is part of the correctness) but I still failed to rewrite things after realizing adjustments were needed. 

Now, on the other side of the grading process, I see many papers that would benefit greatly from some organization.  Not only would it make them easier to grade (certainly a perk!) it would help bolster their grades.  By turning in an electronic version of the assignment, it's much easier for a student to go back and correct mistakes.  If a line in a proof is wrong in a hand-written paper, fixing it nicely means rewriting the entire page.

Computer science students are going to balk at that rewriting.  These are students learning to use the latest programming development environment, each of which lowers the number of keystrokes (or mouse distance) necessary to get their code written. 

Thus I'm highly considering teaching LaTeX the next time I'm in charge of discrete math.  Naturally this would cost me in terms of needing to cover it and make sure everyone knows how to use it.  There are some other downsides: namely that students would have an easier time inappropriately sharing their work.  With any luck they would still stick to the honor code!

The benefits would not just be for this course, however!  Knowing LaTeX is a valuable skill that they could reuse in an Analysis of Algorithms course as well as their other courses and projects.  I continue to replace WYSIWYG editors in favor of LaTeX for many purposes.  Every time I move a document to LaTeX I'm glad I made the switch.

Has anyone had experience forcing students to use (and probably learn) LaTeX?  I taught it once in our programming languages course, but only at the very end and only for two days.  What are some pitfalls or benefits I haven't considered?

An Update on the Summer Workshop in China

From an email from Fraser Stewart:  (I should have posted this sooner, I apologize)

Hi Everybody,

To update you on the status of the proposed workshop in China.  I have been given a budget, which will cover accommodation + food, for around 40 people, as well as a trip to see the terracotta warriors.  However, the event must take place this year.  So I need to set a date for this quickly so I can submit a budget to the financial department of the university, book hotels, rooms for talks and so on.  I would also like to stress that I have a very tight budget, so it may not be possible to cover everybody's expenses, but I will try to cover as many people as possible.

Due to the fact that CMS is taking place in June, and Integers in October, I would like to propose two times that I think will be suitable.

30 August - 3 September and 30 November - 4 December.

My plan is to have 4 days of talks and discussions, and one day to see the terracotta warriors.  We will also be taking submissions, and wish to publish a special edition of Integers.  All submissions will go through the normal peer review process, and a condition of attendance is that you must be willing to review at least one paper.  Also, as I said earlier, the money is very tight, so all attendees must pay their own air fare.

If you could please get back to me ASAP with two pieces of information that would help me out a lot:

1.  If you are willing/able to attend.

2.  The time you feel is most convenient.

Once I've had some responses, and have a better idea of attendance, I will send out a confirmation email and begin the organisation process.  Thank you everybody for your attention, and I hope to see you here.

Take it easy,

Fraser

 Please respond directly to Fraser at: fraseridstewart [at] gmail [dot] com

Update on Upcoming CGT Events

Integers 2013 has been confirmed and there is a possible conference next year in China!  I figured it was best to provide an update on all the upcoming CGT academic events:

Games at Dal(housie): June 4-7, 2013.  Talks will be held on June 5 (tentative) as part of the Canadian Mathematical Society meeting in Halifax, NS.

Integers 2013: The Erdos Centennial Conference in Combinatorial Number Theory: October 24-27, 2013.  This will be held at the University of West Georgia in Carrolton, GA.  The website for this is not yet up, but will hopefully be up soon.

Fraser Stewart is already planning ahead for a conference in China next year.  He wrote to me recently:

My name is Fraser Stewart, and I work for Xi'An Jiaotong University in China.  For those of you who don't know, Xi'An is a very historic and famous city in China, it is most famous for being home to the terracotta warriors.  I'm currently trying to arrange a conference/workshop here on combinatorial game theory, around this time next year.

The university has already said they are happy for me to do this, but I need to get an idea of how many people I should expect to attend.  I also want to publish a Games of No Chance style journal from the conference as well.

I am applying for some money so that I can have some invited speakers, and there will be a chance to do a little sightseeing while you're here.  Unfortunately though, due to the way funds are distributed in China, there won't be any money for air fares (even for invited speakers), so if you do want to come you'll need to arrange your own plane ticket.

If you are interested in coming, then please get back to me.  If you give me a rough time when you'll be available, then that will help me to set a precise date for it.  I do understand this won't be for around a year, so if you don't know yet then that's fine.

You can get back to him by emailing: fraseridstewart [at] gmail [dot] com.  He's hoping to hear back from lots of interested people!

I'm still trying to figure out which of these conferences I'll be able to attend.  Being at a small liberal-arts school doesn't give me much in the way of travel funds, but I'm at least hoping to be at Integers.  If you know that you'll be attending some of these, I'd love to hear about it in the comments!

Saturday: WittCon X

This Saturday marks WittCon X, Wittenberg's own gaming convention! 

As usual I'll be running two magic tournaments.  If you're not a Magic: TG player, make the trip to the center of the gaming universe* for the role playing and board games. 

I look forward to seeing you there! :)

Teaching CGT: speed bumps

A few quick notes on the current games course I'm teaching.  This is a combinatorial games course for undergraduates who are not necessarily math or computer science students. 

Some speed bumps on the road to CGT happiness:

* Math is hard.  Math without numbers is harder.  Often when I ask students to "show" something on the homework, they're not sure how to show the proper amount of work. 

* Values aren't coming soon enough.  I decided to skip ahead to Chapter 5 (we're using Lessons in Play) to get to the values.  The book hints at a lot of values ahead of time, but it would be easier to show more examples with values happening earlier on.  I skipped the end of Chapter 4 and probably should have skipped sooner.

* The book problems are tough.  I've needed to generate homework problems appropriate for undergraduates, which has taken some extra time.  I've shied away from the worksheets I used last time, but perhaps I should reincorporate those.

There are definitely some things that make going ahead easy, though:

* The students are not expecting me to prove things.  It's pretty easy for me to skip the more theoretical material in the book.

* The class is small and flexible.  I've been able to ditch my lecture notes and do other things when it seems appropriate.  I did this in class on Monday.

* I asked the students to force me to clarify whether I mean "ruleset" or "position" whenever I use the word "game".  They're very good at this, to the point where they call out whichever I should have said themselves.

I'm really looking forward to the point where I give students a new game ruleset and they can more deeply explore that on their own.  I really enjoy teaching this course and I'd like to accelerate progress to that point in future iterations.

CGT Upcoming Events and a Wittenberg Games & Topology Talk

I added a section in the sidebar for upcoming CGT events.  Here's some info about 2013 events:

At Dalhousie University in Halifax, Nova Scotia (Canada), the CMS will hold their summer meeting June 4 - 7.  Richard Nowakowski and Paul Ottaway are organizing a special session on CGT as part of the meeting.  There will be more information coming about that.

I missed Games-at-Dal 2012, but if there is enough interest, the 2013 incarnation will take place the weekend following the CMS meeting. 

Also, if the pattern of odd-numbered years continues, Integers 2013 will take place this fall.  I saw dates for October 24-27, but that is from a second-hand source. 

Lots happening this year! 

Our department was lucky enough to host a talk about games (not by me).  On Monday, we had Lynne Yengülalp from the University of Dayton speak about infinite-turn topological games.  The starting position of the game is a topological space.  For both players, a move consists of choosing a non-empty, open (not strictly proper) subset of the previous position.

Even though the move options are the same, the game is strictly partisan: the two players, NOT-EMPTY and EMPTY, have different goals.  If the result of the infinitely-long game is the empty set, then the EMPTY player wins.  Otherwise, the NOT-EMPTY player wins.  This is a bit unintuitive at first, but if you consider the infinite sequence of open sets chosen in accordance with each player's strategy, then it can be the case that the infinite intersection is empty.

Lynne showed an even more unintuitive result for the real line where the NON-EMPTY player loses if they always choose the "biggest" set they can: namely the last position.  Instead, they win if each time they choose any proper open set contained within a closed subset of the last move. 

I don't know much about infinite games, but I'm pretty sure this is still combinatorial.  Either way, it's an excellent application of topology to games!

A Games Class, take Three!

Ahhh, a new year and a new semester!

There's plenty to talk about, but I'd like to begin with a success relevant to teaching.  I am teaching yet another CGT class.  Previously I've taught a Math/CS elective and a first-year seminar to college undergraduates.  This time I am teaching an honors seminar and so far things are going quite well.  I changed my teaching strategy a bit. We'll see how it pans out. 


We're in the third week and so far I haven't touched the book at all.  We've done nothing in class but play games and take notice of a few interesting aspects that come up.  I give them some challenges and let them puzzle through things.  I ask lots of questions and have been very pleased with the answers and ideas they're coming up with.

My goal is to instill motivation.  These are undergraduates, many with a non-math/cs/science background.  They are probably taking this class because it sounds fun (and it is worth Math credit).  Not only will I keep the class fun, by the end, I want them to be constantly asking me: "When are we going to learn how to play this game well?"

Or, even better: "When are we going to learn how to play sums of XXXX and YYYY well?"

The point is that while I can expect them to be motivated to play games and learn new games, I also want them to get a glimpse of how the more advanced material will become relevant to game play.  Perhaps then they'll be dive in to learning that as well.



I've rarely talked about hot games here, which is regrettable.  If you want to use CGT to play games well, determining the temperature of your summands is a vital aspect.  If you want to make the correct play on the sum of a Domineering game and a Clobber game, which of the two should you evaluate first?


We have seen just a few values, but today we'll actually delve into game trees and the "set notation" for positions.  Very soon we'll hit the fundamental theorem and take off from there.