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John Hopkins University
Photo by Cindy Hall

Johns Hopkins Centre for Talented Youth

Paxton Hall —

“The world leader in gifted education since 1979, Johns Hopkins Center for Talented Youth is a nonprofit dedicated to identifying and developing the talents of academically advanced pre-college students around the world. [They] serve bright learners and their families through [their] research, advocacy, and counseling, as well as [their] signature gifted and talented summer, online, international, and family programs.

CTY students comprise the most promising minds of the next generation. There are more than 165,000 CTY alumni around the world, including the founders of Facebook and Google, Regeneron Science Talent Search winners, Rhodes Scholars, and MacArthur Fellows. At CTY, bright students have the chance to participate in challenging educational opportunities they won’t experience anywhere else. Just as important, they’ll find a safe, welcoming circle of peers, mentors, and teachers who understand advanced students. And they’ll make lifelong friends who share their passion for learning.” (from Johns Hopkins website)

Earlier this year, over a period of three weeks from late June to mid-July, I participated in the Johns Hopkins CTY programme at Loyola Marymount University (LMU) in Los Angeles. (CTY campuses are scattered throughout the U.S. and internationally.) To get into the programme, I had to take a preliminary exam which tested me in English and Maths. My results qualified me for a number of courses, and the course I chose was Probability and Game Theory – I would have preferred something a little more advanced, but woefully there were regulations that required you to have taken other CTY courses previously.

CTY was my first-ever experience with dorm life. All 250-ish students on the campus were split into halls, which were then split into two-person dorm groups. I think I was fairly lucky with my assigned roommate, who hardly spoke to me during all three weeks and generally left me in peace. Patrick, if you’re reading this, you played the roommate role to a very satisfactory standard! Each hall had an RA (residential assistant), most of whom were previous CTY students. My hall’s RA was named Luis, and he was a fantastic motivator and friend to all of us during our time at Loyola.

Aside from the course itself, the atmosphere of Loyola during the CTY programme was radically different from any university you might attend in New Zealand. Since it was mid-summer in the northern hemisphere, the air was heavy and tropical. It was a relief to take a cold shower every morning after a long, semi-sleepless night of humidity and heat. During our classes, I also experienced not seventy-four, not seventy-five, but two earthquakes! My classes took place on the top floor of a three-storey building, so the Probability and Game Theory students had a lovely time during the earthquake. In the first earthquake, I initially thought someone was shaking my desk with their foot, but then I realised everyone’s desks were being shaken with everyone’s feet. After a surreal moment when I believed my class had secretly organised a rather lame prank, I correctly figured out that an earthquake was occurring. Apparently earthquakes are a part of everyday life in California, because most of the class glanced around with an exasperated or bored expression before continuing with their work.

The point of CTY is to pack a year-long university course into three weeks, so the schedule was quite intensive. For a student at my age, a typical daily schedule would be as follows:

7 - 9 a.m. – Morning preparations/breakfast

9 a.m. - 12 p.m. – Class

12 - 1 p.m. – Lunch

1 - 3 p.m. – Class

3 - 5:30 p.m. – Activity periods

5:30 - 6:30 p.m. – Dinner

6:30 – 9 p.m. – Class

9 – 10:30 p.m. – Social Time

10:30 p.m. – Lights out

This schedule meant that we had 7.5 hours of class per day for fifteen class days (about one more hour per day than at LPHS), which amounted to more than 110 hours of class time. The meals were held communally in a large cafeteria, which contained seven “mini-restaurants” inside to give some culinary variety. These meal choices changed for every meal of every day, so I was able to taste a new dish three times a day. Social time was the only free time we had, and none of us wanted to waste it by actually being social, so we proposed a change of name to “Antisocial Time”. It didn’t get accepted.

Probability and Game Theory wasn’t a particularly involved or intensive course, but there was still a large amount of information to be learned. Our class started with the classic ice-breaker which involved going around the class and saying your name, and something you liked, as well as the names and “likes” of everyone who had previously had their turn. I was told to start, but in a panic-stricken moment when I couldn’t think of anything I liked, I said that I liked my name. (In case you’ve forgotten, my name is Paxton.) This meant everyone else in the class had to say “Paxton likes his name” at the beginning of their turn. The phrase “Paxton likes his name” quickly evolved into a joke/meme with everyone in my class, which I still cannot explain to this day. Our class began our learning with the basics of probability. We then moved onto advanced applications of combinations, permutations, and compound probabilistic questions involving conditional probability and other variants. We also briefly examined the binomial, Poisson, and normal distributions, and their requirements and uses, as well as expected values and variance/standard deviation. After that, we moved onto games, where we examined the seven main archetypes of games and the Seven Deadly Dilemmas, Nash Equilibria, Pareto-Optimal outcomes, and saddle points. Additionally, we learned about matrices and their applications to many differents aspects of games. Next, we looked at evolution and natural selection, and how populations can change over time to either tend towards a stable equilibrium or deviate from an unstable one. We also looked at political elections and how different sociopolitical systems can affect strategies employed by parties and their politicians. Finally, our class studied different types of auctions, and held a grand auction on the final day with the Monopoly money we had earned from completing in-class games. At the end of each week, we completed an end-of-topic test with exam conditions, which were unimportant other than the teacher seeing how successful they were at teaching. My teacher’s name was Mr. Boone, and he was clearly experienced in the field of Probability and Game Theory. Mr. Boone, if you’re out there, thank you for being an excellent and enthusiastic mentor this year!

My favourite part of my classes was the economical system. Each student was given a small amount of Monopoly money to begin with, and we could win more by doing well in games. Throughout the course, we discussed strategies of many different games, including chess, complex rock-paper-scissors, Coup, Hex, Checkers, and many others. My favourite game went as follows:

  1. 10 “battlefields” are set up using a spreadsheet application on a computer.

  2. Every student is given 100 virtual soldiers to distribute amongst the battlefields.

  3. After every student has written down their distribution of soldiers, the soldiers are entered into the battlefields.

  4. A student gains one point for every other player in a battlefield that deployed less soldiers than them. For example, if Jim places 14 soldiers in Battlefield 8, Chloe places 15, and Bob places 3, Jim gains 1 point (from having more soldiers in Battlefield 8 than Bob) and Chloe gains 2 points (from having more soldiers in Battlefield 8 than both Jim and Bob).

  5. The points are tallied up at the end to decide on an overall winner.

This game was interesting because it involved predicting other people’s strategies if you assume they base their predictions off of your strategies. However, games like this lead into an infinite cycle of predicting different values for each player. Technically, the best strategy is to distribute soldiers equally across the battlefields (with 10 in each one), but the predictability of this can lead to other players distributing their soldiers with 11 in most battlefields, to exploit your strategy and gain lots of points. My winning strategy was to place 14 soldiers in each of the first 7 battlefields, place the remaining 2 soldiers somewhere in the last 3 battlefields, and hope for the best.

Johns Hopkins CTY was a fantastic experience, and I would recommend it to any aspiring academic students.