Hearthstone

Hearthstone is a trading card game released by Blizzard in March 2014. It's available on PC, Mac, iOS, Android, and more platforms because it is built on top of Unity. Hearthstone had 25 million registered players in January 2015. If you come from a traditional pay-to-play sector of the game industry, you could say that Hearthstone has twice more players than World of Warcraft, and be impressed. But if you come from the free-to-play sector of the game industry, you know this number means nothing: the game is free, so players will eventually try it out. In the mobile F2P market, nobody reports "registered players": what matters is the number of monthly users, and the average revenue per user. In fact, if we look at Hearthstone as a free-to-play mobile game, it is an outlier in several ways. And it's not necessarily a bad thing.

First, the business model. Players can earn coins, a soft currency in the game, by completing daily quests. One new quest becomes available per day, each quest takes 1-2 hours to complete, and grants 40-60 coins. Players can also get coins by winning games against other players. The amount is much smaller though: 10 coins every 3 wins (a match takes 10-15 minutes). Each pack of five cards cost 100 coins or $1-$1.5 if bought with real money. Cards can also be crafted from dust, another in-game currency. Dust can be acquired (nearly) only from cards bought with real money. So the game is free to play, but with 5 new cards roughly every 2 days, non-payers will find it excruciatingly slow to progress compared to other free-to-play games.

Second, mudflation. Some cards from the Gnome vs Goblin expansion set clearly outclass cards from the base set. For example, the Murloc Raider from the base set, has 2 attack, 1 HP, and costs 1 mana. The Clockwork Gnome from the expansion has the same stats, AND gives a 1-cost utility card to its owner when killed. I admit that this kind of outclassing also happened between the free cards and paid cards from the base set. For example, the River Crocolisk from the free base set is outclassed by the Amani Berserker and the Bloodsail Raider (both paid/crafted cards). So balance-wise, it's as if the set of paid cards was the first expansion, and Gnome vs Goblin cards the second. Either way, non-payers can't compete against players who purchase (expansion) cards.

Last, the daily quests. Blizzard first came up with daily quests in World of Warcraft, 6-7 years ago, to give people things to do while waiting for the next content patch. They had removed the cap of daily quests completable per day, and realized that "that really leads to burn out". Mobile free-to-play games started using daily quests as a way to retain players, 3-4 years ago. And now, Blizzard is back to using daily quests to retain players. But this time, they cap the quests to 3. Compare this to the dozens of achievements in Clash of Clans, where there's always something to look ahead for. Players could play hours at a time to push for Clash of Clans achievements. But in Hearthstone, quests run out quickly, so there is little reason for players to stay longer than necessary (except maybe leveling up or winning, but the rewards are so much lower than daily quests that they don't seem worth it). I also suspect that players eventually get tired of doing the same quests again and again. Cleaning up Naxxramas brings a good change of pace, and has very interesting mechanics, but each aisle cost 700 coins, so it only happens once every 2 weeks. Too bad ... So daily quests: somewhat good for day-to-day retention, but probably bad for session duration.

Game Architecture and Design - part 1: Design

Game Architecture and Design - part 1: Design, by Rollings and Morris, 2004

Ch1 - First concept

Originality can come from the gameplay, story, setting, characters, interface, or technology. It can also come from unexpected combinations. For example, a vampire living on a foggy island must fight against invading pirates. Present it through Indonesian shadow puppets, or Dia de los Muertos, or The Terror in France. It helps to think of movies, books, or music related to the theme.

Ch2 - Core design

Player goals can range from collecting something, gaining territory, racing, removing obstacles (finding keys to open doors), discovering (eg puzzles), or beating/killing other players. Provide means for these goals, and think about the feelings conveyed.

Emergence can be defined as complexity arising from simple rules. That is, rules interacting with rules or the environment. Populous preachers provide an interesting example of emergence. Preachers can convert warriors to their side unless those warriors are already in battle. Thus the first wave of enemy warriors will be converted by the preachers, but the second wave of warriors will fight with the converted warriors instead of being converted. These two simple rules force the player to regularly check her defenses.

Trivial choices are choices the players will always or never take. They should be avoided or left for the computer/AI to perform for the player. For example, when an ennemy unit is in sight, the player's units should shoot.

Ch3 - Gameplay

Synergies (also from slides by Claypool)

	of scale	of scope
Economy	The more of one unit, the cheaper/better/stronger. Ex: making more knights reduces their shadow cost per unit.	The more of a set, the better. Ex: trident + net, healer + tank + DPS.
Diseconomy	Benefits decrease with quantity.	Ex: mixed troops go as fast as their slowest member.

An interesting decision has an upside, a downside, and the payoff depends on circumstances (eg other players, environment, or self). For example, a Starcraft Terran player can choose to upgrade his Marine's attack range or attack rate. If the opponent plays Zergs, upgrading the attack rate is a very good choice. If the opponent plays Protoss, Marines are generally not the way to go (unless for surprise effect in a Marine-Vulture rush).

The shadow cost of a unit is any requirement the player had to pay before buying that unit. For example, knights require the cavalry technology ($100) and stables ($200). Knights can be purchased at the stables for $50. Thus making the first knight has a direct cost of $50 and a total shadow cost of $100 + $200 = $300. So overall, the knight costs $350. Making a second knight still costs $50, but reduces the shadow cost per knight to $300/2 = $150. Overall, making 2 knights costs $50 + $150 = $200 per knight. The tenth knight still costs $50, but decreases the shadow cost per knight to $30. At that point, the overall cost of a knight is $50 + $30 = $80.

Supporting investments are remotely related to the player's goal. For example, one needs to build farms to produce food to feed knights. Farms are a 2-degree supporting investment (farm - food - knights). Upgrading the damage of knights is a 1-degree supporting investment (upgrade - knights).

Costs (whether normal costs, supporting investments, or shadow costs) also depend on the environment. In Age of Empires, a unit costs 40 woods and takes 40 seconds to build. In the early game, things start slowly, so the expensive part is the 40 woods. Mid-game, events happen quickly, so the expensive part is 40 seconds. End-game, wood is depleted, so 40 woods is expensive again.

Strategic (ie long-term) choices will later impact tactical (short-term) choices.

Impermanence is an interesting choice: should I receive armor+100 for 30 seconds, or armor+5 forever?

Versatile choices are good for beginners. In an RTS, speed makes units more versatile.

Ch5 - Balance

Rewards = gameplay payoffs + graphics eye-candy.

Component balance = comparing unit A to unit B.

Attribute balance = comparing attack range to attack power (in a small map, attack range is not as important as attack power).

Ch6 - Look and feel

A list of storytelling techniques.

Obstacles: the player has to decipher/fight/think about the events to make the plot progress

Foreshadowing: prepare for the plot by giving a hint/preview. Ex: in an RTS, a couple clubmen attack my settlement. They were only scouts of a larger army ...

Personalization: saving the world is cliche and bad. Instead, the sexy princess asks ME to save her. Saving the world is a side-effect. The player identifies with his avatar during gameplay AND cutscenes. If the avatar has 2 hours to find a cure for himself, the player cares.

Resonance: The most subtle consists of repeated images that defy instant critical analysis. More direct: visual symbols that directly express the subtext.

Resistance: elements that delay the unfolding of the story. Helps suspend disbelief. The best way to involve the hero in a crazy story is by having him refuse at first. Ex: "please save the president" - "no, i'm retired" (this surprises the audience) - the bad guy kidnaps his daughter - "OK I'll do it"

Plot point: confound expectations or change the story's direction. 3 types: reversal (traitor!), discovery (a change from ignorance to knowledge, usually most effective when paired with reversals), and calamity (Gandalf dies at the beginning of the journey!). Ideally, each level begins and ends with a plot point, ideally during gameplay rather than during a cutscene. Early plot points deepen the story, later plot points clear u[ mysteries. Small plot points every 30 mins, big plot points every 3h.

Suspense: fear and expectation.

Dialogue: not needed if images can convey the idea better. Can give more colorful details.

Theme: Do not answer the questions you ask. Ex in Matrix: What is reality? How powerful is love?

Resolution: should be hard-won (satisfaction from effort), not obvious, satisfying (morally or aesthetically), consistent (with what happened so far), and achieve closure (solve problems of the story). Could use self-sacrifice at the end: when the avatar dies, the story naturally ends for the player.

Change: Change in the status quo causes the action. At the end, the hero must have changed in some ways (he learned or failed to learn something, grew up, ...).

Dominion's balance

Chapel

One of the cards in the Dominion base set is considered slightly better than most: the Chapel. Some simply say This is the best card in the game.. Others suggest that Chapel is very overpowered and should cost more. Vaccarino, Dominion's designer, is quite present on board game forums, and has stepped up to answer players' suggestions. Surprisingly, he admitted himself that Chapel is the most powerful Dominion card relative to its cost. This is the occasion to glean interesting tidbits about game balance!

First, since both players can buy the same cards, poorly balanced cards don't make the game unfair, [...] but they do make the game worse. It seems that as long as an unbalanced card makes the game fun, it should stay (and probably be tweaked).

Let's start with adjusting the cost. If Chapel cost more, it would be much weaker, and would not be used at all. This would reduce the number of options available in the game. Since it's more fun to have more options, increasing the cost is not a good solution. Ideally, everything gets played sometimes, and the only weak cards are those that are overrated. That is why to keep the metagame and discussion interesting, Vaccarino would rather avoid commenting himself.

This does not mean that overpowered cards are better than underpowered cards: if a card is so strong it is unavoidable, then cards that do not combo well with it will never be played, which is a waste. When using Chapel, a lot is left up to you. This provides a lot of diverse game play, which means Chapel has a strong play value, and the game benefits from it overall. As they progress, players learn using Chapel in new ways, which is a long-term rewarding experience:

1. why would I ever buy this when Witch isn't out?
2. trash your Estates with it and just have one dead card instead of three
3. trash your coppers [and estates] with it, and get a thin deck
4. is Chapel / Militia better so I can hurt other Chapel decks, or should I go Chapel / Spy to ensure trashing 4 cards
5. Chapel / Throne Room / Remodel

Another player suggested nerfing Chapel from trashing 4 cards to only 3 cards. Vaccarino seems to agree: in general, overpowered or underpowered cards can only be fixed by changing what the card does, not by changing their cost. But during playtesting, Chapel with "trash up to 3" was way slower than trashing up to 4, and Vaccarino couldn't win with it.

And this is how Chapel stayed at trashing up to 4 cards for a cost of 2 coins.

Playtesting

The play space of Dominion is quite big: there are around 10^15 possible combinations of 10 cards among the 157 available as of 2012. Therefore not all combinations of cards can be checked during playtesting. Since games get played way more than they get playtested, there may be some card combos that go unchecked until release. If a single card is overpowered, it is quite easy to spot and will be fixed. Two-card combos happen more rarely, so if one of them is overpowered, it may not be spotted as easily, but will also matter less. As for overpowered three-card combos, the Dominion developers aren't necessarily finding them. But if one happens during a game, and a player figures it out, it is highly unlikely that the player will face these three cards again in another game.

Playtesting can also reveal interesting/core design ideas. For example, Vaccarino was worried that drawing your whole deck would be bad. Soon [he] realized it was in fact fun.

Dominion's ecosystem

Without going into too many details, Dominion is a medieval-themed deck-building card game designed by Donald Vaccarino. The base set was released in 2008 and received a bunch of awards. A total of 8 expansions have been following, released every 6 months. Most of the cards of the 8 expansions were already designed and bundled in sets since 2008.

In Dominion, the optimal strategy depends on which cards are already in your deck, what the other players do, what cards are available to add to your deck, and a small amount of (somewhat controllable) luck. The game has been so carefully tuned and playtested that some reviewers consider it too safe and overbalanced, overdesigned and overdeveloped. Dominion's balance is so interesting that it deserves an article in itself.

Looking at the complex interactions between cards, Dominion reminds of Magic the Gathering. For example, expert players talk about engines, a concept similar to Magic's deck types, but (I'd say) deeper. In fact, the MtG analogy is not surprising, given that Vaccarino is a veteran MtG player who pitched several design ideas to the MtG designers in the late 1990s.

After having played around 100 games, Dominion also reminds of Chess: it has traditional openings, annotated games, and a vocabulary very game-specific (e.g. greening or stalling). Dominion is a very deep game.

Expansions

Of the 8 Dominion expansions, some have been received more favorably than others. For example, Alchemy is the third expansion. It adds potions, a new currency, and not too many people enjoy playing just Alchemy games. On the other, the fourth expansion is called Prosperity, and it adds a lot of over-the-top cards: compare, for example, Market from the basic game to Grand Market in Prosperity. This expansion is certainly the most well-received.

The lesson here seems to be: make more awesome versions of what exists already, and adding extra currencies like Potions makes the game more complicated, but not necessarily more fun.

Dominion's unofficial ecosystem

A lot of unofficial projects emerged around Dominion. For example, a card set constructor helps you determine which cards to pick for your non-digital game(s) with friends. An AI simulator enables experts to polish their strategies by scripting basic AIs and running thousands of games between those AIs. The AI is provided from external files, and the returned graphs plot the average number of points earned per turn against the number of turns. As an example, this technique was used on the basic set of the first Dominion. There are also fan-made expansions, a zombie retheme, and a stand-alone program to play Dominion by yourself against AIs.

Since at least 2010, an online server called isotropic has been running Dominion games online. Its interface is very simple, and a lot of players have been enjoying the fact that it is free and of relatively good quality. Vaccarino has even been using it to playtest his expansions with select players. Along isotropic, there used to be councilroom, a website used to measure various statistics about Dominion cards from isotropic game logs. A lot of expert players seem to have enjoyed the stats reported by councilroom. And there used to be a free iPhone app that allowed people to play Dominion online with other people, but it was discontinued in April 2012.

Dominion generated dozens of projects run by motivated fans. How could a game publisher channel these fans? And how much control should be exerted?

Balance of Power - Crawford 1986

Notes from Balance of Power, a book by Chris Crawford published in 1986.

Games vs simulations

Games differ from simulations in three ways. First, games carry an artistic message, with unquantifiable concepts and feelings. Second, games simplify reality: they only keep the conflicts inherent in the situation, and unlike in real life, they provide clear and emotionally satisfying resolutions to those conflicts. Yet games maintain a level of realism appropriate to the audience. Finally, games are accessible; there is no need to study the manual.

Balance of power, in short

The player controls one of the two superpowers, the USA or the USSR, during the Cold War. Each turn, both superpowers send money, weapons, troops, or diplomatic pressure onto other countries to trigger insurgencies, coups d'etat, or Finlandization favorable to them. For example, the USSR can send money to Cuba.

If a superpower contest the actions taken by the other superpower, then a crisis testing the player's brinksmanship follows. Either the player stands firm on its ground (whether s/he was contesting or not), and brings the crisis one DEFCON level higher, ie one step closer to World War III and a nuclear holocaust, or s/he pulls back. For example, think about the Cuba missile crisis of 1962.

When a superpower stands firm and wins the crisis, it gains prestige points. A minor country such as Nicaragua is worth 2 points, while a country like East Germany is worth 200 points. The further down in a crisis a superpower backs down, the more it loses prestige. When the highest DEFCON level is reached, the game is lost for both players.

The game ends after eight turns. The superpower with most prestige points win.

Balance of insurgencies

Insurgencies consist of rebels trying to take over the government of a minor country. The strength of any armed faction is measured from its number of soldiers and its number of weapons. If 100 government forces share 1 weapon, then the government's power should be low, and a superpower providing a couple weapons would really increase its strength. Similarly, 1 government force with 100 weapons should be weak. Thus, the strength of an armed faction is the harmonic mean of the number of soldiers and the number of weapons. It is optimal when each soldier has a weapon.

Balance of crises

Nastiness is a game-wide variable; it describes how slippery taking actions in the world has become. When nastiness is high, the AI is more likely to contest the player's actions, start crises, and refuse to back down. Nastiness increases after each crisis or military intervention of a superpower, and decreases slowly every turn.

Pugnacity is a superpower variable; it describes how trustworthy the superpower is considered by minor countries. Pugnacity increases when the superpower is aggressive and wins crises, and decreases when a superpower backs down in crises. If a superpower backs down late in a crisis, it loses a lot of pugnacity.

Combined, nastiness and pugnacity amplify the amplitude of missteps; an error in judgement can cause the end of the game. This is exactly what Crawford was trying to convey about brinksmanship.

MapReduce for MMOs

MapReduce is a powerful tool to parallelize batches of computations. MMOs may sometimes have to run batches, but from what local game companies tell me, nobody in the game industry is currently using MapReduce. I guess, this is mostly due to studios not knowing what to do with it. Here are some examples.

Business intelligence

Basic metrics such as weekly play time or stop rate can give a rough perspective of the retention of an MMO. These metrics can be estimated with a couple SQL queries on dumps of the production database(s). It starts taking more time and effort to distinguish accross server shard, faction, race, or class. Still, a SQL script running for a few hours can do the job. Fancier analyses such as machine learning or social network graphs explorations take even more time and effort. MapReduce can be used to tune machine learning algorithms through Mahout, and even to process graphs (Google's Pregel also seems interesting for parallel processing of graphs: the Pregel version of PageRank takes 15 lines of code).

Detecting bots, hacks, or gold farmers is not as straightforward, but I think it is doable. First, the typical deviant behaviors have to be determined and made explicit by humans. For instance, speed-hackers send too many messages per second to the server, while gold farmers interact with less players, but more intensely, than normal players. Then, detecting deviant behaviors can be a machine learning classification or a graph parsing problem. In both cases, MapReduce can help.

Game-specific

Matchmaking and ladder: Some pre-calculations or updates to parameters of the ladder and match-making algorithms could be done offline by a small MapReduce cluster. A player's skill is unlikely to change much in 12 hours, so a cron task could run the job twice a day. According to Josh Menke from Blizzard, matchmaking involves gradient descent or Gaussian Density Filtering. Not sure whether Mahout supports GDF, but gradient descent is supported.

Tuning and balancing can take days for system designers. MapReduce could do that automatically: each mapper job is given a particular set of system parameters: player 1 has skill A (cost x SP and inflicts y damage) and skill B (cost z SP and heals w HP), player 2 has skill C (...) and skill D (...). Mappers run a few hundred Monte-Carlo simulations of a player 1 versus player 2 match with a fixed set of parameters (player1:A,B; skillA:x,y; skillB:z,w; ...). When done, mappers pass average statistics (win/loss ratio, average amount of gold at the end of the match, ...) of the 100 matches to reducers who sort them. The interesting configurations for balance are those with a win/loss ratio close to 50%. Naturally, this brute-force way of balancing assumes a proficient AI, and designers will still have to tweak the configurations returned by MapReduce so that they feel fun.

Practical concerns

Engineering detail: MMOs have hundreds of shards, but really only one MapReduce cluster should be needed. Each shard could send its jobs to the MapReduce cluster when it needs them done, and wait asynchronously for the MapReduce answer on a particular port. If the MapReduce job uses data from the production database, producing a daily dump may induce a temporary extra load on the shard's database machines, but this should be fine during empty hours.

MapReduce can be a double-edged sword if overused. Exploring the parameter space of learning algorithms too aggressively may lead to less accurate models.

Edit: Some people have been using MapReduce for analytics: mogade's platform and keighl have been using it through mongodb, but it's more of an engineering constraint (scatter-gather queries in a nosql DB to build a ladder board) than an analytics or machine-learning endeavor.

Rules of Engagement - Pardo at GDC 2008

Pardo R. 2008, Rules of Engagement: Blizzard’s Approach to Multiplayer Game Design

A talk from Rob Pardo which was actually first delivered at GDC 2008. The talk has already been covered elsewhere. You can also find the slides with Q&A of GDC 2008. Anyway, here are my take-aways.

• Implement the multiplayer part of the game first, then the story and single-player components.
• In PVP, focus on balance, skill differentiation (e.g. reflexes for FPS, multitasking and strategic thinking for RTS, knowledge of the mechanics for both RTS and FPS, economic dominance), and ladders/ratings. For co-op games, focus on the communication between players and complementary classes. Ex: in Warcraft 3, a mine is considered 'full' when 5 peons work on it; the economic part is dumbed-down to encourage the players to focus on the micro-management of fighting units.
• Avoid differentiation on map knowledge: it's not really a skill. Instead, reveal the map but keep a fog of war (like in Starcraft 2), so that players know the flow of the map and where the resources are, and can pick their strategy accordingly.
• Everything should feel overpowered, not mediocre.
• Balance first for the expert, then for the novice.
• Balance is affected by the maths, but also by the UI (e.g. WoW's UI mods, or the possibility to select only up to 12 units in Starcraft 1 as opposed to an arbitrary large number of units in Starcraft 2), maps/level design, special effects (e.g. too much blurs the vision, cf the War of Emperium of RO set /mineffect by default to limit the visual flood of skill effects)
• Players hate loosing, hence make games shorter so that they can play more games per play session, and eventually win some.
• Reward the behaviors you want people to do/make it a bonus
• Tie art and game design together. The appearance of Heavy of Team Fortress is explicit: tough, lots of HP, and lots of damage.
• Spectatorship enables empathy with the players, cf Poker became more popular when hole cameras were introduced because the audience understands better what's going on.
• It does not make sense for warriors to cast spells, therefore they don't have mana but rather they have rage.

Human-Currency Interaction: Learning from Virtual Currency Use in China

Yang Wang and Scott Mainwaring, 
“Human-Currency Interaction”: Learning from Virtual Currency Use in China, 
CHI 2008

• 50 semi-structured interviews on the use of RMT in China during Summer 2007. Respondents of all ages, playing WoW, Mir2, MapleStory ,Second Life and others.
• Gateway currency = legally convert real money into IG time or currency: Q coin, WoW 66-hour play card. Game-specific currency = in-game gold.
• Realness: students and young professionals consider gateway and game-specific currencies as both virtual and real. For older adults, the currencies are purely and solely virtual. Virtual currencies are dishonest, they are masquerading as an innocuous, too-easy-to-spend plaything, while in fact they represent a lot.
• Trust: face-to-face cash transactions. Need to meet sellers/buyers in person to be sure they are doing their part => meet in a wang ba, both avatars and human beings face each other. Online trusted third-parties require credit card => not for kids. Face-to-face = hassle, but it's also fun to meet IRL other players.
• Account sharing: Pros = with friends, try other characters. Cons = they can steal your stuff, you give them the password you use in many other applications, including RL ones (e.g. email). How to allow account sharing without compromising player security and privacy?
• Fairness: small buyers ($10/month in RMT) find unfair that some players can spend 10-100 times more than them. Buying from other players is felt as less unfair, and seems to alter the game balance less, than buying from the game company.

[Literature] Fundamentals of Game Design, ch 11: Balance

Balance deals with fairness as perceived by players, difficulty, and ensuring that skill (and not chance) is the main factor in player success. Players left-behind should be able to catch up. Stalemates should be avoided because they make some players feel like they played in vain (in other words, better players should always win). No sudden drops or peaks in difficulty. No sudden loss of the game without having previously given the player adequate information about his decisions. Respect genre: no logic puzzle inside a flight simulator.

Avoid dominant strategies

If entities are perfectly balanced and the player can see it obviously from the entities' external stats, then the game looks bland. Therefore, there should be shadow costs. Shadow costs are eventually learned by players after a while if they are not completely hidden. They should not be completely hidden, otherwise the player wonders why his performance fluctuates. More on shadow costs from Ian Schreiber.

Transitive relationships (A>B and B>C implies A>C) are good for player upgrades (sword A gives more atk than sword B). Intransitive relationships (rock paper scissors) are better with unequal costs and gains because players may take risks (and be rewarded for the risks taken). In fact, ideally, all units should be orthogonally different: they should differ in at least 2 dimensions, or have at least one capability that no other unit in the game has. Orthogonally different units prevent dominant strategies because all units are needed to reach the goal. Ex: in Chess, using the Queen only because she's the strongest is a losing strategy.

Chance

Chance can be used in frequent low risk and low-reward challenges. Allow the player to choose how much to risk. Skill is taking the good risks with enough information given: Poker players can decide to lose very little if they have a bad hand this turn: they do not bet much. Good luck cancels bad luck over time. In the end, skill makes the difference. Do not use chance for large issues unless the player knowingly takes the risk.

PvP

Symmetric PvP games can get boring: players end up using the same strategy. It can be hard for some symmetric games (Go or RTS) to have a non-cheating AI better than humans. Players accept a cheating AI (able to see units in fog of war, faster production, ...) in very hard mode, not in easy. Basically, the game becomes asymmetric when players accept a handicap.

Difficulty

See also Ian Schreiber's game balance class.

At least two factors are outside designer's control. Players have a previous experience acquired by playing similar games of the genre. Players have also a native talent (hand-eye coordination, reasoning, ...). Other factors that the designer can control to adjust the perceived difficulty are: intrinsic skill, stress, power provided and IG experience.

• Absolute difficulty of a challenge = skill + stress required compared to the trivial case (static, harmless, one-shot-killed enemy in an FPS)
• power provided = avatar's strength, subject to feedback loops. Ex: spell, powerful sword, HP, ...
• relative difficulty = absolute difficulty - power provided.
• IG experience = how often the player has been exposed to similar challenges throughout the game.

perceived difficulty = absolute difficulty - power provided - IG experience.

Problem with adaptive difficulty: player may learn to trick the AI in pretending to be bad throughout the game and play well at the very end to crush the AI. Moreover, finding a relevant success metric is sometimes hard. Adaptive difficulty should not be obvious to the player, otherwise it feels like patronizing. Adaptive difficulty can be used to make the game harder for players who choose it, though.

Positive feedback

Discourages stalemate and rewards success usefully (not just cosmetically). To control positive feedback,

• Rewards should not be too big
• increase absolute difficulty as player gains rewards, so that relative difficulty stays in control
• allow players to team up against the leader
• make victory conditions unrelated to player power
• use chance to decrease player rewards (random loot, ...)

Tips

Stagnation happens when the player does not know what to do because she does not have enough information. Ex: finding a secret exit door hidden somewhere in a Doom level. To avoid stagnation, give hints.

Players should not have to waste time on trivialities (micromanagement) when they want to take higher-level decisions (strategic positioning of armies), unless they ask for it. Ideally, the game should let the player decide the levels she wants to be in charge of. Experts can choose to micromanage.

How to tune easily:

• Factorize mechanics shared by multiple entities,
• Modify one parameter at a time to see its effect,
• To measure the effect of a parameter, double or halve it,
• Keep track of the tuning done so far, so that you do not do the same tweak twice (saves time)

[Literature] Game Balance ch10 - Economics and Multiplayer Dynamics

My notes from course 10 of the Game Balance class of Summer 2010, by Ian Schreiber.

Economy

In an economic system, players can generate, consume/destroy, or trade resources in a zero-sum fashion (what a player consumes is what another can not consume). Supply and demand curves:

• supply = f(price) is monotonic (increasing): if I sell for $5, then I also can sell for $10
• demand = f(price) is decreasing: if I accept to buy for $10, I also accept to buy for $5

Market price = where the 2 curves intersect. Prices fluctuate as players need or produce items. Prices fluctuate more if there are fewer players. Demand curves affect each other:

• substitutes: SP potion (+ casting Heal spell) is a substitute for HP potion. Increasing supply of X means decreasing demand of Y.
• item sets/collectibles: when together, sword X + shield Y give +10atk bonus. Increasing supply of X means increasing demand of Y.

The price per unit can increase or decrease depending on how many of that unit the player already has. If more units of the same kind brings increasing bonuses, then marginal cost decreases. If each unit costs more and more, the game is more stable and homogeneous.

Demand increases with scarcity. Example in FPS: ammo can be limited (player don't shot all the time, therefore it'd make sense if they died in one shot) or infinite (trigger happy, players should only loose a bit of life when they're hurt). In RTS, limited number of mines to get gold from means shorter games, whereas more and bigger mines means longer games (and more military encounters).

Closed-system = game systems that are self-contained, nothing outside of them can influence what's inside. Somehow, gold farmers open the closed economies of MMOGs, making them harder to design and control. The game should not allow players who have more RL money to have more power, it should just allow more options/variety. Experts using cheap/default CCG decks should beat novices using expensive/rare decks. Yet RL money could be used to speed up progression/avoid grinding.

Inflation happens in MMOs because the game is positive sum (money comes from quests and monsters). New players will never catch up unless negative-sum (sinks) or zero-sum elements are included. Negative-sum/Sinks can be: NPC, repair and death penalties, luxury items, or even tax richest players and give that money to poor players (Robin Hood transforming positive-sum into zero-sum). Zero-sum can be: player-bound/non-tradable items, quests can be repeated but reward only once. Nothing tradable also is a solution.

Trading mechanics

By giving players resources they do not need, they'll have an incentive to trade. 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).

• future agreements: I give X now for Y now and Z later. Players could renege, making them more suspicious when trading with delays.
• scope: powerful resources (eg victory points in Catan) should not be tradable. Tradable resources become more fluid.
• time and phases: players can trade all the time, and trades could take effect at once. Or trading could be limited to certain phases (every 5 turns, or before player starts his building phase) and/or this phase could be timed (eg 5-min timer to bargain).
• evenness: gifts (0 for n) vs even trades (1 for 1) vs uneven trades (1 for n)
• quantification: trading can happen only once per turn/per hour, or as much as player wants. Number of exchanged objects may be bounded as well.
• tax: if trading coalitions are too powerful, put a tax as a cost to trade
• forced: I look at the cards in your hand and pick the best, and give you in exchange my worse card.

Auctions

Auctions = players' willingness to pay for a resource. Auctions work best when the actual cost is variable, different between players, and situational. Each time players decide how much the resource is worth to them, they are making an «interesting choice».

• Many types of auctions (increasing, blind, decreasing, ...),
• with different kinds of rewards (winner gets the entire lot, or first pick in the draft, and/or looser gets bonus or penalty),
• different payers (top bidder, top 2 bidders, top and bottom bidders, all players, ...),
• different recipients (bank = deflation, shared fund, or to other players),
• different events when no one bids (resource given to a random player, or more resources are added to the current resource and the auction restart, or resource is just discarded)

Misc. problems

Name	Problem	Solution
Turtling	Everybody shelters and nobody actually plays because attacking seems more costly and inefficient than defending and waiting for opportunities.	Give incentives to attack (when players wins, she gets more resources next turn), or force players to attack (player has to draw and play one card each turn, and 90% of cards are attack cards).
Kill the leader and sandbagging	Players recognize a clear leader, Players see their best chance to win as eliminating the leader, Players coordinate to attack the leader Players fear to become leader, and play suboptimally	Hidden scores make it impossible to know who is the leader, or make it obvious that eliminating the leader is not the best chance to win, or make the game non-PVP, or make players not able to team-up against another/give advantage when a player defends against many
Kingmaking	One player recognizes they cannot win, Player recognizes that they can give support to any leading player, Losing player chooses one leading player to win	Make players believe they can always win, or make it impossible to know which action will make a king, or make it impossible to choose who to make king, or simply do not allow last players to help leaders
Elimination	Player is killed at the beginning of the game and has to wait for the game to end	Players can only eliminate others if they are strong enough to eliminate all others, or the goal can be to collect points (instead of killing others), or when one player dies, the game stops immediately or within a certain time, and winner is current leader, or make the killed player take control of NPC, or make it interesting to look at other players playing (cf Mafia or Werewolf), or let killed players have goals as well (Cosmic Encounter or BSG)

Final note: balance is not always a must-have. Some games are ostensibly unfair but fun nevertheless. In single-player games, progression matters more than fairness. The unfairness of some one-against-many multiplayer games sometimes makes them fun.

[Literature] Game Balance ch9 - Intransitive mechanics

My notes from course 9 of the Game Balance class of Summer 2010, by Ian Schreiber.

Reminder: “intransitive” is just a geeky way of saying “games like Rock-Paper-Scissors” – that is, games where there is no single dominant strategy, because everything can be beaten by something else. Ex:

• fighting games: blocks > throws > normal > blocks
• RTS: fliers > infantry > archers > fliers
• Advance Wars, and several FPS: Tank > Recon > Anti-tank weapon/infantry > Tank
• visible long-range atk unit > visible med range atk unit with radar > invisible short-range atk unit > visible long-range atk unit without radar
• Magic cards: (X/Y = X atk and Y HP). 3/2 > 1/3 > 2/1 with first strike > 3/2.

Intransitive mechanics are more interesting than transitive ones, esp in PvP games. Players can change strategies in mid-game, or bluff. Balancing is achieved by putting a probability ratio on how often each element of the chain will be used: Rock: 50%, Paper: 20%, Scissors: 30% (= 5:2:3).

Solving RPS

1. Normal-form representation: The payoff matrix consists of: my choices in the rows, the opponent's choices in the columns, and my payoffs in the cells. r, p, and s are the probabilities that my opponent throws rock, paper, and scissors. R, P, and S are the expected payoffs for each of my choice when I choose them during the game.
2. The matrix leads to 3 equations of 3 variables (R = s-p, etc ...)
3. If I know what my opponent plays on average, I know r, p, and s. Therefore I can get my payoffs: R, P and S.
4. The best strategy to use is the one with highest payoff.

Theorems from game theory

• Symmetric games have the same optimal strategy for all players. (Opponent's proba of choosing Rock is same as ours)
• All actions worth taking at all have equal payoffs. (R=P=S)
• In symmetric zero-sum games (eg RPS), all actions worth taking at all have a payoff of zero.

Games are solved considering each player plays optimally (unlike the previous section where I knew r, p, and s). As a side note, a symmetric game is represented using an anti-symmetric matrix. Also, note that the opponent's probabilities r, p, and s must always satisfy r + p + s = 1.

A choice is dominated if one of the other choices is always better. In that case, optimally, the dominated choice will never be picked. Hence, the dominated choice can be removed from the list of choices.

Solving "Rock wins count double"

1. Wins by R count as double. The game is still symmetric: payoffs are the same for the 2 players, the matrix remains anti-symmetric.
2. Obtain 3 equations from the payoff matrix. Each of those equations equals to 0 (cf 3rd theorem above).
3. Solve
4. Conclude: P will be played 50% of the time if wins by R count double.

RPS with costs and partial wins

Solving K(night) - A(rcher) - F(lier), the three being units of a RTS game with costs and partially beating each other. For example, a Knight costing 50g will kill an Archer but lose 20% of its life in the process. What differs is only the payoffs matrix. Solving the equations is the same. Result: k:a:f = 14:10:13.

-	k	a	f
K	50-50 = 0	(-50*0.2)+75 = +65	-50
A	-75+(0.2*50) = -65	75-75 = 0	(-75*0.4)+100 = +70
F	+50	-100+(75*0.4) = -70	100-100 = 0

Asymmetric payoffs

1. If player A wins double with R, but not player B, then there are 2 matrices to look at (one per player).
2. The game is not symmetric anymore, therefore R, P, and S are not 0, and they are different for each player (strictly positive for the player with a bonus, strictly negative for players with handicap). Solve A's matrix: r:p:s = 3:5:4 (interestingly, R has highest payoff but is played least often).
3. Solve B's matrix: r:p:s = 4:5:3.
4. With each of the solution, it's possible to get X and Y.

3-player RPS

In the 3-player case, let's assume I score two points when I beat both of the 2 other players (I play S, they play P and P), and I score one point when I am tie with one player and beat the other (I play R, they play R and S). In that normal case, the intuition is 1:1:1 because it's not different from the 2-player RPS. Hence let's say that wins with R count double (but not the losses). Hence, R vs SS gives +4 (instead of +2), and S vs RS gives -2 (instead of -1). The solution is: r:p:s = 3:4:3.

[Literature] Game Balance ch7 - Advancement, progression and pacing

My notes from course 7 of the Game Balance class of Summer 2010, by Ian Schreiber.

Progression is ...	in games that are ...
absolute	PvE/single player
relative to other players	PvP/multiplayer

Flow has two problems: different player audiences have different skills, and players learn throughout the game.
Balance = overall game difficulty, does not solve these problems. Balance only matches audience expectation.
Progression/Pacing = keeping the player in the flow zone. As player skill increases, so do challenges. Progression ensures the game ends in the time frame said by the box (1min for arcade, 40h for RPG, etc.). If the game is endless, then progression = end-game rewarding structure(s).

When transitioning from mid- to end- or elder game, the objectives change from progressing to something else. Game designer has to find something for the player to do. Ex: WoW guild raiding or making your house cute in Farmville/Sims. Problems: some players may like the progression game but not the elder game. The power gathered during progression game should be available and enjoyable during elder game.
Tips:

• As playtesters test the game, they become experts => the game gets tuned harder => make the game easier at the end, and/or keep some playtesters for the end.
• Let players adjust the difficulty themselves (more challenging but also more rewarding levels or adjusting the difficulty level at any time). In PVP, difficulty adjustment should be voluntary (handicap, resources at the beginning, ...).

PVE

Perceived difficulty = (game power challenge + game skill challenge) - (player power + player skill), with:

• Game power challenge = stats (doubling opponents HP makes the game harder)
• Game skill challenge = new enemies or better AI, direct challenge to the player's skill (you need to play better) and not a player's power (you need more hit points to win). A game designer can control power-related, but not skill-related components of difficulty.

Large luck component or shallow mechanics: a short increase in player skill as the player masters what little they can at the beginning. Then skill plateau (player is as good as she can ever be). A minute to learn, a minute to master. This is the design of educational games (where skill is not the priority).

Giving practice zones where new weapons or powers are acquired makes players learn/increase their skill faster. Skill gating = progressively harder challenges, guarantee that if players complete a challenge, then they are ready for the next. Skill gating != practice zones.

Psychology: “reward schedule” or “risk/reward cycle”: you don’t just want the players to progress, you want them to feel like they are being rewarded for playing well. Reward not too rarely and not too often. Many small rewards are more efficient than a single big reward. Regular rewards = bad. Reward for something players were looking for (otherwise the game seems too easy) and not for a random event (eg "inflict exactly 123 dmg"). 3 kinds of rewards related to progression: increasing player power, level transitions, and story progression.

Increasing player power

If the most fun toy in your game is only discovered 2/3rds of the way through, that’s a lot of time the player doesn’t get to have fun. How do you actually keep the player engaged when you've given away all the cool toys early in the game? One way is if your mechanics have a lot of depth, you can just present unique combinations of things to the player to keep them challenged and engaged. Warning: this is really hard to do in practice. You can also use other rewards more liberally after you shut off the new toys: more story, more stat increases, more frequent boss fights or level transitions. Also, toy upgrades.
Better shorten the game than have it too long and boring.

Level transitions

Each level takes a little bit longer than the last: fast progression at start engages player into the game, later levels can be longer because player wants to know the end of the plot.

Story progression

Story really IS a reward. There should be a match between story complication/climax curve and the difficulty curve. Ex: tutorial = exposition scene, miniboss = rising action, final boss = final climax. Final boss should not be as demanding on player skill as kill 10 rats.

Pattern: do not reveal the story only during level transition; instead, revealing additional background story immediately after a fight (even an easy one) makes players feel like they earned it. (But do not do that all the time otherwise it becomes predictble!)

PvP

Acquiring more power than opponents = primary reward. PvP has more options to play with than PVE because everything is relative, there's no defined level/stats to reach to be "strong".

negative feedback loops => more power when behind and less power when ahead => best player alternates => depends on opponents, no one is left behind (ex: Mario Kart with dynamic difficulty adjustment).
positive feedback loop => more power brings more power => best stays best => independent of the opponents, game ends faster, bad start is deadly (ex: League of Legends).

	positive sum	negative sum	zero sum
Definition	sum of all player resources increases over time	players lose power over time. Goal = lose power more slowly than opponents.	fixed amount of resources on the table
Example	Catan, Agricola	Chess	Poker
Positive feedback
Negative feedback			Solution: Each player spends time in the lead before one player's final blow ends the game.

When both players have realized who is going to win, the game should end quickly.

[Literature] Game Balance ch6 - Situational balance

My notes from course 6 of the Game Balance class of Summer 2010, by Ian Schreiber.

If 10% of monsters are dragons, "double dmg to dragons" = 10% * 2dmg + 90% * 1dmg = 1.1dmg overall.
Situational balance = depends on the situation in the game; the cost is fixed cost, but the value changes depending on the situation. Ex: in DND, if atk + 1d20 >= AC then hit. Is +1atk (for player) balanced with +1def (for my opponent)?

• yes if 1 vs 1 (+1 on each side)
• no if enemies attack more often than player (because player will roll more often on AC than on atk) (eg 4 trash mobs vs one player)
• no if player(s) attack(s) more often than enemies (more rolls on player's atk) (eg player group vs boss)

=> Level design tip: player should be outnumbered half of the time, and outnumber the enemies half of the time if atk and def have the same cost and value. This adds replay value ("I could start a new game with 20atk/80def instead of 50atk/50def")

Versatility

In FPS, players usually have a close+strong+fast, a far+strong+slow and a far+weak+fast weapon. If player can switch weapons quickly, then it's as if the player had all of them at once. The overall price becomes the sum of all of these weapons, they should not be balanced individually.

A character/weapon is more versatile if it is able to handle more situations (Swiss-army knife). Examples:

• RTS: archer very strong against flying creatures and very weak against footmen. If wizard is (a bit) strong against flying AND footmen, wizard is more versatile than archer.
• FPS: knife = good in tight rooms VS snipers = good in large open-spaces VS machine gun = average on any map (= versatile weapon). Machine gun is the most valuable choice for players when they do not know which map is going to be played.

Solution against versatility: cost for switching can be time (it takes 5s to switch weapons), money, frequent weapon reload, etc. If switching is free, then player accumulates everything and uses each tool when he needs it. If inventory is limited, player will look for optimizations (eg only get fire and wind swords if you can only get 2 swords of the 4 elements). Balance depends on how fast player should be receiving new items.

• fast: price = constant (but player earns more and more as he progresses, so player gets swords quickly)
• faster and faster: "Since you’re such a good customer, you can have a 10% discount on all future swords."
• slow: prices increase

Two kinds of versatility:

• Ability of a single game object to be useful in different situations
• Ability of the player to change between game objects (if this type of versatility increases, then the value of each object's versatility decreases)

Shadow costs

Object cost = resource cost (how much player buys it) + shadow cost (maintenance, etc.). Shadow costs can be sunk costs or opportunity costs.

Sunk cost

Sunk cost = pre-requisites/tech tree costs. Examples:

• building a RTS unit may require buildings + techs. Building only 1 unit = lot of sunk cost, building many units = factored sunk cost
• WoW tech tree: powerful ability now VS weak ability now opening VERY powerful ability later?
• buying expensive shop discount card or a potion-making machine VS buying cheap potions repetitively?

Opportunity cost

Opportunity cost = how much versatility is reduced = when a choice prevents the player from taking another action later on. When an action adds constraint, how much is it as a cost? Examples:

• Protection from Fire costs 10 G. Protection from Ice costs 10 G. How much costs Fire+Ice protection?
  • 10G if player knows opponents' atk ahead of time,
  • 20G if player can not know,
  • 15G if player can not know but can purchase the other one if you guessed wrong.
  Giving hints (eg if player is told about a red dragon, she expects fire) reduces the cost.
• strong single-target VS weak AoE
• Alternates: Situational objects that can be brought into play if needed, but the player isn’t forced to use them when suboptimal.
• Metagame combo: not useful on its own, but useful if paired with something else (eg support class in MMO, building a CCG deck); the game should be balanced assuming optimal play, not average, because players will become good and play well anyway.
• RPG multi-classing and 'either/or' choices: lvl 10 thief = lvl 10 warrior = lvl 7 thief-warrior. Cost = more than either but less than both.

[Literature] Game Balance ch5 - The human-side of probabilities

My notes from course 5 of the Game Balance class of Summer 2010, by Ian Schreiber.

The more randomness in a game, the more casual it is: there are fewer strategic choices. Less randomness means more of the fate of the game lies in the player’s choices. That’s not always the case, though. Ex: TicTacToe has no randomness, but is not about skill. Other counter-example: a Poker hand is random, but there are skilled Poker players.
Skill dominates (over luck) if the player is rewarded for predicting and/or responding to the randomness. Ex: one can base his decision on probabilities in Poker, but not in Black Jack.
There is no skill in executing a difficult pattern that you’ve practiced (eg counting your hand or memorizing cards in BlackJack). Skill appears in planned, successful and unexpected decisions.
Luck can be carefully increased to even the playing field. Ex: headshots make it possible for weaker players to sometimes luckily kill better players. Head shooting is also a high-level skill. How much luck or skill a game should have depends on the target population: social games and kid games = luck, hardcore games = skill.
How to transform skill into luck:

• replace player choices by dice rolls
• throw less dices (so that there is no law of large numbers, hence less prediction)
• increase the impact of random events on the game state
• increase the range of randomness (like changing a d6 roll to a d20 roll)

Human biases

Humans tend to remember things that happen the least often, or forget those who are unpleasant (eg match loss), hence they tend to overestimate their level. Humans have a flawed understanding of probabilities, hence showing the actual probabilities will actually make them feel like something is wrong/broken. Here are a bunch of biases humans are subject to:

selection bias	improbable but memorable events are seen as more likely than they really are
self-serving bias	"unlikely" (5%) is interpreted as "nearly impossible" (0.01%) when the odds are in your favor. However, "unlikely" (5%) is interpreted as "possible" (30%) when the odds are not in your favor.
attribution bias	positive random result is assumed to be because of a player’s skill, negative random result is assumed to be bad luck/cheating
anchoring	over-evaluation of the first/biggest number seen. Ex: losing 2/3 of the trials is not as bad as losing 20/10 of the trials. Consequence: small base dmg but high bonus dmg = player likely to underestimate.
gambler's fallacy	assumption that a string of identical results reduces the chance the string will continue
hot-hand fallacy	assumption that a string of identical results increases the chance the string will continue

Ethics

Dishonest game design = make the players believe they are very likely to win. It increases excitement and anticipation of hitting a jackpot. Hence it keeps them engaged. Ex: dishonest car dealership: show VERY big prices first to anchor the customer, then show "normal" big prices: they look like small prices.
Honest game design = tell the player one thing, but actually do something else. Examples:

• If the player has 75% chance of winning, under the hood roll the number as if it were 95%.
• If the player gets a failure, make the next failure less likely, and the one after that even less likely (= avoid long streaks)
• Hot-hand streaks should happen in a positive feedback loop, to counteract the greater chance of a miss after a string of hits (ie give bonuses when series of wins)

But also, stay ethical as much as possible. Display wins, losses and various stats to enable players to grasp their actual skill and to "prove" the game is not unfair/imbalanced or that the AI is not cheating.

Saving

In a game where the player can save anywhere at any time, players are likely to save just before an important roll, and keep reloading until their roll succeeds.

• Naive solution: do not re-generate the random number each time they reload => new problem: players can now anticipate future rolls (the seed has not changed).
• Alternate solution: the player can save anywhere, but the total number of saves is limited (cf the original Tomb Raider) => new problem: players need to know how far apart they should save on average so that in the end of the game, they still can save.

[Literature] Game Balance ch4 - Cards, Dice, and Other Randomness

My notes from course 4 of the Game Balance class of Summer 2010, by Ian Schreiber.

Monte Carlo simulation = good way to approximate stats when the maths are too hard.

Dices are used for independent game events: each dice roll is independent of the previous roll. XdY = throw X items that have Y sides at the same time (ex: 1d6 = one 6-sided dice). For custom dices, eg a 6-sided dice with 1-1-1-2-2-3 on the sides: p(1)>p(2)>p(3).
More dice = less random (= smaller std deviation)> Example: p(7) for 1d10 is 1/10, but it is 10/32 for 5d2.

Cards are used for dependent game events: some events may not happen again if they have happened a certain number of times Revealing information as the game goes does not change the odds in previous player choices, but it changes the odds of non-player variables. Famous related problems: Monty Hall's 3 doors or families with at least one boy.

[Literature] Game Balance ch3 - Transitive Mechanics and Cost Curves

My notes from course 3 of the Game Balance class of Summer 2010, by Ian Schreiber.

An intransitive game is like Rock-Paper-Scissors, where everything is better than something else and there is no single “best” move. In contrast, in transitive games, some elements are just flat out better than others, and we balance that by giving them different costs.

The cost is expressed in terms of game resource(s) (eg money, wood, existing units, items, technology, skills, ...) but can also consist of temporal restrictions (eg single-use constraint on a particular item, or a bonus being limited in time). A player wil pay a cost if she can see benefits to her situation (eg better stats, bonus skill). The goal for the game designer is to reach benefits = cost. In other words, if the weapon is overpowered, then either decrease its power (or any benefit) or increase its price (or any cost). Overpowered <=> undercosted.

A cost curve is a game balance technique designed to put everything in terms of the resource cost. In some games, you can choose to make an increasing, linear or decreasing curve, all of them might be balanced, but they have different effects on the gameplay. In Magic: the Gathering you get one Mana per turn. If you were the designer and you made a cost curve that was increasing, so that each additional point of mana gives you more benefit than the last, you’ll have a game where late-game cards are really powerful and early-game cards are pretty weak, so you’ll have a game that is heavily weighted towards late-game play. If the cost curve is decreasing, it puts more of a focus on the early game. The curve depends on the game duration you expect.

How to build or reverse-engineer a cost curve?

1. Start with objects that have only one little effect: is their effect cost linear, exponential or log?
2. then, combine effects; does having +2atk AND +5def in the same item more expensive than having them separately?
3. then, look at limited or random effects
4. then, keep in mind the metagame (ex: all goblins in the battlefield get a bonus => full goblin deck gets OP)

"Reverse-engineering" the transitive costs and benefits from an existing game means solving (mostly) linear equations. Ex: 2HP+1atk=5po and 3HP+2atk=10po => Xpo/HP and Ypo/atk. There might be inconsistencies/exceptions for elements "manually" balanced. Creating from scratch a cost curve = intuition + playtesting, then maths with later additions to the game. Guidelines to create a cost-curve:

• A limited benefit is always worth something.
• If an item gives the player the choice between benefit X or benefit Y, then the cost of this item is more than the cost of X + the cost of Y. Choice has a price.
• Too weak is better than too powerful.

There is an "escalation of power" problem for CCG or MMO (mudflation), or any game which elements are persistent. When some elements are slightly overpowered, players find them after a while and these items become the standard. For the next expansion, the cost curve has to raise to adapt to these OP items, and the new set of items is balanced in this new higher curve. It forces players to buy things at each update, but it should not be too obvious, otherwise players will see it and leave the game. => Do it VERY slowly.

[Literature] Game Balance ch2 - Numerical Relationships

My notes from course 2 of the Game Balance class of Summer 2010, by Ian Schreiber.

Numbers only have meaning in relation to each other. A few kinds of numerical relationships:

• identical (1:2:3:4)
• linear (2:4:6:8)
• exponential (2:4:8:16)
• triangular (1:3:6:10)

It is much easier to balance a system when you can put everything in terms of a single central resource. For example in CRPG such as Final Fantasy, everything can be put in terms of HP (gold is used to buy stuff to reduce dmg, hence increasing HP). In 2D platformers, the loss condition is lives (sometimes, it is score), and everything is tied to it.

Various loops in CRPG

XP - encounters: more encounters gets you more XP. Your level increases, and so do your stats, which in turn lets you face more encounters. The feedback loop here is not exactly positive, because as the level increases, the number of encounters needed to level up increases (non-linearly).

Equipment - encounters: Fight monsters, get gold, use it to buy better equipment, which lets you fight better monsters for even more gold and so on. This stops being a positive feedback loop at some point because there’s a limited set of equipment you can buy, and the best stuff requires you to travel to distant towns which can’t be reached from the start.

Gold - encounters: get more gold, which lets you buy keys, which lets you progress to new areas, which gets you to more dangerous and advanced encounters for more gold. Truly positive.

In RPG, the XP system serves as a negative feedback loop: higher-level players need to kill more monsters than low-level players. The designer can know quite precisely the level of the player, which makes it easy to design adequately challenging enemies. A fast leveling at the start is useful: it hooks up the player.

[Literature] Game Balance ch1 - Intro

My notes from course 1 of the Game Balance class of Summer 2010, by Ian Schreiber.

What is game balance:

• for single player games, it is difficulty, pacing, character progression
• for multiplayer, advantage at the beginning of the game, strategies (any strategy could be viable OR some are more viable than others (could be overpowered)) or game objects

How to balance a game:

• intuition (from experience, not teachable),
• playtesting (statistical analysis, rely on player skill: novices could never find a needed good strategy),
• math (numbers are everywhere in games)

Playtest is really needed for interconnected systems, because modifications can have rippled effects.
Player skill can make a difference in exploiting an imbalance.

Some game vocabulary

• deterministic. Deterministic + perfect information = solvable.
• solvable: has a single, knowable “best” action to take at any given point in play, and the player can know this action (it is undesired in games if it's trivial); including humans in the loop (like in Poker) fixes the problem of solvability
• intransitive (eg in rock paper scissors, paper > rock and rock > scissors, but paper is not > scissors)
• symmetric (means balance at the beginning, but not between game objects or strategies)
• metagame: can be balanced as well, and definitely affects the game balance: drafting and rarity for trading card games, analyzing opponents' strategies to win the next Poker game, capping the salary of sport players so that most clubs can afford recruiting them

Tips

When trying to fix an unbalance, ask where it really comes from
If you do not know how much an advantage a beginning side is in a RTS like Warcraft3, you can let the playtesters bid in auctions for their beginning side. Knowing how much they give makes you know how much is necessary to balance the beginning state.
Allowing players to cooperate to kill the strongest player can balance a diplomacy game, but also sometimes only make it last longer and be more annoying (players do not want to appear too strong)

Ethnographic play on a 25-rate RO private server

I wanted to play RO for some days. Something quick, but not too easy, and with not too many people to have to talk to while leveling. Kind of a nostalgic try. So I picked a private server which drop and XP rates are 25. That means killing a monster brings 25 times more XP to the avatar than on the official servers, and a 1% chance to drop an item becomes 25% on this server. I conducted an «ethnographic» play: based on my (relatively extended) knowledge of the game I analyzed the server through player avatars in the game but also on the control panel of the website. I found the private server on ratemyserver.net (RMS), but I will not write its name here so that nothing bad happens to its administrator. Launching a private server is an illegal activity after all.

Demographics

At 3pm on Friday, the control panel showed 2 players were connected: T an Assassin and J a Hunter, both around level 80. These are the most solo classes of the game. When I logged in, it was not long before T arrived and, without a word, sent me an invitation to join guild G1, which he was the guild master of. I accepted, and saw in the guild panel that J the Hunter was also in the guild. Three days later, on Sunday night, there were 9 players connected on the server at 7pm. Among them, 4 belonged to guild G1, 2 to guild G2, 2 were not in a guild and 1 was an AFK merchant, used as a mule selling items to other players.

As mentioned before, the guild master of guild G1 was T, an Assassin. He had spent the last 2 days camping equipment on a low-level randomly-appearing monster called Ghostring. He had reached level 98 and had not made any other character. He was very confident and experienced in the game, and gave advice to the other 2 players he had recently recruited in his guild. IRL he was a 19-year-old jobless American. He started playing RO in 2007, had played on iRO Loki (official international server) and 5 other (much more populated) private servers, ranging from 6 to very high rates.
The sub Guild Master was J, the Hunter. He had actually played a lot and was now a lvl-96 Sniper. He had managed to collect a few Field Manuals in fishing, a custom activity of the server. When used by a player, manuals give 3 times more XP for 30 minutes. Although J seemed less confident than T, he said he started playing RO in 2006 on RuRO, the official Russian server. He gave spontaneously several items to other guild members. J and T talked quite much together in the guild chat. IRL, J was a 19-year-old Russian who worked in a call-center. He found his job boring and managed to play at work.
A was recruited after J. He was a lvl-90 Monk, a quite complex class combining support and high damage attacks. He was a basic member of the guild but talked a lot with J and T when he was connected. Each of them gave advice about where to XP or which equipment to get. He said he started playing on several euRO free-trial accounts in 2004, and tried another private server later. He looked quite unexperienced. IRL, he was a 19-year-old German working in a call-center as well (but not playing at work). When they realized through the guild chat that they were all the same age and two of them had the same job, they enthusiastically sent Facebook invitations to each other.
B was a lvl-96 Rogue recruited last. Rogues are a mixed class between Assassin and Hunter. B was not connected at that time.

In the other guild, the guild master was a quite experienced lvl-98 Hunter very in view on the forum. He had, among others, argued that the custom items provided by the administrator were balanced while another player thought they were not. The second player in the guild was a cheerful Bard, a support and/or high-attack version of Hunter. I was enrolled by him in the guild, and he even asked if I needed any piece of equipment. During week days, they were never connected before 5pm, I concluded they worked or went to school. Most of the time they were connected, the guild chat stood silent. When they happened to speak, it was in German to each other and out of the guild chat. Later, the Bard added that the 25-rate server opened following the wipe of a high-rate server. Maybe they knew each other before the low-rate server opened?

Server features

The capital city was Prontera. @go was given to players, but not @storage or @warp; this meant players had to go back to the capital to go where they wanted or use their storage. In my opinion, this increased the frequency of little social events that happened in the capital between players. The custom NPC were those usually found on any private server; they were:

• The Warpra teleports players wherever they want for free. This solves the problem of long and boring transportation time when there is no player to teleport other players to their destination.
• The Healer heals players and solves the scarcity of support-class avatars who, most of the time, need a group to XP quickly.
• Stat and Skill Reseter: resets the avatar skill and stat points. If a player wants to change his character build (eg from a Support Paladin to a Tank Paladin), she can.
• Job Master saves players the time to do job changing quests.
• Banker, Identifier, Bonus skill giver (to save time to the player), Universal Renter (for Cart, Falcon or mount)

There was also a Kafra Employee that lets the player save his respawn point when dead or open his storage, but this is an NPC found on official servers as well. A vending zone had been added as well where Merchants could set up their shops, but the server population was too small to have any virtual economy. The guild versus guild event, the WoE, was supposed to happen twice a week but was deactivated by S, the administrator of the server, probably because there were not big enough guilds.

S was German, although his advertising for the server on RMS mentioned the server and forum language was English. He came on the forum once or twice a day to reply to suggestions or technical problems with the game. He did not harass players for votes or donations, and stayed remarkably quiet. In the game, his player account was the Monk A. As a Game Master, He never improvised any live event for the players. Technically, he designed and coded his own website and control panel, manipulated client-side files, added and edited a few small NPCs in the game, tried (and failed...) to balance his custom items (eg the fishing rewards) but never seemed to have modified the server source code.

Conclusion

Certainly, the players from this private server had different origins (Russia, Germany, France, US) and had different gaming expertise. However, all the players were all males of the same age (16-25) and had all tried official servers and/or private servers before. They all played solo but their belonging to a guild showed they wanted to socialize with other players. Alone Together.

This private server had several custom hats. They all required grinding at least a hundred items, and rewarded the player with unbalanced items (eg inflicting +12% damage on other players). Somehow, it was too easy, but players did not seem to see it this way, or at least they did not complain about it - for now... I doubt the administrator had the community management, game design, programming, and graphic skills required to make his server grow as much as he would like to, but I am sure he had the will. Private server administrators are a particular kind of consumer of MMOG company's products - they use the game client. Of course, this is an illegal activity, or maybe a not-yet-channeled activity. MMOG companies could choose to design their games and pay attention to these determined and skilled consumers. They could be included in the product community as content contributors.