Game Balance Concepts

Level 10: Final Boss

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This Week

Welcome to the final week of the season. This week I didn’t know ahead of time what to do, so I intentionally left it as an unknown on the syllabus as a catch-all for anything interesting that might have come up over the summer. As it turns out, there are four main topics I wanted to cover today, making this the longest post of all of them, so if you have limited time I suggest bookmarking this and coming back later. First I’d like to talk a bit about economic systems in games, and how to balance a system where the players are the ones in control of it through manual wealth generation and trading. Then, I’ll talk about some common multiplayer game balance problems that just didn’t fit anywhere else in the previous nine weeks. Third, I’ll get a bit technical and share a few tips and tricks in Excel. Lastly, I’ll return to last summer with this whole concept of “fun” and how this whole topic of game balance fits into the bigger picture of game design, because for all of the depth that we’ve gone into still feels like a pretty narrow topic sometimes.

Economic Systems

What is an economic system?

First, we use the word “economy” a lot, even in everyday life, so I should define it to be clear. In games, I’ll use the word “economy” to describe any in-game resource. That’s a pretty broad term, as you could take it to mean that the pieces in Chess are a “piece economy” – and I’d argue that yes, they could be thought of that way, it’s just not a particularly interesting economy because the resources can’t really be created, destroyed or transferred in any meaningful way. Most economies that we think of as such, though, have one or more of these mechanics:

Still, any of those elements individually might be missing and we’d still think of it as an economy.

Like the creation of level design tools, tabletop RPGs, or metrics, creating an economic system in your game is a third-order design activity, which can make it pretty challenging. You’re not just creating a system that your players experience. You’re creating a system that influences player behavior, but then the players themselves are creating another social system within your economic system, and it is the combination of the two that the players actually experience. For example, in Settlers of Catan, players are regularly trading resources between them, but the relative prices of each resource are always fluctuating based on what each individual player needs at any given time (and usually, all the players need different things, with different levels of desperation and different ability to pay higher prices). The good news is that with economies, at least, a lot of human behavior can be predicted. The other good news is that in-game economies have a lot of little “design knobs” for us designers to change to modify the game experience, so we have a lot of options. I’ll be going over those options today.

Supply and Demand

First, a brief lesson from Economics 101 that we need to be aware of is the law of supply and demand, which some of you have probably heard of. We assume the simplest case possible: an economy with one resource, a really large population of people who produce the resource and want to sell it, and another really large population of people who consume the resource and want to buy it. We’ll also assume for our purposes that any single unit of the resource is identical to any other, so consumers don’t have to worry about choosing between different “brands” or anything.

The sellers each have a minimum price at which they’re willing to part with their goods. Maybe some of them have lower production costs or lower costs of living than others, so they can accept less of a price and still stay in business. Maybe others have a more expensive storefront, or they’re just greedy, so they demand a higher minimum price. At any rate, we can draw a supply curve on a graph that says that for any given price (on the x-axis), a certain number or percentage of sellers are willing to sell at that price (on the y-axis). So, maybe at $1, only two sellers in the world can part with their goods at that price, but at $5 maybe there are ten sellers, and at $20 you’ve got a thousand sellers, and eventually if you go up to $100 every single seller would be willing to sell at that price. Basically, the only thing you need to know about supply curves is that as the price increases, the supply increases; if ten people would sell their good at $5, then at $5.01 you know that at least those ten sellers would still accept (if they sold at $5 then they would clearly sell at $5.01), and you might have some more sellers that finally break down and say, okay, for that extra penny we’re in.

Now, on the other side, it works the same but in reverse. The consumers all have a maximum price that they’re willing (or able) to pay, for whatever reason. And we can draw a demand curve on the same graph that shows for any given price, how many people are willing to buy at that price. And unlike the supply curve, the demand curve is always decreasing; if ten people would buy a good at $5, then at $5.01 you might keep all ten people if you’re lucky, or some of them might drop out and say that’s too rich for their blood, but you certainly aren’t going to find anyone who wouldn’t buy at a lower price but would buy at a more expensive price.

Now of course, in the real world, these assumptions aren’t always true. More teenagers would rather buy $50 shoes than $20 shoes, because price has social cred. And some sellers might not be willing to sell at exorbitantly high prices because they’d consider that unethical, and they’d rather sell for less (or go out of business) than bleed their customers dry. But for our purposes, we can assume that most of the time in our games, supply curves will increase and demand curves will decrease as the price gets more expensive. And here’s the cool part: wherever the two curves cross, will generally turn out to be the actual market price that the players all somehow collectively agree to. Even if the players don’t know the curves, the market price will go there as if by magic. It won’t happen instantly if the players have incomplete information, but it does happen pretty fast, because players who sell at below the current market price will start seeing other people selling at higher prices (because they have to) and say, hey, if they can sell for more than I should be able to also! And likewise, if a consumer pays a lot for something and then sees the guy sitting next to them who paid half what they did for the same resource, they’re going to demand to pay a whole lot less next time.

Now, this can be interesting in online games that have resource markets. If you play an online game where players can sell or trade in-game items for in-game money, see if either the developer or a fansite maintains a historical list of selling prices (not unlike a ticker symbol in the stock market). If so, you’ll notice that the prices change over time slightly. So you might wonder what the deal is: why do prices fluctuate? And the answer is that the supply and demand are changing slightly over time. Supply changes as players craft items and put them on sale, and that supply is constantly changing; and demand also changes, because at any given time a different set of players is going to be online shopping for any given item. You can see this with other games that have any kind of resource buying and selling. And because the player population isn’t infinite, these things aren’t perfectly efficient, so you get unequal amounts of each item being produced and consumed over time.

Now, that points us to another interesting thing about economies: the fewer the players, the more we’ll tend to see prices fluctuate, because a single player controls more and more of the production or consumption. This is why the prices you’ll see for one Clay in the Catan games change a lot from game to game (or even within a single game) relative to the price of some piece of epic loot in World of Warcraft.

Now, this isn’t really something you can control directly as the game designer, but at least you can predict it. It also means if you’re designing a trading board game for 3 to 6 players, you can expect to see more drastic price fluctuations with fewer players, and you might decide to add some extra rules with less players to account for that if a stable market is important to the functioning of your game.

Multiple resources

Things get more interesting when we have multiple goods, because the demand curves can affect one another. For example, suppose you have two resources, but one can be substituted for another – maybe one gives you +50 health, and the other gives you +5 mana which you can use as a healing spell to get +50 health, so there’s two different items (with similar uses) so if one is really expensive and one is really cheap you can just buy the cheap one. Even if the two aren’t perfect substitutes, players may be willing to accept an imperfect substitute if the price is sufficiently lower than the market value for the thing they actually want, and the price difference between what people will pay for the good and what they’ll pay for the substitute tells you how efficient that substitute is (that is, how “perfect” it substitutes for the original).

On the flip side, you can also have multiple goods where the demand for one increases demand for the other, because they work better if you buy them all as a set (this is sort of the opposite of substitutes). For example, in games where collecting a complete set of matching gear gives your character a stat bonus, or where you can turn in one of each resource for a bonus, a greater demand for one resource pulls up the demand for all of the others… and once a player has some of the resources in the set, their demand for the others will increase even more because they’re already part of the way there.

By creating resources that are meant to be perfect or imperfect substitutes, or several resources that naturally “go together” with each other, you can change the demand (and therefore the market price) of each of them.

Marginal pricing

As we discussed a long time ago with numeric systems, sometimes demand is a function of how much of a good you already have. If you have none of a particular resource, the first one might be a big deal for you, but if you have a thousand of that resource then one more isn’t as meaningful to you, so demand may actually be on a decreasing curve based on how many of the thing you already have. Or maybe if you can use lots of resources more efficiently to get larger bonuses, it might be that collecting one resource means your demand for more of that resource increases. The same is true on the supply side, where producing lots of a given resource might be more or less expensive per-unit than producing smaller amounts. So you can add these kinds of mechanics in order to influence the price; for example, if you give increasing returns for each additional good that a player possesses, you’ll tend to see the game quickly organize into players going for monopolies of individual goods, as once a player has the majority of a good in the game they’re going to want to buy the rest of them. As an example, if you have decreasing returns for players if they collect a lot of one good, then adding a decreasing cost for producing the good might make a lot of sense if you want the price of that good to be a little more stable.

Scarcity

I probably don’t need to tell you this, but if the total goods are limited, that increases demand. You see this exploited all the time in marketing, when a company wants you to believe that they only have limited quantities of something, so that you’ll buy now (even at a higher price) because you don’t want to miss your chance. So you can really change the feeling of a game just by changing whether a given resource is limited or infinite.

As an example, consider a first-person-view shooting video game where you have limited ammunition. First, imagine it is strictly limited: you get what you find, but that’s it. A game like that feels more like a survival-horror game, where the player only uses their ammo cautiously, because they never know when they’ll find extra or when they’ll run out. Compare to a game where you have enemies that respawn in each area, random item drops, and stores where you can sell the random drops and buy as much extra ammo as you need. In a game like that, a player is going to be a lot more willing to experiment with different weapons, because they know they’ll get all of their ammo back when they reach the next ammo shop, which makes the game feel more like a typical FPS. Now compare that with a game where you have completely unlimited ammo so it’s not even a resource or an economy anymore, where you can expect the player to be shooting more or less constantly, like some of the more recent action-oriented FPSs. None of these methods is “right” or “wrong” but they all give very different player experiences, so my point is just that you increase demand for a good (and decrease the desire to actually consume it now because you might need it later) the more limited it is.

If the resources of your game drive players towards a victory condition, making the resource limited is a great way to control game length. For example, in most RTS games, the board has a limited number of places where players can mine a limited amount of resources, which they then use to create units and structures on the map. Since the core resources that are required to produce units are themselves limited, eventually players will run out, and once it runs out the players will be unable to produce any more units, giving the game a natural “time limit” of sorts. By adjusting the amounts of resources on the map, you can control when this happens; if the players drain the board dry of resources in the first 5 minutes, you’re going to have pretty short games… but if it takes an hour to deplete even the starting resources near your start location, then the players will probably come to a resolution through military force before resource depletion forces the issue, and the fact that they’re limited at all is just there to avoid an infinite stalemate, essentially to place an upper limit on game length.

With multiplayer games in a closed economy, you also want to be very careful with strictly limited goods, because there is sometimes the possibility that a single player will collect all of a good, essentially preventing anyone else from using it, and you should decide as a designer if that should be possible, if it’s desirable, and if not what you can do to prevent it. For example, if resources do no good until a player actually uses them (and using them puts them back in the public supply), then this is probably not going to be a problem, because the player who gets a monopoly on the good has incentive to spend them, which in turn removes the monopoly.

Open and closed economies

In systems, we say a system is “open” if it can be influenced by things from outside the system itself, and it is “closed” if the system is completely self-contained. Economies are systems, and an open economy has different design considerations than a closed economy.

Most game economies are closed systems; you can generate or spend money within the game, but that’s it, and in fact some people get very uncomfortable if you try to change it to an open system: next time you play Monopoly, try offering one of your opponents a real-world cash dollar in exchange for 500 of their Monopoly dollars as a trade, and see what happens — at least one other player will probably become very upset!

Closed systems are a lot easier to manage from a design standpoint, because we have complete control as designers over the system, we know how the system works, and we can predict how changes in the system will affect the game. Open economies are a lot harder, because we don’t necessarily have control over the system anymore.

A simple example of an open economy in a game is in Poker if additional player buy-ins are allowed. If players can bring as much money as they want to the table, a sufficiently rich player could have an unfair advantage; if skill is equal, they could just keep buying more chips until the luck in the game turns their way. To solve this balance problem, usually additional buy-ins are restricted or disallowed in tournament play.

Another place where this can be a problem is CCGs, where a player spending more money can buy more cards and have a greater collection. Ideally, for the game to be balanced, we would want larger collections to give players more options but not more power, which is why I think rarity shouldn’t be a factor in the cost curve of such a game, at least if you want to maximize your player base. If more money always wins, you set up an in-game economy that essentially has a minimum bar for money to spend if you want to be competitive, and in the real world we also have supply and demand curves, and the higher your initial required buy-in is, the fewer people who will be willing to pay (and thus the smaller your player base).

There are other games where you can buy in-game stuff with real-world cash; this is a typical pattern for free-to-play MMOs and Facebook games, and developers have to be careful with exactly what the player can and can’t buy; if the player can purchase an advantage over their opponents, especially in games that are competitive by nature, that can make the game very unbalanced very quickly. (It’s less of an issue in games like FarmVille where there isn’t really much competition anyway.)

Some designers intentionally unbalance their game in this way, assuming that if they create a financial incentive to gain a gameplay advantage, players will pay huge amounts; and to be fair, some of them do, and if the game itself isn’t very compelling in its core mechanics then this might be the only thing you can fall back on to make money, but if you set out to do this from the start I would call it lazy design. A better method is to create a game that’s actually worth playing for anyone, and then offer to trade money for time (so, maybe you get your next unlock after another couple of hours of gameplay, and the gameplay is fun enough that you can do that without feeling like the game is arbitrarily forcing you to grind… but if you want to skip ahead by paying a couple bucks, we’ll let you do that). In this way, money doesn’t give any automatic gameplay advantage, it just speeds up the progression that’s already there.

One final example of an open economy is in any game, most commonly MMOs, where players can trade or “gift” resources within the game, because in any of those cases you can be sure a secondary economy will emerge where players will exchange real-world money for virtual stuff. Just google “World of Warcraft Gold” and you’ll probably find a few hundred websites where you can either purchase Gold for real-world cash, or sell Gold to them and get paid in cash. There are a few options you can consider if you’re designing an online game like this with any kind of trade mechanic:

You’ll also want to consider whether players are allowed to sell their entire character, password and all. For Facebook games this is less of an issue because a Facebook account links to all the games and it’s not so easy for a player to give that away. For an MMO where each player has an individual account on your server that isn’t linked to anything else, this is something that will happen, so you need to decide how to deal with that. (On the bright side, selling a whole character doesn’t unbalance the game.)

In any case, you again want to make sure that whatever players can trade in game does not unbalance the game if a single player uses cash to buy lots of in-game stuff. One common pattern to avoid this is to place restrictions on items, for example maybe you can purchase a really cool suit of armor but you have to be at least Level 25 to wear it.

Inflation

Now, remember from before that the demand curve is based on each player’s maximum willingness to pay for some resource. Normally we’d like to think of the demand curve as this fixed thing, maybe fluctuating slightly if a different set of players or situations happen to be online, but over time it should balance out. But there are a few situations that can permanently shift the demand curve in one direction or another, and the most important for our purpose is when each player’s maximum willingness to pay increases.

Why would you change the amount you’re willing to pay? Mostly, if you have more purchasing power. If I doubled your income overnight but Starbucks raised the price of its coffee from $5 to $6, if you liked their coffee before you would probably be willing to pay the new price, because you can afford it.

How does this work in games? Consider a game with a positive-sum economy: that is, it is possible for me to generate wealth and goods without someone else losing them. The cash economy in the board game Monopoly is like this, as we’ve discussed before; so is the commodity economy in Catan, as is the gold economy in most MMOs. This means that over time, players get richer. With more total money in the economy (and especially, more total money per player on average), we see what is called inflation: the demand curve shifts to the right as more people are willing to pay higher prices, which then increases the market price of each good to compensate.

In Catan, this doesn’t affect the balance of the game; by the time you’re in the late game and willing to trade vast quantities of stuff for what you need, you’re at the point where you’re so close to winning that no one else is willing to trade with you anyway. In Monopoly the main problem, as I mentioned earlier, is that the economy is positive-sum but the object of the game is to bankrupt your opponents; here we see that one possible solution to this is to change the victory condition to “be the first player to get $2500” or something like that. In MMOs, inflation isn’t a problem for the existing players, because after all they are willing to pay more; however, it is a major problem for new players, who enter the game to find that they’re earning one gold piece for every five hours of play, and anything worth having in the game costs millions of gold, and they can never really catch up because even once they start earning more money, inflation will just continue. So if you’re running an MMO where players can enter and exit the game freely, inflation is a big long-term problem you need to think about. There are two ways to fix this: reduce the positive-sum nature of the economy, or add negative-sum elements to counteract the positive-sum ones.

Negative-sum elements are sometimes called “money sinks,” that is, some kind of mechanism that permanently removes money from the player economy. The trick is balancing the two so that on average, it cancels out; a good way to know this is to actually take metrics on the total sum of money in the game, and the average money per person, and track that over time to see if it’s increasing or decreasing. Money sinks take many forms:

To reduce the positive-sum nature of the economy is a bit harder, because players are used to going out there, killing monsters and getting treasure drops. If you make the monsters limited (so they don’t respawn) then the world will become depopulated of monsters very quickly. If you give no rewards, players will wonder why they’re bothering to kill monsters at all. In theory you could do something like this:

One other, final solution here is the occasional server reset, when everyone loses everything and has to start over. This doesn’t solve the inflation problem – a new player coming in at the end of a cycle has no chance of catching up – but it does at least mean that if they wait for everything to reset they’ll have as good a chance as anyone else after the reset.

Trading

Some games use trading and bartering mechanics extensively within their economies. Trading can be a very interesting mechanic if players have a reason to trade; usually that reason is that you have multiple goods, and each good is more valuable to some players than others. In Settlers of Catan, sheep are nearly useless to you if you want to build cities, but they’re great for settlements. In Monopoly, a single color property isn’t that valuable, but it becomes much more powerful if you own the other matching ones. In World of Warcraft, a piece of gear that can’t be equipped by your character class isn’t very useful to you, no matter how big the stat bonuses are for someone else. By giving each player an assortment of things that are better for someone else than for them, you give players a reason to trade resources.

Trading mechanics usually serve as a negative-feedback loop, especially within a closed economy. Players are generally more willing to offer favorable trades to those who are behind, while they expect to get a better deal from someone who is ahead (or else they won’t trade at all).

There are a lot of ways to include trading in your game; it isn’t as simple as just saying “players can trade”… but this is a good thing, because it gives you a lot of design control over the player experience. Here are a few options to consider:

Auctions

Auction mechanics are a special case of trading, when one player auctions off their stuff to the other players, or where the “bank” creates an item out of thin air and it is auctioned to the highest bidding player. Auctions often serve as a self-balancing mechanic in that the players are ultimately deciding on the price of how much something is worth, so if you don’t know what to cost something you can put it up for auction and let the players decide. (However, this is lazy design; auctions work the best when the actual cost is variable, different between players, and situational, so that figuring out how much it’s worth is something that changes from game to game, so that the players are actually making interesting choices each time. With an effect that is always worth the same amount, “auction” is meaningless once players figure out how much it’s worth; they’ll just bid what it’s worth and be done with it.)

Auctions are a very pure form of “willingness to pay” because each player has to decide what they’re actually willing to pay so that they can make an appropriate bid. A lot of times there are meta-considerations: not just “how much do I want this for myself” but also “how much do I not want one of my opponents to get it because it would give them too much power” or even “I don’t want this, but I want an opponent to pay more for it, so I’ll bid up the price and take the chance that I won’t get stuck with it at the end.”

An interesting point with auctions is that normally if the auction goes to the highest bidder, that the item up for auction sells for the highest willingness to pay among all of the bidders – that’s certainly what the person auctioning the item wants, is to get the highest price. But in reality, the actual auction price is usually somewhere between the highest and second highest willingness to pay, and in fact it’s usually closer to the second-highest, although that depends on the auction type: sometimes you end up selling for much lower.

Just as there are many kinds of trading, there are also many kinds of auctions. Here’s a few examples:

Even once you decide on an auction format, there are a number of ways to auction items:

Even once you decide who gets what, there are several ways to define who pays their bid:

Even if you know who has to pay what bid, you have to decide what happens to the money from the auction:

Lastly, no matter what kind of auction there is, you have to decide what happens if no one bids:

Needless to say, there are a lot of considerations when setting up an in-game economy! Like most things, there are no right or wrong answers here, but hopefully I’ve at least given you a few different options to consider, and the implications of those.

Solving common problems in multiplayer

This next section didn’t seem to fit anywhere else in the course so I’m mentioning it here, so if it seems out of place, that’s why. In multiplayer free-for-all games where there can only be one winner, there are a few problems that come up pretty frequently, that can either be considered a balance or imbalance depending on the game, but they are things that usually aren’t much fun so you want to be very careful of them.

Turtling

One problem, especially in war games or other games where players attack each other directly, is that if you get in a fight with another player – even if you win – it still weakens both of you relative to everyone else. The wise player reacts to this by doing their best to not get in any fights, instead building up their defenses to make them a less tempting target, and then when all the other players get into fights with each other they swoop in and mop up the pieces when everyone else is in a weakened state. The problem here is that the system is essentially rewarding the players for not interacting with each other, and if the interaction is the fun part of the game then you can hopefully see where this is something that needs fixing.

The game balance problem is that attacking – you know, actually playing the game – is not the optimal strategy. The most direct solution is to reward or incentivize aggression. A simple example is in the board game RISK, where attackers and defenders both lose armies so you’d normally want to just not attack, so the game goes to great lengths to avoid turtling by giving incentives to attack: more territories controlled means you get more armies next turn if you hold onto them, same for continent bonuses, and let’s not forget the cards you can turn in for armies but you only get a card if you attack.

Another solution is to force the issue by making it essentially impossible to not attack. As an example, Plague and Pestilence and Family Business are both light card games where you draw 1 then play 1. A few cards are defensive in nature, but most cards hurt opponents, and you must play one each turn (choosing a target opponent, even), so before too long you’re going to be forced to attack someone else – it’s simply not possible to avoid making enemies.

Kill the leader and Sandbagging

One common problem in games where players can directly attack each other, especially when it’s very clear who is in the lead, is that everyone by default will gang up on the leader. On the one hand, this can serve as a useful negative feedback loop to your game, making sure no one gets too much ahead. On the other hand, players tend to overshoot (so the leader isn’t just kept in check, they’re totally destroyed), and it ends up feeling like a punishment to be doing well.

As a response to this problem, a new dynamic emerges, which I’ve seen called sandbagging. The idea is that if it’s dangerous to be the leader, then you want to be in second place. If a player is doing well enough that they’re in danger of taking the lead, they will intentionally play suboptimally in order to not make themselves a target. As with turtling, the problem here is that players aren’t really playing the game you designed, they’re working around it.

The good news is that a lot of things have to happen in combination for this to be a problem, and you can break the chain of events anywhere to fix it.

If you choose to remove the negative feedback of kill-the-leader, one thing to be aware of is that if you were relying on this negative feedback to keep the game balanced, it might now be an unbalanced positive feedback loop that naturally helps the leader, so consider adding another form of negative feedback to compensate for the removal of this one.

Kingmaking

A related problem is when one player is too far behind to win, but they are in a position to decide which of two other people wins. Sometimes this happens directly – in a game with trading and negotiation, the player who’s behind might just make favorable trades to one of the leading players in order to hand them the game. Sometimes it happens indirectly, where the player who’s behind has to make one of two moves as part of the game, and it is clear to everyone that if they make one move then one player wins, and another move causes another player to win.

This is undesirable because it’s anticlimactic: the winner didn’t actually win because of superior skill, but instead because one of the losing players liked them better. Now, in a game with heavy diplomacy (like the board game Diplomacy) this might be tolerable; after all, the game is all about convincing other people to do what you want. But in most games, the winners both feel like the win wasn’t really deserved, so the game designer generally wants to avoid this situation.

As with kill-the-leader, there are a lot of things that have to happen for kingmaking to be a problem, and you can eliminate any of them:

Player elimination

A lot of two-player games are all about eliminating your opponent’s forces, so it makes sense that multi-player games follow this pattern as well. The problem is that when one player is eliminated and everyone else is still playing, that losing player has to sit and wait for the game to end, and sitting around not playing the game is not very fun.

With games of very short length, this is not a problem. If the entire game lasts two minutes and you’re eliminated with 60 seconds left to go, who cares? Sit around and wait for the next game to start. Likewise, if player elimination doesn’t happen until late in the game, this is not usually a problem. If players in a two-hour game start dropping around the 1-hour-50-minute mark, relatively speaking it won’t feel like a long time to wait until the game ends and the next one can begin. It’s when players can be eliminated early and then have to sit around and wait forever that you run into problems.

There are a few mechanics that can deal with this:

Excel

Every game designer really needs to learn Excel at some point. Some of you probably already use it regularly, but if you don’t, you should learn your way around it, so consider this a brief introduction to how Excel works and how to use it in game design, with a few tricks from my own experience thrown in. For those of you who are already Excel experts, I beg your patience, and hope I can show you at least one or two little features that you didn’t know before. Note: I’m assuming Excel 2003 for PC; the exact key combinations I list below may vary for you if you’re using a different version or platform.

Excel is a spreadsheet program, which means absolutely nothing to you if you aren’t a financial analyst, so an easier way of thinking about Excel is that it’s a program that lets you store data in a list or a grid. At its most basic, you can use it to keep things like a grocery list or to-do list in a column, and if you want to include a separate column to keep track of whether it’s done or not, then that’s a perfectly valid use (I’ve worked with plenty of spreadsheets that are nothing more than that, for example a list of art or sound assets in a video game and a list of their current status). Data in Excel is stored in a series of rows and columns, where each row has a number, each column has a letter, and a single entry is in a given row and column. Any single entry location is called a cell (as in “cell phone” or “terrorist cell”), and is referred to by its row and column (like “A1” or “B19”). You can navigate between cells with arrow keys or by clicking with the mouse.

Entering data into cells

In general, each cell can hold one of three things: a number, written text, or a computed formula. Numbers are pretty simple, just type in a number in the formula bar at the top and then hit Enter, or click the little green checkmark if you prefer. Text is also simple, just type the text you want in the same way. What if you want to include text that looks like a number or formula, but you want Excel to treat it as text? Start the entry with a single apostrophe (‘) and then you can type anything you want, and Excel will get the message that you want it to treat that cell as text.

For a formula, start the entry with an equal sign (=) and follow with whatever you want computed. Most of the time you just want simple arithmetic, which you can do with the +, -, * and / characters. For example, typing =1+2 and hitting Enter will display 3 in the cell. You can also reference other cells: =A1*2 will take the contents in cell A1, multiply by 2, and put the result in whatever other cell there is. And the really awesome part about this is that if you change the value in A1, any formulas that reference it will change automatically, which is the main thing Excel does that saves you so much time. In fact, even if you insert new rows that change the actual name of the cell you’re referencing, Excel will change your formulas to update what they’re referencing.

Adding comments

Suppose you want to leave a note to yourself about something in one of the cells. One way to do this is just to put another text field next to it, of course, although as you’ll see getting a lot of text to display in one of those tiny cells isn’t trivial – you can type it all in, of course, but there are times when that’s not practical. For those cases you can instead use the Comment feature to add a comment to the box, which shows up as a little red triangle in the corner of the cell. Mousing over the cell reveals the comment.

Moving data around

Cut, copy and paste work pretty much as you’d expect them to. You can even click and drag, or hold Shift while moving around with the arrow keys, to select a rectangular block of cells… or click on one of the row or column headings to select everything in that row or column… or click on the corner between the row and column headings (or hit Ctrl-A) to select everything. By holding Ctrl down and clicking on individual cells, you can select several cells that aren’t even next to each other.

Now, if you paste a cell containing a formula a whole bunch of times, a funny thing happens: you’ll notice that any cells that are referenced in the formula keep changing. For example, if you’ve got a formula in cell B1 that references A1, and you copy B1 and paste into D5, you’ll notice the new formula references D4 instead. That’s because by default, all of these cell references are relative in position to the original. So when you reference A1 in your formula in B1, Excel isn’t actually thinking “the cell named A1”… it’s thinking “the cell just to the left of me in the same row.” So when you copy and paste the formula somewhere else, it’ll start referencing the cell just to the left in the same row. As you might guess in this example, if you paste this into a cell in column A (where there’s nothing to the left because you’re already all the way on the left), you’ll see a result that’s an error: #REF! which means you’re referencing a cell that doesn’t exist.

If you want to force Excel to treat a reference as absolute, so that it references a specific cell no matter where you copy or paste to, there are two ways to do it. First is to use a dollar sign ($) before the column letter or row number or both in the formula, which tells Excel to treat either the row or column (or both) as an absolute position. For our earlier example, if you wanted every copy-and-paste to look at A1, you could use $A$1 instead.

Why do you need to type the dollar sign twice in this example? Because it means you can treat the row as a relative reference while the column is absolute, or vice versa. There are times when you might want to do this which I’m sure you will discover as you use Excel, if you haven’t already.

There’s another way to reference a specific, named cell in an absolute way, which is mostly useful if you’re using several cells in a bunch of complicated formulas and it’s hard to keep straight in your head which cell is which value when you’re writing the formulas. You can give any cell a name; the name is just the letter and number of the cell by default, it’s displayed in the top left part of the Excel window. To change it, just click on that name and then type in whatever you want. And then you can reference that name anywhere else in the spreadsheet and it’ll be an absolute reference to that named cell.

Sorting

Sometimes you’ll want to sort the data in a worksheet. A common use of Excel is to keep track of a bunch of objects, one per row, and each attribute is listed in a separate column. For example, maybe on a large game project you’ll have an Excel file that lists all of the enemies in a game, with the name in one column, hit points in another, damage in another, and so on. And maybe you want to sort by name just so you have an easy-to-lookup master list, or maybe you want to sort by hit points to see the largest or smallest values, or whatever. This is pretty easy to do. First, select all the cells you want to sort. Go to the Data menu, and choose Sort. Next, tell it which column to sort by, and whether to sort ascending or descending. If you’ve got two entries in that column that are the same, you can give it a second column as a tiebreaker, and a third column as a second tiebreaker if you want (otherwise it’ll just preserve the existing order when it sorts like that). There’s also an option for ignoring the header row, so if you have a header with column descriptions at the very top and you don’t want that sorted… well, you can just not select it when sorting, of course, but sometimes it’s easier to just select the whole spreadsheet and click the button to ignore the header row. If you accidentally screw up when sorting, don’t panic – just hit Undo.

Sometimes you realize you need to insert a few rows or columns somewhere, in between others. The nice thing about this is that Excel updates all absolute and relative references just the way you’d want it to, so you should never have to change a value or formula or anything just because you inserted a row. To insert, right-click on the row or column heading, and “insert row” or “insert column” is one of the menu choices. You can also insert them from the Insert menu.

If you need to remove a row or column it works similarly, right-click on the row or column heading and select “delete.” You might think you could just hit the Delete key on the keyboard too, but that works differently: it just clears the values of the cells but doesn’t actually shift everything else up or left.

Using your data

Sometimes you’ve got a formula you want copied and pasted into a lot of cells all at once. My checkbook, for example, has formulas on each row to compute my current balance after adding or subtracting the current transaction from the previous one, and I want that computation on every line. All I had to do was write the formula once… but if I had to manually copy then paste into each individual cell, I’d cry. Luckily, there’s an easy way to do this: Fill. Just select the one cell you want to propagate, and a whole bunch of other cells below or to the right of it, then hit Ctrl+D to take the top value and propagate it down to all the others (Fill Down), or Ctrl+R to propagate the leftmost value to the right. If you want to fill down and right, you can just select your cell and a rectangular block of cells below and to the right of it, then hit Ctrl+D and Ctrl+R in any order. You can also Fill Up or Fill Left if you want, but those don’t have hotkeys; you’ll have to select those from the Edit menu under Fill. As with copying and pasting, Fill respects absolute and relative references to other cells in your formulas.

There’s kind of a related command to Fill, which is useful in a situation like the following example: suppose you’re making a list of game objects and you want to assign each one a unique ID number, and that number is going to start at 1 and then count upwards from there, and let’s say you have 200 game objects. So in one column, you want to place the numbers 1 through 200, each number in its own cell. Entering each number manually is tedious and error-prone. You could use a formula, like, say, putting the number 1 in the first cell, let’s say it’s cell A2, and then in B2 put the formula =A2+1 (which computes to 2), then Fill Down that formula to create the numbers all the way down to 200. And that will work at first, but whenever you start reordering or sorting rows, all of these cells referencing each other might get out of whack, and it might work or it might not but it’ll be a big mess regardless. And anyway, you don’t really want a formula in those cells anyway, you want a number.

You could create the 200 numbers by formula on a scratch area somewhere, then copy, then Paste Special (under the Edit menu), and select Values, which just takes the computed values and pastes them in as numbers without copying the formulas. And then you just delete the formulas that you don’t need anymore. That would work, and Paste Special / Values is an awesome tool for a lot of things, but it’s overkill here.

Here’s a neat little trick: just create two or three cells and put the numbers 1, 2, 3 in them. Now, select the three cells, and you’ll notice there’s a little black square dot in the lower right corner of the selection. Click on that, and drag down a couple hundred rows. When you release the mouse button, Excel takes its best guess what you were doing, and fills it all in. For something simple like counting up by 1, Excel can figure that out, and it’ll do it for you. For something more complicated you probably won’t get the result you’re looking for, but you can at least have fun trying and seeing what Excel thinks you’re thinking.

Functions

Excel comes with a lot of built-in functions that you can use in your formulas. Functions are always written in capital letters, followed by an open-parenthesis, then any parameters the function might take in (this varies by function), then a close-parenthesis. If there are several parameters, they are separated by commas (,). You can embed functions inside other ones, so one of the parameters of a function might actually be the result of another function; Excel is perfectly okay with that.

Probably the single function I use more than any other is SUM(), which takes any number of parameters and adds them together. So if you wanted to sum all of the cells from A5 to A8, you could say =A5+A6+A7+A8, or you could say =SUM(A5,A6,A7,A8), or you could say =SUM(A5:A8). The last one is the most useful; use a colon between two cells to tell Excel that you want the range of all cells in between those. You can even do this with a rectangular block of cells by giving the top-left and bottom-right corners: =SUM(A5:C8) will add up all twelve cells in that 3×4 block.

The second most useful function for me is IF, which takes in three parameters. The first is a condition that’s evaluated either to a true or false value. The second parameter is evaluated and returned if the condition is true. The third parameter is evaluated and returned if the condition is false. The third parameter is optional; if you leave it out and the condition is false, the cell will just appear blank instead. For example, you could say: =IF(A1>0,1,5) which means that if A1 is greater than zero, this cell’s value is 1, otherwise it’s 5. One of the common things I use with IF is the function ISBLANK() which takes a cell, and returns true if the cell is blank, or false if it isn’t. So you can use this, for example, if you’re using one column as a checklist and you want to set a column to a certain value if something hasn’t been checked. If you’re making a checklist and want to know how many items have (or haven’t) been checked off, by the way, there’s also the function COUNTBLANK() which takes a range of cells as its one parameter, and returns the number of cells that are blank.

For random mechanics, look back in the week where we talked about pseudorandomness to see my favorite three functions for that: RAND() which takes no parameters at all and returns a pseudorandom number from 0 to 1 (it might possibly be zero, but never one). Changing any cell or pressing F9 causes Excel to reroll all randoms. FLOOR() and CEILING() will take a number and round it down or up to the nearest whole number value, or you can use ROUND() which will round it normally.

FLOOR() and CEILING() both require a second parameter, the multiple to round to; for most cases you want this to be 1, since you want it rounding to the nearest whole number, but if you want it to round up or down to the nearest 5, or the nearest 0.1, or whatever, then use that as your second parameter instead. Just to be confusing, ROUND() also takes a second parameter, but it works a little differently. For ROUND(), if the second parameter is zero (which you normally want) then it will round to the nearest whole number. If the second parameter is 1, it rounds to the nearest tenth; if the second parameter is 2, it rounds to the nearest hundredth; if the second parameter is 3, it rounds to the nearest thousandth; and so on – in other words, the second parameter for ROUND() tells you the number of digits after the decimal point to include in the significance.

RANK() and VLOOKUP(), I already mentioned back in Week 6; they’re useful for when you need to take a list and shuffle it randomly.

Multiple worksheets

By default, a new Excel file has three worksheet tabs, shown at the bottom left. You can rename these to something more interesting than “Sheet1” by just double-clicking the tab, typing a name, and hitting Enter. You can also reorder them by clicking and dragging, if you want a different sheet to be on the left or in the middle. You can add new worksheets or delete them by right-clicking on the worksheet tab, or from the Insert menu. Ctrl+PgUp and Ctrl+PgDn provide a convenient way to switch between tabs without clicking down there all the time, if you find yourself going back and forth between two tabs a lot.

The reason to create multiple worksheets is mostly for organizational purposes; it’s easier sometimes if you’ve got a bunch of different but related systems to put each one in its own worksheet rather than having to scroll around all over the place to find what you’re looking for on a single worksheet.

You can actually reference cells in other worksheets in a formula, if you want. The easiest way to do it is to type in the formula until you get to the place where you’d type in the cell name, then use your mouse to click on the other worksheet, then actually click on the cell or cells you want to reference. One thing to point out here is that it’s easy to do this by accident, where you’re entering something in a cell and don’t realize you haven’t finished, and then you click on another cell to see what’s there and instead it starts adding that cell to your formula; if that happens or you otherwise feel like you’re lost and not sure how to get out of entering half of a formula, just hit the red X button to the left of the formula bar and it’ll undo any typing you did just now.

Graphing

One last thing that I find really useful is the ability to create a graph, great for looking graphically at your game objects when they relate to each other. Select two or more rows or columns, each one is just a separate curve, then select the Insert menu, then Chart. Select XY(Scatter) and then the subtype that shows curvy lines. From there, go through the wizard to select whatever options you want, then click Finish and you’ll have your chart.

One thing you’ll often want to do with graphs is to add a trendline; right-click on any single data point on the graph, and select Add Trendline. You’ll have to tell it whether the trendline should be linear, or exponential, or polynomial, or what. On the Options tab of the trendline wizard, you can also have it display the equation on the chart so you can actually see what the best-fit curve is, and also display the R-squared value (which is just a measure of how close the fitted curve is to the actual data; R-squared of 1 means the curve is a perfect fit, R-squared of 0 means it may as well be random… although in practice, even random data will have an R-squared value of more than zero, sometimes significantly more). If you’re trying to fit a curve, as happens a lot when analyzing metrics, you’ll probably want to add these right away.

Another thing you should know is that by default, the charts Excel makes are… umm…  really ugly. Just about everything you can imagine to make the display better, you can do: adding vertical and not just horizontal lines on the graph, changing the background and foreground colors of everything, adding labels on the X and Y axis, changing the ranges of the axes and labeling them… it’s all there somewhere. Every element of the graph is clickable and selectable on its own, and generally if you want to change something, just right-click on it and select Format, or else double-click it. Just be aware that each individual element – the gridlines, the graphed lines, the legend, the background, the axes – are all treated separately, so if you don’t see a display option it probably just means you have the wrong thing selected. Play around with the formatting options and you’ll see what I mean.

Making things look pretty

Lastly, there are a few things you can do to make your worksheets look a little bit nicer, even without the graphs, even if it’s just cells. Aside from making things look more professional, it also makes it look more like you know what you’re doing 🙂

The most obvious thing you can do is mess with the color scheme. You can change the text color and background color of any cell; the buttons are on a toolbar in the upper right (at least they are on my machine; maybe they aren’t for you, if not just add the Formatting toolbar and it’s all on there). You can also make a cell Bolded or Italicized, left or right justified, all the other things you’re used to doing in Word. Personally, I find it useful to use background color to differentiate between cells that are just text headings (no color), cells where the user is supposed to change values around to see what effect they have on the rest of the game (yellow), and cells that are computed values or formulas that should not be changed (gray), and then Bolding anything really important.

You also have a huge range of possible ways to display numbers and text. If you select a single cell, a block of cells, an entire row or column, or even the whole worksheet, then right-click (or go to the Format menu) and select Format Cells, you’ll have a ton of options at your disposal. The very first tab lets you say if this is text or a number, and what kind. For example, you can display a number as currency (with or without a currency symbol like a dollar sign or something else), or a decimal (to any number of places).

On the Alignment tab are three important features:

One thing you’ll find sometimes is that you have a set of computed cells, and while you need them to be around because you’re referencing them, you don’t actually need to look at the cells themselves – they’re all just intermediate values. One way to take care of this is to stick them in their own scratch worksheet, but an easier way is to stick them in their own row or column and then Hide the row or column. To do that, just right-click on the row or column, and there’s a Hide option. Select that and the row or column will disappear, but you’ll see a thick line between the previous and next columns, a little visual signal to you that something else is still in there that you just can’t see. To display it again, select the rows or columns on either side, right-click and select Unhide.

If you want to draw a square around certain blocks of data in order to group them together visually, another button in the Formatting tab lets you select a border. Just select a rectangle of cells, then click on that and select the border that looks like a square, and it’ll put edges around it. The only thing I’ll warn you is that when you copy and paste cells with borders, those are copied and pasted too under normal conditions, so don’t add borders until you’re done messing around (or if you have to, just remove the borders, move the cells around, then add them back in… or use Paste Special to only paste formulas and not formatting).

Another thing that I sometimes find useful, particularly when using a spreadsheet to balance game objects, is conditional formatting. First select one or more cells, rows or columns, then go to the Format menu and select Conditional Formatting. You first give it a condition which is either true or false. If it’s true, you can give it a format: using a different font or text color, font effects like bold or italic, adding borders or background colors, that sort of thing. If the condition isn’t true, then the formatting isn’t changed. When in the conditional formatting dialog, there’s an “Add” button at the bottom where you can add up to two other conditions, each with its own individual formatting. These are not cumulative; the first condition is always evaluated first (and its formatting is used if the condition is satisfied). If not, then it’ll try the second condition, and if not that it’ll try the third condition. As an example of how I use this, if I’m making a game with a cost curve, I might have a single column that adds up the numeric benefits minus costs of each game object. Since I want the benefits and costs to be equivalent, this should be zero for a balanced object (according to my cost curve), positive if it’s overpowered and negative if it’s underpowered. In that column, I might use conditional formatting to turn the background of a cell a bright green color if benefits minus costs is greater than zero, or red if it’s less than zero, so I can immediately get a visual status of how many objects are still not balanced right.

Lastly, in a lot of basic spreadsheets you just want to display a single thing, and you’ve got a header row along the top and a header column on the left, and the entire rest of the worksheet is data. Sometimes that data doesn’t fit on a single page, but as you scroll down you forget which column is which. Suppose you want the top row or two to stay put, always displayed no matter how far you scroll down, so you can always see the headings. To do that, select the first row below your header row, then go to the Window menu and select Freeze Panes. You’ll see a little line appear just about where you’d selected, and you’ll see it stay even if you scroll down. To undo this, for example if you selected the wrong row by accident, go to the Window menu and select Unfreeze Panes (and then try again). If you want instead to keep the left columns in place, select the column just to the right, then Freeze Panes again. If you want to keep the leftmost columns and topmost rows in place, select a single cell and Freeze Panes, and everything above or to the left of that cell is locked in place now.

About that whole “Fun” thing…

At this point we’ve covered just about every topic I can think of that relates to game balance, so I want to take some time to reflect on where balance fits in to the larger field of game design. Admittedly, the ultimate goal of game design depends on the specific game, but in what I’d say is the majority of cases, the goal of the game designer is to create a fun experience for the players. How does balance fit in with this?

When I was a younger designer, I wanted to believe the two were synonymous. A fun game is a balanced game, and a balanced game is a fun game. I’m not too proud to say that I was very wrong about this. I encountered two games in particular that were fun in spite of being unbalanced, and these counterexamples changed my mind.

The first was a card game that I learned as Landlord (although it has many other names, some more vulgar than others); the best known is probably a variant called The Great Dalmuti. This is a deliberately unbalanced game. Each player sits in a different position, with the positions forming a definite progression from best to worst. Players in the best position give their worst cards to those in the worst position at the start of the round, and the worst-position players give their best cards to those in the best position, so the odds are strongly in favor of the people at the top. At the end of each hand, players reorder themselves based on how they did in the round, so the top player takes top seat next round. This is a natural positive feedback loop: the people at the top have so many advantages that they’re likely to stay there, while the people at the bottom have so many disadvantages that they’re likely to stay there as well. As I learned it, the game never ends, you just keep playing hand after hand until you’re tired of it. In college my friends and I would sometimes play this for hours at a time, so we were clearly having a good time in spite of the game being obviously unbalanced. What’s going on here?

I think there are two reasons here. One is that as soon as you learn the rules, it is immediately obvious to you that the game is not fair, and in fact that the unfairness is the whole point. It’s not that fairness and balance are always desirable, it’s that when players expect a fair and balanced game and then get one that isn’t, the game doesn’t meet their expectations. Since this game sets the expectation of unfairness up front, by choosing to play at all you have already decided that you are willing to explore an unbalanced system.

Another reason why this game doesn’t fail is that it has a strong roleplaying dynamic, which sounds strange because this isn’t an RPG… but at the same time, players in different seats do have different levels of power, so some aspect of roleplaying happens naturally in most groups. The players at the top are having fun because “it’s good to be king.” The players at the bottom are also having fun because there’s a thrill of fighting against the odds, striking a blow for the Little Guy in an unfair system, and every now and then one of the players at the bottom ends up doing really well and suddenly toppling the throne, and that’s exciting (or one of the guys on top crashes and falls to the bottom, offering schadenfreude for the rest of the players). For me it’s equally exciting to dig my way out from the bottom, slowly and patiently, over many hands, and eventually reaching the top (sort of like a metaphor for hard work and retirement, I guess). Since the game replicates a system that we recognize in everyday life where we see the “haves” and “have-nots,” being able to play in and explore this system from the magic circle of a game has a strong appeal.

The second game I played that convinced me that there’s more to life than balance, is the (grammatically-incorrectly titled) board game Betrayal at House on the Hill. This game is highly unbalanced. Each time you play you get a random scenario which has a different set of victory conditions, but most of them strongly favor some players over others, and most don’t scale very well with number of players (that is, most scenarios are much easier to win or lose if there are 3 players or 6 players, so the game is often decided as a function of how many players there are and which random scenario you get). The game has a strong random element that makes it likely one or more players will have a very strong advantage or disadvantage, and in most scenarios it’s even possible to have early player elimination. Not that it has to do with balance, but the first edition of this game also has a ton of printing errors, making it seem like it wasn’t playtested nearly enough. (In fact, I understand that it was playtested extensively, but the playtesters were having such a fun time playing that they didn’t bother to notice or report the errors they encountered.)

In spite of the imbalances, the randomness and the printing errors, the game itself is pretty fun if you play in the right group. The reason is that no matter what happens, in nearly every game, some kind of crazy thing happened that’s fun to talk about after the fact. The game is very good at creating a story of the experience, and the stories are interesting. Partly this has to do with all of the flavor text in the game, on the cards and in the scenarios… but that just sets the haunted-house environment to put the players in the right frame of mind. Mostly it’s that because of the random nature of the game, somewhere along the line you’ll probably see something that feels highly unlikely, like one player finding a whole bunch of useful items all at once, or a player rolling uncharacteristically well or poorly on dice at a key point, or drawing just the right card you need at just the right time, or a player finding out the hard way what that new mysterious token on the board does. And so, players are willing to overlook the flaws because the core gameplay is about working together as a team to explore an unfamiliar and dangerous place, then having one of your kind betray the others and shifting to a one-against-many situation, and winning or losing as a coordinated team. And as a general game structure, that turns out to be unique enough to be interesting.

Now, player expectation is another thing that is a huge factor in Betrayal. I’ve seen some players that didn’t know anything about the game and were just told, “oh, this is a fun game” and they couldn’t get over the fact that there were so many problems with it. When I introduce people to the game, I always say up front that the game is not remotely balanced, because it helps people to enjoy the experience more. And incidentally, I do think it would be a better game if it were more balanced, but my point is that it is possible for a game design to succeed without it.

So, at the end of the day, I think that what game balance does is that it makes your game fair. In games where players expect a fair contest, balance is very important; for example, one of the reasons a lot of players hate the “rubber-banding” negative feedback in racing games, where an AI-controlled car suddenly gets an impossible burst of speed when it’s too far behind you, is that it feels unfair because real-life racing doesn’t work that way. But in a game like The Great Dalmuti which is patently unfair, players expect it to be unbalanced so they accept it easily. This is also why completely unbalanced, overpowered cards in a Trading Card Game (especially if they’re rare) are seen as a bad thing, but in a single-player card-battle game using the same mechanics they can be a lot of fun: for a head-to-head tabletop card game players expect the game to provide a fair match, so they want the cards to be balanced; in the case of the single-player game, the core of the game is about character growth and progression, so getting more powerful cards as the game progresses is part of the expectation.

Just like everything in game design, it’s all about understanding the design goals, what it is you want the player to experience. But if you want them to experience a fair game, which is at least true in most games, then that is the function of balance. In fact, the only games I can think of where you don’t want balance are those where the core gameplay is specifically built around playing with the concept of fairness and unfairness.

If You’re Working on a Game Now…

Well, you’re probably already using Excel in that case, so there’s not much I can have you do to exercise those skills that you’re not already doing.

If your game has a free-for-all multiplayer structure, ask yourself if any of the problems mentioned in this post (turtling, kill-the-leader, sandbagging, kingmaking, early elimination) might be present, and then decide what (if anything) to do about them.

If your game has an economic system, analyze it. Can players trade? Are there auctions? What effect would it have on the game if you added or removed these? Are there alternatives to the way your economic system works now that you hadn’t considered?

Homework

Since it’s the end of the course, there are two ways to approach this. One is to say, no “homework” at all, because hey, the course is over! But that would be lazy design on my part.

Instead, let me set you a longer challenge that brings together everything we’ve talked about here. Make a game, and then apply all the lessons of game balance that you can. Spend a month on it, maybe more if it ends up being interesting, and then you’ll have something you can add to your game design portfolio. It’s up to you whether you want to do this, of course.

Some suggestions:

References

I found the following two blog posts useful to reference when writing about auctions and multiplayer mechanics, respectively:

http://jergames.blogspot.com/2006/10/learn-to-love-board-games-again100.html#auctions

and

http://pulsiphergamedesign.blogspot.com/2007/11/design-problems-to-watch-for-in-multi.html

In Closing…

I’d just like to say that putting this information together over this summer has been an amazing experience for me, and I hope you have enjoyed going on this journey with me.

You might be wondering if I’m going to do something like this again in the future. You can bet the answer to that will be yes, although of course I don’t know exactly what that will be. Expect to see an announcement here when I’m setting up the courses for Summer 2011, if you want to take part.

Enjoy,

– Ian Schreiber

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