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Too Cool for School: Headmaster’s Design Concept

Cole Wehrle
United States
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"Work as if you live in the early days of a better nation"
I’ve spent the past few weeks working on a new design. The game is, in some ways, an experiment for me. I wanted to take a break from my thematically dense design, Pax Pamir, and spend some time constructing a eurogame—maybe even the sort of game that I could market to a publisher. I wanted the rules overhead to be light (no more than a couple pages) and the components to be simple. There are no cards or special dice, no fancy spinning gears or miniatures, just some cubes, some tiles in a few shapes, and a board.

I had a basic idea of the game’s mechanical construction. Players would play a tile laying game to build their schools, then players would play an area-majority game to see which school was the best at getting their cubes into the most high valued areas. The thematic concept quickly followed. Players take the role of enterprising principals in the for-profit education industry and they would run prep schools whose prestige depends upon what kinds of colleges they can get their students into.

However, whatever the cogency of this thematic and mechanical paring, I couldn’t help but think that I wouldn’t be interested enough in the game to put effort into its design. I don’t find engine builders very interesting. Tile games are rife with special powers and random draws. I started to wonder if this idea was worth the effort. Then I had a thought. What if I used this design to critique the things I didn’t like about the engine-builder genre? What if the game were an anti-euro?

So, I established a couple of ground rules: there would be no random tile draws and no direct ownership. Players would only be temporary custodians of their schools. Any engine they might build could be snatched away if they didn’t guard it. Players had to keep a keen eye on one another. With this in mind, the theme changed slightly. What if the players were trying not to boost their school’s prestige, but their own instead? What if the schools were only a means to an end?

This was an idea I liked quite a bit.

Turns and the Turning of the Seasons

Soon after I began the design process, it became pretty apparent that the temptation to 18xx-ify my little euro needed to be resisted, if I were to keep the rules tight and straightforward. To this end I began thinking about the ways I might deeply integrate my theme within the game’s mechanical framework. The sequence of play seemed like a good starting point.

I knew I wanted to keep the game under an hour so I decided to limit it to four turns. Those corresponded easily enough to the four years of secondary school here in the States. I also knew that there would be a lot of things happening each turn so I decided to organize the various phases around the school year in order to help the players keep things straight.

The four seasons are pretty well balanced in terms of how much they ask the players to do and think about. For instance, the build phase in summer is perhaps the game’s most critical phase and includes 3-5 rounds of play. In contrast, most of the spring season’s phases involve bookkeeping. As soon as I had the basic turn structure figured out I began laying out the board so that the players could easily follow the sequence of play visually as they moved through the parts of a turn.

(Note: the actual play test boards don’t have that silly paper texture which is here only for contrast).

So, play begins on the left side of the board and then moves across the top right and then down. This processional layout allowed me to surround each section with the relevant information. In local tests, there have been almost no references to the rulebook during play thanks to this design.

You’ll also note that, unlike most tile laying games, tiles are placed directly on the board in Headmaster. There are two reasons for this. First, in the promotion phase, players who are the most desirable corporate employees (read most profitable) may switch schools. Secondly, there are no tile draws in Headmaster. T here are new tiles which are released each turn, but, the primary way that tiles get built is when they are released back into the build pool when players demolish them. In other words, rather than a draw pool, the current school building trends determine which tiles will be available. To emphasize t his, the schools are placed right in the middle of the board where players cannot but help notice what the others are doing.

Human Resources

Speaking of tiles, it’s probably about time to talk about them. Currently the game has 70 tiles. They come in four sizes and two broad types (basic and advanced). At the start of the game, players will take random sets of tiles and place them in a way to partially complete their first school. The tiles they choose not to use will be gathered to form the start pool. In addition, players will draw advanced tiles and place them on future turns (on the left side of the board). In a full game, there will be about twenty unused tiles so there is plenty of variance.

Tiles depict various icons which players will need to use in order to create competitive schools. These icons represent the schools various resources, from liberal arts classrooms to science labs and SAT cram schools and gymnasiums and dormitories. Some tiles have half-symbols on them which, when paired with symbols of the same shape/color, create additional symbols through their synergy with other tiles.

Now, all of this might sound like the stuff of engine-builders, but players operating under that assumption are likely to dig themselves into tough spot. Rather, players would be better served if they thought about the management of their schools resources as participation in an area majority game. The goal is not to have large numbers of a certain type of a symbol, just more than everyone else. Furthermore, schools that are built for academic success are often not very profitable, which means such principals are likely to find themselves out-of-work and searching for any second tier school they can find.

Sealing the Bids

One of the game’s most problematic elements this design was the college admissions process by which schools are evaluated and players are rewarded for all of their clever building. It was originally conceived as a blind bind. I’m normally quite suspicious of blind bidding, but it allows us to play through our play test games efficiency and so I kept it. However soon we began thinking of alternate methods for deploying our students across the various schools. We tried lots of different methods, some chaotic and others completely transparent. Much to my surprise, I eventually decided to keep the sequential blind bids, but it wasn't an easy decision and I thought I should take some account of that action.

First, I should provide some background. There are four areas where players might send their students in Headmaster. In order to send a student to a particular area, that area’s GPA cost must be paid by the school and the areas with the higher potential payoff have the higher cost. I say “potential” because the payoff is only assed once everyone has sent their students. Each area only grants points to the player who puts the most and second most students in each area will gain any points.

This means players need to think carefully about their GPA to student ratio and their position on the turn order track (which determines which school wins ties in case several schools having the same number of cubes in an area).

This later point is really, really important. With only between 4 and 10 students in play per player, ties are common occurrences. In fact, after a few play tests I started to worry about the possibility that the tiebreaker was simply too powerful. I’ll have more to say about this later.

Anyway, back to the bid. I worried that the blind bid of our early play tests was putting too much chaos in this phase. Why was this a bad thing? Well, this phase was the “payoff” phase. The phase where the good schools would get rewarded and the bad schools get stuck with few points. If I had a deployment system, where players placed one cube at a time on the areas, it would produce a much narrower range of results. Or, if I wanted to even further reduce chaos, I could use a single round of deployment, where, in turn order, players would deploy their entire groups of students.

But, it wasn’t long before I started to realize something critical that I had overlooked. This phase wasn’t about assessing a schools value, it was about trying to maximize your schools value in order to maximize your victory points. At the end of each turn of the game, players get victory points depending on their schools performance and this little chart:

This is the most important piece of information in the game. When I typeset the rules for my blind playtesters, I’m going to use every trick in the graphics design book to emphasize its importance. Here’s what it says. It doesn’t matter how good your school is, it matters that your school was better than another players school. And, what’s more, in the later parts of the game it’s going to matter a lot more. In the course of the game it means that those who just try to build awesome schools are going to have those schools snatched away by folks with the liquidity to do it, and those players are going to win because the later turns are simply worth more than the earlier turns.

This has really important implications for the game’s admission system. If it were just about assigning value, I would leave that to some algorithm and have my students divide their GPA into their students or some such nonsense. That would not be interesting. But a sealed bid introduces the possibility that a players plans can be upset by another schools seemingly irrational bid. A school that is likely stuck with a low rank could then make a high tactical sacrifice in order to hurt a powerful school’s relative rank. Such moves would be tough calls to make, and the sealed bid provides them cover to do that.

But, this brought me back to the problem of the tiebreaker. Sealed bids can be chaotic, and, with so many tiebreakers in a game, I wondered if I was courting disaster by overemphasizing the importance of turn order. To this end, I decided to turn to game theory and build a payoff matrix.

In order to not get bogged down in the huge number of possibilities of my game, I decided to simplify my game somewhat. Here are the rules of my simulation:

1. There are two player positions: the player and everyone else.
2. The positions are symmetrical. Each position has 6 cubes and 10 GPA points to spend.
3. 2nd place scores will only be awarded if the player is within 1 cube of the first player with the caveat that If a player bids nothing they can win nothing.
4. The player does NOT have the tiebreaker.

To further simply things I decided to imagine that bids for all areas occur at the same time. For the sake of further simplicity I decided to remove the lowest value area.

Okay, according to these rules I created the following for dominate strategies and a payoff matrix:

So, as you can see, the tiebreaker is really critical. In fact, if you average all of the results you get a -1.5 payoff, against player one (Note: the real theoretical payoff is actually much worst if we assume that player two is going to press their advantage, but I won’t bog down this post with the details). At any rate, it was enough to get me worried so I decided to see what would happen if I made the positions asymmetric. I created four “High GPA strategies” which gave the players 15 gpa points, 2 high cube strategies which gave the player 10 cubes and two strategies which mixed them in various ways.

As you can see the advantage swings to the resource advantaged player with an average payoff of +.58. In other words, the tiebreaker can be accounted for with a few extra resources. Still, there are some matches here that don’t make any sense, especially when I introduced the fourth scoring area (+1/0 with 0 GPA cost). That area helps players avoid a disastrous deployment if they know that they’ve lost some of the other high value areas. By having a segmented blind bid, players can usually minimize their losses.

So, as I said before, blind bidding provides cover for players to disrupt one another. With a standard deployment, say a single cube a time, a dominate player can quickly recognize what is happening and adjust their strategy to something more conservative. With sequential blind bids in order of a college value, players in a strong position are unable to press their advantage and there are far many options for player positions to disrupt one another’s rank. It’s not a perfect system, but that’s okay. I want the game to have a strong strategic element and that often means that players must deal with the consequences of poor play. Still, the blind bid presents some interesting considerations for both those in the lead and those far behind.

Next year...

Elements of Headmaster's design have been incubating for years and I’m very pleased with its current development and the speed with which it has become a viable and interesting game. It also provided me with a mental break from Pax Pamir that has already proved immensely fruitful for that game's continued development and research.
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Sun Oct 5, 2014 6:23 pm
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