Student Responses on First Day Survey in Games & Gambling

I've been teaching in front of a college classroom every semester since I graduated from my undergrad institution back in 2005.  In that time, I believe I've given a first day survey every semester (except maybe my first).  The classes that I've taught have changed over the years (as has the institutions where I teach) - and the survey has changed as well, but the goal of the survey remains the same.  I want to get to know my students as people AND I want to know what they know (and what they think they know) coming into the course.

I asked the students a variety of questions on the survey - but I've only highlighted the "interesting" questions.

Why did you sign up for this course?

• Looked like a fun and informative course to fill a distribution requirement  (9 people)
• Heard it was a fun class (1 person)
• Love games (1 person)
• For distribution (without any mention of fun/interesting)  (3 people)
• Variety in math classes (3 people)

Note:  The first question was a short answer so I categorized the answers as best I could.

If you had to, which ONE of the following games would you play (with the goal to make money at a casino):  

• Craps:   1
• Roulette:  3
• Blackjack:  11
• Slot Machines:  2
• Keno: 0

The first question was designed to figure out my audience.  The second was designed to figure out what preconceived notions the students had in regards to gambling.  I also had a series of true/false and a few ranking questions on the survey (interesting to me but probably not great blogging fodder).

What information can I glean from the two selected questions?  Looking at question #1, it seems clear that the majority of the students signed up because the class sounded like a fun way to earn their mathematics distribution credit.  While some mathematicians may cringe at that idea, I think it's awesome.  It's not easy to have a non-majors mathematics class that the students are excited about before they even step foot in the classroom.

The second question was interesting to me because the majority of the class decided that Blackjack was the way to go if the goal was making money.  It's clear to me that movies like 21 (plus the glamorized depictions of casinos in movies like Ocean's 11 have an effect on people).  It was also interesting that no one chose Keno (a wise move by the way) despite the fact that Keno is also available at a lot of non-casino locations (including the Maryland state lottery).

I should mention (for those that are curious) that there isn't exactly a "correct" answer to the second question.  Keno is clearly wrong in terms of things like expected value - but if you only have $1 to bet, you have a slim chance at winning say $10,000 in Keno - unlike any other game in the list!  I didn't ask for any sort of written explanation from the students so I don't have any idea why each student chose the game they did.  The real value (for me) will be the follow-up survey at the end of the semester where I'll put the same question with a spot for a written explanation.  We'll see what they glean from the semester's worth of material!

Another Semester is About to Begin

Another semester is about to begin, only this time my teaching load feels a lot lighter!  Once again, I'm teaching two sections of Calculus I (with labs) and a section of the course I developed last semester (Mathematics of Games and Gambling).  The Games and Gambling course went quite well last semester though I don't have the results of the anonymous survey that all our students take at the end of the semester.  I expect there will be a few complaints but for the most part I'm expecting good things.

So where does that leave me for Spring 2013*?
*It's weird writing 2013 isn't it?

Well, I have two big goals for the semester.
1.  In Games & Gambling:  Tailor the course to the individuals in the class.  In other words, don't fall into the trap of doing exactly what I did last semester simply because the lessons are complete.  Last semester I tried to hit the interests of the students, let's do it again.
2.  In Calculus I:  Come up with some way to make labs enjoyable learning experiences rather than current Mathematica syntax heavy monstrosities that they are now.  I did manage to rewrite one lab last semester and had fairly good results - so I know it's possible.

  What are your teaching goals for the upcoming semester?

Instant Insanity

Although one might take the title of this particular blog post to be an assessment of the craziness that is the end of another semester, I assure it's not meant to be that way.  Quite the opposite in fact.  My semester went quite well, especially the Mathematics of Games and Gambling class that I designed and taught for the first time.  As I've down throughout the semester (though admittedly not nearly as often as I would have liked), it's time for another update for the course (here's a link to my last few course updates...published back in September and another in October).

Throughout the semester, I covered a variety of topics in the class (as a reminder, the class was designed for non-mathematics majors to take as an elective to fulfill distribution requirements).  The topics that covered included (but are not limited to):

• Chuck-a-Luck
• Roulette
• Craps
• Keno
• Five Card Stud
• Texas Holdem
• Lotteries
• Instant Insanity

It is the final topic that shall be the focus of today's entry.  

For a few semesters now, I've lobbied my mathematics department to allow me to teach an experimental course.  For the longest time, I wanted to do a 300-level Introduction to Graph Theory course.  Alas, our mathematics major is quite small (and most of our majors aim to teach at secondary schools so their electives get filled by education required classes like geometry).  As such, it has been deemed unlikely that I could ever get enough students to adequately fill up a Graph Theory course.

Last spring, I changed gears and proposed the Mathematics of Games and Gambling course instead.  As you can guess, that was approved (and has, for the record, been approved for the upcoming spring semester as well).  Although I couldn't teach graph theory, I still managed to find a way to squeeze in a few days of graph theory (at a basic level) by using the 1980s puzzle "Instant Insanity."

Before I describe how I taught the lesson, I will say that overall the lesson went extremely well.  I even put a question on the final exam which almost every student got correct!  If you have taught a lesson using Instant Insanity (or something similar), I'd love to hear about it.  If you happen to be inspired in some way to use what I did in your own classroom, I'd love to hear about your experiences when they happen!

Our class periods are just over an hour long, so for the first class of the unit I showed the students the original Instant Insanity advertisement after a short PowerPoint presentation that covered the various graph vocabulary that I wanted the students to know.  

The terms weren't difficult, but they weren't all simplistic either (bipartite graphs).  

The next class was much more of a riot (for me anyhow).  I gave each student a colored sheet Instant Insanity puzzle blocks which they had to cut-out and tape together.  Watching college students do something that many haven't done since a middle-school art class was definitely amusing (and somehow a bit worrisome too)!

After constructing the blocks, the students spent the remaining time trying to solve the puzzle.  While a few did succeed, the majority of the class did not successfully complete the confounding game.  I didn't provide any hints as they left class that day, though I did encourage them to find a "mathematical way to solve the puzzle."  

The final day of the lesson was the big one - how to solve Instant Insanity puzzles using graph theory. To begin, we discussed how each block could be "unfolded" to a two dimensional image.  

From there, we can easily pair the opposite sides.

Once the three pairs are made (front/back, top/bottom, left/right), all you need is a graph with four vertices (one for each of the four possible colors).  Draw an edge that for each of the three pairings.  For example, if the top color is blue and the bottom color is red, there should be an edge connecting the blue vertex to the red one.  If the left and right colors both happen to be yellow, there would be a loop connecting yellow to itself.  In total, there should be three edges for each graph (one graph per each of the four cubes).  

Using the four graphs (or if you prefer, a single graph that combines the four small graphs), you then look for a path that uses an edge from each cube once and that makes each of the four vertices have degree two.  Once you find one such solution, find a second solution.  The first solution corresponds to the front and back of the four cubes.  The second solution corresponds to the left and right.   Note:  Once you've found the front/back and left/right, the top/bottom is forced (and therefore you do not need to worry yourself about those)!

I've skipped over a few of the finer details, but in essence that's how you solve an Instant Insanity puzzle.  For those who want to give it a go, here are three puzzles.  It should be noted that some puzzles may not be solvable.

Good luck!

Letters of Recommendation...

Although I love almost all aspects of my job, there are a few things that I don’t necessarily look forward to doing.  One such thing is writing letters of recommendation.  Around this time of year, many of our undergraduate seniors are preparing for graduate school – and part of that preparation requires them to secure X numbers of letters of recommendation. 

Don’t get me wrong, I love (most) of our seniors – and I definitely want to write them great letters.  I truly believe that they will do well in whatever program they choose, none of that is the issue at hand here.  No, the issue is all on me.  I’m a harsh critic of myself, and while you probably can’t tell based on the drivel that I put on this blog (among the two blogs that I maintain), I do care.

A lot. 

Letters of recommendation are one of those things that can be super easy to write for a select student or two each year, but for the rest of the students…  Oh boy.  They can be exceedingly difficult, especially for students who I only had for a class or two or perhaps for a student who didn't get the best grades and/or perhaps didn't stand out in some other spectacular way.

For those of you who write letters for your students (or anyone for that matter), how do you do it?  How do you make the letters unique (or don’t you worry about that)?  Personally, I think a truly personalized letter is better – but then again, I've never served on an admissions committee.  I can’t say that I know for sure what they look for – and if I did, well, I’d guess my own letter writing skills would be a bit better!

The Price is Right LIVE: A Review

As I mentioned a few days ago, I took my Mathematics of Games and Gambling class to see a showing of The Price is Right LIVE at our local community arts center.  The show was last night and while I haven't seen my class yet to get their impressions of the show, here is my personal review of the Price is Right traveling show.

In a word:  Semi-lame.

Ok, that's not even a real word, but it's how I feel.

The good:

Many of people's favorite games are present.  Punch-a-Bunch, Plinko, Cliffhangers, Any Number, and Hole in One were all played.  The had one group of three people spin the big wheel.  Two people got the chance to play for the Showcase (only one showcase - both players bid at the same time).

The bad:

The show started late and ended early (or so it seemed).  Extremely short amount of time spent actually playing any games.  They showed a bunch of video clips from old shows - but nothing that you can't find on YouTube (for free).  The prizes were borderline good for most of the show...certainly not great (even with lowered expectations).  There was a refrigerator as a prize and a billiard table used as big prizes (neither were actually given away).  The small (initial bid) prizes included a 4 handheld phone system for a house (seriously, who uses those any more?), a pair of diamond earrings, a popcorn machine, and a vacuum.

The terrible:

The final showcase consisted of:
A new car (Nissan Versa I believe?)
A 3-day cruise to the Bahamas
An iPod touch
A 50 inch flat screen tv

The first contestant bid $19,000 and change.  The second contestant bid $20,000 and change.

For the traveling show, the person who is closest to the actual price (without going over) wins ONE of the items in the showcase - in this case, the 3-day cruise.  In order to win ALL of the items, you had to be within $100 of the actual price (i.e. not going to happen)!

Actual retail price (according to the show)?  $14,000 and change.

The show ended on that note.  A seemingly bogus final showcase, a pair of losing contestants, and a bunch of audience members feeling like the contestants were cheating.  The best line I overheard while leaving the theater:  "If a new car really cost $14,000, then everyone would have a new car."

Never mind all the other stuff in the showcase...

Since I was curious, here's a few numbers that I found via internet research*:
*note, all prices are guesses, I have no idea what the brands/companies were for some of the prizes
Price of 2012 Nissan Versa starting at:  $10,999 (from Nissan's website)
3-day Cruise:  $299
50 inch TV:  LG ($699.00)  one of the cheapest options
iPod touch:  $179.00
Total:  $12,176

So is the game rigged?  Well, I say yes but only because they make you think the showcase prizes are great when in reality they aren't nearly so good.  I also found it weird that in Punch-a-Bunch, the host knew exactly where the one $2500 prize was hiding...and it appeared to be printed on a larger card.  Makes me wonder if that particular hole had two cards residing in it, a $50 or similar prize if the contestant happened to select it and the big prize otherwise (the host showed the big prize to "prove" the fairness of the game).  I say when you have to "prove" that you are on the up-and-up, you probably aren't really on the up-and-up.

My suggestion to anyone who might see one of the live shows in their area - bid $1 and nothing more on the final showcase.  Chances are, your opponent will over bid and you then you win the cruise.  Don't bother trying to get too close, it won't work!

What I don't understand is why the producers of the show don't want to have one person win the cruise.  If the price is really only $300, that's paid for in a matter of 10 balcony tickets...a mere drop in the bucket.  Why have people leave angry (even if the pricing seems fair now that I looked up all the costs)?  If one of the two people had won the cruise, I think the entire audience mood at the end of the show would have been much better.

I also question the length of the show.  In a typical TV episode (granted, I'm sure footage is cut in order to fit it in 60 minutes - with commercials), there are six games played, the big wheel is spun by two groups of three people, and there are two final showcases.

In the travel show, there were only five games played, the big wheel was spun by ONE trio of contestants, and there was only one final showcase.  The entire show lasted just over an hour - and much of that time was "wasted" by showing the aforementioned video footage of old shows and for people making their way to the stage.

In the end, I'm interested to hear my students' take on the show, but for me, I can't in good conscience recommend anyone go to the show.  You'll have more fun watching old clips on your computer - save the price of the ticket.