How board and various other games are balanced - a brief overview of the ways

A week ago, I talked to the developer of developing children's games, a psychologist, beautiful Lady Susan, who seems to be not even suspecting about math. She gave me one of the most beautiful game balance methods for practicing, explaining how she did one of her games. But more about that later, there are a lot of letters.

The ultimate goal of any game balancing is to increase the return of players or the time of the game. That is, the mechanics playability:

• There should not be an unequivocal ultimatum winning strategy, otherwise the game will lose its variability and interest.
• The player must feel that the game depends on his actions and skills. Otherwise, get Mass Effect, which, rather, the film, rather than RPG.
• The balance must be “amortized”, that is, to forgive some mistakes - otherwise, a millisecond delay in clicking Starcraft on the first worker due to the “scourge effect” would cause a loss after 4 hours of an ideal game. Our table formula - 5-7 important decisions per game, two can make a mistake.
• Nastol has a social condition: players should not fall in the course of the play - it should be interesting for everyone to the end.

Now - methods.
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Model limitations

Board games are extremely rarely covered by automated tests. Such things are made of personalities known to me, perhaps, only by Sid Meier, Vlaada Khvatil and a couple of not-so-well-known game designers. In other cases, the following occurs:

1. Empirical balancing. As a rule, a game developer is familiar with mathematics, intuitively understands the applied aspects of either game theory or discrete mathematics, and, in general, makes the right decisions.
2. Then there are game tests in a limited circle of "pros". Here the task is to find balance vulnerabilities. In general, the same empirical tests, only by a crowd of pentesters. As a rule, this is a hundred batches, that is, for statistical methods it is not enough, but for empirical methods it is just right. In this case, the author completes something in the process, so it is rare when one set of rules is played over 30 games.
3. After the game is placed in a public beta on "people from the street" to check the learning curve. Here you can already collect statistics, but, as a rule, this is not required.

An example of such manual balancing is Mr. Yanni’s “ Hive ”. When he made an addition that added the woodlouse to the hive (the action is roughly comparable to adding a new chess piece), he first tested with friends for about two months, then showed the game designers to everyone he knew and collected opinions, then launched a beta tournament in the electronic tournament system tests, and then later released a plastic figure directly for sale and introduced it into a stable release in electronic versions.

I note that the board game has an average life of 6 parties. 10 people will play 3-4 games in a year, two more will be cut every weekend, and about every hundredth will be preparing for the tournament. Therefore, the main task of balance is not a tournament, as in online games, but socially so that no one will fall out and everyone will feel how they make decisions. The balance is connected with the learning curve - given the extremely limited attention span and the wild lack of time, you need to use intuitive players to balance things (a la “shotgun can not be weaker than a pistol”).

Methods

Author's ass filing
This method we discussed above. He often remains basic in practice.

Sawing off that pokes out
Sequential testing and manual slew of the most multi-raking strategies. This “alignment” is very similar to the debugging of Monte-Carlo group algorithms or genetics on an incomplete selection, and gives about the same result. That is, it helps in 90-95% of cases.

Resource balance
This is a more interesting thing. For each object in the game, a single price is calculated in a certain resource. Naturally, the most difficult thing is to come up with an evaluation function. The same MTG, for example, absolutely exactly grew from empiricism (I and II editions) to non-domination (III and IV editions) and by the sixth edition went the resource path. Roughly speaking, you know that a small animal with a price of 2 mana will have attack 2 and protection 2 by default in any environment. For example, can make it 3/3? Of course, you can, just need to hang the property that it is 1/1, if in the previous move the enemy was not damaged. For each "bun" from the standard, we give "drubek" - some kind of drawback. Want 2/2 and flight? Ok, only the brute at the entrance to the game will take 2 hits from you. Want 7/1? You can, but it will live one move, and you have to kill another creature to call it. And so on. You take the standard and start dancing around it, creating pros and cons, so that they end up in approximately 85% of the corridor from the standard.

Subject-related balance
This is when the plot "pulls out" weak balance states. For example, you have a branch in RPG pumping pistols and, say, plasma machine guns. In the same Shadowrun (new) development options are the same. At later skill levels, the gun gives double-triple shots, increased damage and quick reload. Damage per turn is the same as from a good lineup from a machine gun at close range. A player, like, will not turn out to be an inept sucker for the final game. This balance is a resource one.

And the plot is that you can leave the gun weak, but compensate for it with the same than in the real world. For example, greatly complicate the search for cartridges for a machine gun or increase their price in the game world, then make missions to penetrate where the gun can be carried, and the machine gun is no longer there, make instant duels like in westerns, when it is more important that etc.

Every time a storyline depends on your mechanic skill or hacking castles in a role-playing game - this is also it.

Rock Paper Scissors
The basis of balance is decision making by players. When the balance is “too even,” it is impossible to achieve the formation of individual strategies and playing styles. Therefore, the balance should only converge as a whole, but not in detail. In detail, some chaos is needed, and there should be quite a lot of it. The most frequent example of such a balance is the construction of three basic strategies (“magician, fighter, thief”, “aggression, control, combination”, “developer, designer, tester”, “shotgun, rifle, sniper”). They beat each other in a circle, and therefore the player’s task is to actually, in a sense, bluff and guess the actions of the opponent. The same strategy introduces randomness into the game and allows beginners to sometimes beat pros when guessing.

An example of the most effective and most "unbalanced" stuff in shooters is often a shotgun. This is a melee weapon. Using resource methods and statistics to build an evaluation function to calculate a resource, we, for example, know that a weapon must do 100 damage per minute at a distance of 100 meters. We make 500 units, but in the “droubek” we give 5 meters, and we also make weapons heavy, awkward, slowly recharging and with small ammunition. Here, two branches are launched at once - the choice of strategy (the task of “papika” with a shotgun — suddenly appear strictly close to the potential frags) and the skill (you need to aim very accurately and calmly). Similarly - a good sniper. Creates the same requirements for strategy and skill, but defines a different strategy for player behavior.

Another type of risk control is the method of leveling the losing and winning players with a random one. This is necessary, for example, when a player is already seriously losing, but there is still half of the game. Either he leaves the game and gives up without interest ... or you give him some tools to recover. Most often this is a strong risk. The losing player can use techniques and strategies that give a high chance (more than 50%) of a critical error, but at the same time she is not afraid of him, because he already loses. It turned out - lucky, they are again with the winner on an equal footing. It did not work - well, ok, it was interesting and fun. And as soon as the players are aligned, the risk-taking techniques will not be both - after all, the “droubek” in this situation becomes significant for the outcome of the game. Quite good about these nuances is Cyrlin in his “Play to Win” (which we somehow translated - read, he delved into the balance when the games were without patches at all).

In sports, this situation is somewhat similar to the story, when even the goalkeeper is used as one of the attacking players in the final minutes of the match. Yes, yes, you can already guess - this not only returns the player to the game, but is also very heroically spectacular. About this then tell stories.

Another important thing in non-determinism or the role of a random house is that there are no ready-made winning strategies. In the same checkers, it is impossible to win in a game for black with a mathematically optimal white game. In Go, in theory, too, but there is still not enough of our computing power for this, so there is uncertainty in Go, but in drafts it is not. If you remember the machines with Pakman - there they specially introduced the random to select the direction of the ghosts so that the players in the arcades did not memorize the optimal paths of walking through the levels. When writing AI enemies, it is also often used by random to choose between two similar solutions.

Auto Balance
Usually the game with all its forces tends to be in balance, and the players brazenly swing its state. In the mechanics of auto-balancing - the opposite.

The game situation is often quite diverse, and different strategies will be optimal in the current game. Accordingly, as a rule, one more example of “auto-balancing” is introduced into complex games - this is when the players themselves determine what is more important now.

Example. In the basic resource strategy, you know, for example, the following gradation of rewards: 20 rounds = 100 coins, first aid kit = 50 coins. At the resource level, 20 rounds are always more important than first-aid kits simply because they are more statistically expensive. But in a particular situation, the first aid kit may be more necessary. It creates an auction situation when the players themselves set the price for the resource they need. As a result, it may turn out that exactly in our lot a first-aid kit costs 150 coins, and no one needs ammo at all.

Such things can be done by draft (two captains stand in front of a gymnasium and choose one player for their teams one by one), auctions (players make bets on equipment), placing items at the level (more people ran for the right one — automatically more competition) and etc.

An alternative to auto-balancing is resource balancing by “pulling up” laggards , for example, by creating negative feedback. The higher the level of the hero - the less experience give monsters. The lower - the more. Accordingly, mistakes and absurd situations at the first levels are amortized by the fact that at the end of the heroes there is a difference of 3-4% with a 2-fold difference in the experience indicator. Not everyone likes this, but this is the way of online gaming most often.

Another interesting mechanic of autobalance is to provide a choice not between game values, but between game and real values ​​(IRL). For example, drafts with valuable cards on the secondary market, a choice in the direction of game currency (which can be resold in the secondary market or pay an account for it), and so on.

The next type of auto-balancing is diplomacy . If there are transactions between players in the game, they will be able to unite into alliances. This means that the most "protruding" risks getting a hat from everyone at once, dissatisfied with the fact that he wins.

In this regard, the same “Overboard!” Is especially cool - there, in general, the characters on the boat first "scout" each other, then the remaining batch is in two bundles-unions - one controls the resources, the second is dissatisfied. From time to time there is a split in the controlling ligament due to the conditions of victory (“Why did Snob seize so much? Let him give me a diamond that he took!”), Which immediately changes the ligaments and creates a new, more complex conflict. Bundles purely due to the "physics" of the game are constantly recombined and interchanged, and the players in them too. That is, the strongest gets a paddle on the head simply because he is strong. And even an ally friend will help to beat him, because after all the task he has is for the beaten friend to survive, not for him to win. Victory saves for themselves.

Guessing intentions and bluffs

The essence of the strategy is the optimization of the parameter set. Accordingly, anticipating the optimal actions of the enemy, you can take effective countermeasures. However, the enemy may suspect this and use the wrong parameters that you are expecting. This is how the game's “unraveling” scheme is formed, when it is clear what action it leads to, and bluffing. This is one of the strongest factors of balance and learning curve - first, players increase their skills, trying to predict the results of tuning parameters (they learn the art of the game, reveal hidden information on the behavior of other players), and then play with the other, not with mechanics, but with only as a language.

Learning curve

Let us return to the very beginning of the topic to the dialogue with the beautiful lady and the fact that the balance is connected with the learning curve. It is connected, in particular, by the fact that when the state of the system changes, you should see feedback from the game. For example, it is easy to train a dog to do the right thing, immediately giving it a bone. But it is very difficult to teach her, giving her a mountain of bones in a day or two - she just does not catch the connection, despite the increased size of the reward. It is the same with the players, and there is just a wonderful article about this from Danila Cook from Epic - so we transferred it to the new year here .

So, the problem. There is a game “Sovushki, ay!”, Where children must bring owls to the nest until the dawn comes. Owls are on the track, consisting of colored circles:



Players have cards with circles. Here the left player has red, orange and green circles. Accordingly, he can choose any owl and move it to the nearest free circle of the same color.

If the nearest circle is busy, the owl is placed on the next one of the same color.

The optimal strategy of this game is not to “scatter” owls for a great distance, but at the same time to occupy identical cells so that the distant one jumps across the field.



As it quickly turned out, children do not understand this. Bullshit when I tested, it was also not understood by some humanitarian adults. One guy, for example, chose the longest tactical step of the owl on our tests, but did not calculate the next 2-3 moves. As part of its course, the planning horizon tragically ended. Children take the “beloved” owl (and don't care that they are the same) and lead it.

And the task of the game is to teach children to do something in a team, that is, so that it would be useful for everyone at once. That is, to show them that a move is shorter, but useful to others may in the future be better than a long one, but only for oneself.

But even after explanations with words, losses and demonstration of optimal games, very young children and some especially gifted adults did not understand. And again, they either led a beloved owl, or made long moves.

The problem is that, due to an accident in about 10-20% of cases, it still gave a victory. Suzen, the author of the game, tried to tighten the victory conditions to include auto-balancing on strategy. But she faced the fact that with the wrong moves, children lose, and do not have time to learn - they are upset by the chain of losses. The problem, obviously, is that the feedback loop is too long. We need some thing that gives positive feedback immediately during the course, and not at the end of the game. Evaluation function to understand the child made a strong move or weak.

Stop and think about what you would do in this scenario.

Summary

So, most often:

1. Empirically and on the basis of a small set of tests, an evaluation function for balance is built.
2. A resource standard is identified for each object, and then the objects are trimmed and vary for the depth of the game, that is, the possibility of building individual strategies.
3. Some non-determinism is introduced (most often by chance) for a variety of games and avoiding victory automation. Because life is a random.
4. Reactive methods are introduced to equalize the players: diplomacy, negative feedback, risk balance.
5. If necessary, an out-of-game motivation is established to perform some actions.

But, of course, practice is more severe. In practice, one hell before the appearance of the service pack 2, you still play late beta.

There are also specific mechanics, for example, on the wiki - see the basketball patches and the principle of the “golden age”, plus follow the links. Denk (from the point of view of the game designer) and Sirlin (from the point of view of the player-tournament player) have a very good selection of near balance items.