A funny example of the application of game theory can be found in the fantasy book by Anthony Pierce "The Brave Golem"
Lots of text
“The point of what I’m going to show you all,” Grundy began, “is to gain the required number of points. The scores can be very different - it all depends on the combination of decisions that are made by the participants in the game. For example, suppose each participant testifies against their playmate. In this case, each participant can be awarded one point!
- One point! - said the Sea Witch, showing an unexpected interest in the game. Apparently, the sorceress wanted to make sure the golem had no chance of the demon Xanth being pleased with it.
- Now let's assume that each of the participants in the game does not testify against his comrade! - continued Grundy. - In this case, each can be awarded three points. I would especially like to point out that as long as all participants act in the same way, they will be awarded the same number of points. No one has any advantage over others.
- Three points! Said the second witch.
- But now we have the right to suggest that one of the players began to testify against the second, and the second is still silent! Said Grundy. - In this case, the one who gives these testimonies gets five points at once, and the one who is silent does not get a single point!
- Aha! - both witches exclaimed in one voice, licking their lips predatory. It was clear that both of them were clearly going to get five points.
- I was losing points all the time! The demon exclaimed. - But you have only outlined the situation so far, and you have not yet presented a way to resolve it! So what is your strategy? No need to waste time!
- Wait, I'll explain everything now! Exclaimed Grundy. - Each of us four - there are two of us golems and two witches - will fight against their opponents. Of course, the witches will try not to yield to anyone in anything ...
- Of course! The two witches exclaimed again in unison. They perfectly understood the golem at a glance!
“And the second golem will follow my tactics,” Grundy continued unperturbed. He looked at his double. - You, of course, know?
- Oh sure! I'm your copy! I perfectly understand everything what you think!
- That is great! In that case, let's make the first move so that the demon can see everything for himself. Each fight will have several rounds so that the whole strategy can manifest itself to the end and give the impression of a coherent system. Perhaps I should start.
- Now each of us must make marks on our sheets of paper! - the golem turned to the witch. - First, draw a smiling face. This will mean that we will not testify against a fellow prisoner. You can also draw a frowning face, which means that we think only of ourselves and give the necessary testimony to our comrade. We both realize that it would be better if no one turned out to be that frowning face, but, on the other hand, a frowning face gains certain advantages over a smiling one! But the bottom line is that each of us doesn't know what the other will choose! We will not know until the playmate reveals his drawing!
- Start you bastard! The witch swore. She, as always, could not do without abusive epithets!
- Ready! - exclaimed Grundy, drawing a large smiling face on his piece of paper so that the witch could not see what he portrayed there. The witch made her move, also depicting a face. Presumably, she certainly portrayed an unkind face!
“Well, now all we have to do is show each other our drawings,” Grandi announced. Looking back, he opened the drawing to the public and showed it in all directions so that everyone could see the drawing. Grunting something displeased, the Sea Witch did the same.
As Grundy had hoped, an angry, displeased face looked from the drawing of the witch.
“Now you, dear spectators,” said Grandi solemnly, “you see that the witch chose to testify against me. I'm not going to do that. Thus, the Sea Witch scores five points. And I, accordingly, do not get a single point. And here…
A light noise rolled through the rows of spectators again. Everyone clearly sympathized with the golem and longed for the Sea Witch to fail.
But the game has just begun! If only his strategy was correct ...
- Now we can move on to the second round! - announced Grundy solemnly. - We must repeat the moves again. Everyone draws a face that is closer to him!
And so they did. Grundy now portrayed a sullen, displeased face.
As soon as the players showed their drawings, the audience saw that both of them were now portrayed with angry faces.
- Two points each! Said Grundy.
- Seven two in my favor! - shouted the witch happily. - You can't get out of here, you bastard!
- Let's start again! Exclaimed Grundy. They made another drawing and showed them to the public. The same angry faces again.
- Each of us repeated the previous move, behaved selfishly, and therefore, it seems to me, it is better not to award points to anyone! - said the golem.
- But I still lead the game! - said the witch, happily rubbing her hands.
- Okay, don't make a noise! Said Grundy. - The game is not over. Let's see what happens! So, dear audience, we are starting the fourth round!
The players made the drawings again, showing the public what they had drawn on their sheets. Both sheets again showed the viewers the same evil faces.
- Eight - three! Shouted the witch, bursting into evil laughter. “You dug your own grave with your foolish strategy, golem!
- Round five! Shouted Grundy. The same thing was repeated as in the previous rounds - again angry faces, only the score changed - it became nine or four in favor of the sorceress.
- Now the last, sixth round! - announced Grundy. His preliminary calculations showed that this particular round should become fateful. Now the theory had to be confirmed or refuted by practice.
Several quick and nervous movements of the pencil on the paper - and both drawings appeared before the eyes of the public. Again, two faces, now even with bared teeth!
- Ten - five in my favor! My game! I won! - the Sea Witch cackled.
“You really won,” Grundy agreed grimly. The audience was eerily silent.
The demon moved his lips to say something.
“But our competition is not over yet! - shouted loudly Grundy. - It was only the first part of the game.
- Give you forever! The demon Xant grumbled in displeasure.
- It's right! Said Grundy calmly. - But one round does not solve anything, only methodicalness indicates the best result.
Now the golem approached the other witch.
- I would like to play this tour with another opponent! He announced. - Each of us will depict faces, as it was the previous time, then will demonstrate the drawn to the public!
And so they did. The result was the same as the last time - Grundy painted a smiling face, and the witch - so generally a skull. She immediately gained an advantage of as much as five points, leaving Grundy behind.
The remaining five rounds ended with the results that could be expected. Again the score was ten or five in favor of the Sea Witch.
- Golem, I really like your strategy! - the witch laughed.
- So, you watched two rounds of the game, dear viewers! Exclaimed Grundy. - Thus, I scored ten points, and my rivals - twenty!
The audience, which was also counting the points, nodded their heads mournfully. Their count was the same as that of the golem. Only a cloud named Frakto seemed quite pleased, although, of course, it did not sympathize with the witch either.
But Rapunzelia smiled approvingly at the golem - she continued to believe in him. She may have remained the only one who believed him now. Grundy hoped that he would justify this boundless trust.
Now Grundy approached his third rival - his double. He was to be his last opponent. Quickly scratching their pencils on the paper, the golems showed them to the public. Everyone saw two laughing faces.
- Note, dear viewers, each of us chose to be a kind cellmate! Exclaimed Grundy. - Therefore, none of us got the necessary advantage over the opponent in this game. Thus, we both get three points and proceed to the next round!
The second round has begun. The result was the same as the previous time. Then the remaining rounds. And in each round, both opponents scored three points again! It was just incredible, but the audience was ready to confirm everything that was happening.
Finally, this tour came to an end, and Grundy, quickly running his pencil over the paper, began to calculate the result. Finally he announced solemnly:
- Eighteen to eighteen! In total, I scored twenty-eight points, and my opponents scored thirty-eight!
“So you lost,” announced the Sea Witch happily. - Thus, one of us will be the winner!
- Perhaps! Said Grundy calmly. Now there was another important point. If everything goes as they intended ...
- We need to see it through to the end! - exclaimed the second golem. “I also have to fight two Sea Witches, too! The game is not over yet!
- Yes, of course, come on! Said Grundy. - But only be guided by the strategy!
- Oh sure! - assured his double.
This golem approached one of the witches and the tour began. It ended with the same result with which Grundy himself came out of a similar round - the score was ten or five in favor of the sorceress. The witch was downright beaming with inexpressible joy, and the audience sullenly fell silent. Demon Xanth looked somewhat tired, which was not a good omen.
Now it was time for the final round - one witch had to fight against the second. Each had twenty points in assets, which she could get by fighting with golems.
- And now, if you will allow me to score at least a few extra points ... - conspiratorially whispered the Sea Witch to her double.
Grundy tried to keep calm, at least outwardly, although a hurricane of conflicting feelings raged in his soul. His luck now depended on how correctly he predicted the possible behavior of both witches - after all, their character was, in essence, the same!
Now was perhaps the most critical moment. But if he was wrong!
- Why on earth should I give in to you! Croaked the second witch to the first. - I myself want to score more points and get out of here!
- Well, if you are behaving so impudently, - the applicant yelled, - then I will trim you now so that you will no longer look like me!
The witches, giving each other hating glances, drew their drawings and showed them to the public. Of course, nothing else, except for two skulls, simply could not be there! Each of them scored one point.
The witches, cursing each other, proceeded to the second round. The result is again the same - again two roughly drawn skulls. Thus, the witches gained one more point. The audience diligently recorded everything.
This continued in the future. When the tour ended, the weary witches discovered that they each had scored six points. Draw again!
- Now let's calculate the results and compare everything! Said Grandi triumphantly. “Each of the witches scored twenty-six points, and the golems scored twenty-eight points. So what do we have? And we have the result that golems have more points!
A sigh of surprise rolled through the spectators. Excited spectators began to write columns of numbers on their sheets of paper, checking the correctness of the count. Many during this time simply did not count the number of points scored, believing that they already knew the result of the game. Both witches began to growl with indignation, it is not clear who exactly was blaming for the incident. The demon Xant's eyes lit up again with alert fire. His trust was justified!
“I ask you, dear audience, to pay attention to the fact,” Grandi raised his hand, demanding that the audience calm down, “that none of the golems won a single round. But the final victory will still be for one of us, of the golems. The results will be more telling if the competition continues further! I want to say, my dear viewers, that in the eternal duel, my strategy will invariably turn out to be a winning one!
The demon Xanth listened with interest to what Grundy was saying. Finally, emitting a puff of steam, he opened his mouth.
- What exactly is your strategy?
- I call her "Be firm, but honest"! - explained Grundy. - I start the game honestly, but then I start to lose, because I come across very specific partners. Therefore, in the first round, when it turns out that the Sea Witch begins to testify against me, I automatically remain the loser in the second round - and so it continues until the end. The result may be different if the witch changes her tactics of playing the game. But since she could not even think of such a thing, we continued to play according to the previous pattern. When I started playing with my doppelganger, he treated me well, and I treated him well in the next round of the game. Therefore, our game also went differently and somewhat monotonously, since we did not want to change tactics ...
- But you haven't won a single round! The demon objected in surprise.
- Yes, and these witches have not lost a single round! - confirmed Grundy. - But the victory does not automatically go to the one for whom the tours are left. The victory goes to the one who scored the most points, which is a completely different matter! I managed to score more points when we played with my doppelganger than when I played with witches. Their selfish attitude brought them a momentary victory, but in the longer term it turned out that it was because of this that they both lost the game entirely. This often happens!
Finally, we got around to continuing the story about game theory with real examples of its use in our project. But before that, let's take a short excursion into the classification of games in order to use it to describe to you in all their glory two of our game events: "Big Fight" and "Conquest of the Quarter".
It would be boring just to talk about different types of games (especially since Wikipedia has already done this), so we will show you about them.
Idea of classification
All currently existing games are divided into two types. But which ones
Mathematicians have always had a soft spot for binary and binary systems, and game theory authors are no exception. Therefore, when creating a game classification, they acted extremely cunningly: they identified several sub-classifications (definitions), in each of which there can be only two mutually exclusive types of games:
- Classification on equality of moves: symmetrical and asymmetrical games.
- Classification by the size of the win: games with zero and non-zero sum.
- Classification if possible cooperation of players: cooperative and non-cooperative games.
- Classification in order of making moves: parallel and sequential games.
- Classification according to information available to players: games with complete and incomplete information.
Thus, any game could be described using its position in one or another definition. The more definitions, the more accurately the game is described.
So, for example, the game parchis familiar to many (she is shesh-besh, she is ludo, she is patolli, she is mandavoshka) is:
- symmetrical;
- with zero sum;
- cooperative;
- consistent;
- with complete information.
The picture shows the work of a folk craftsman, a "gift edition" of this game with the decoration of the playing field.
But enough preludes, let's classify.
Symmetrical and asymmetrical games
First, the actions of the players are equally applicable: they have the same consequences for all players. The latter presuppose the existence of some kind of inequality between players in one form or another (resources, awareness, available moves, etc.).
Symmetrical games, as a rule, include session games, in which the players initially stand in the same conditions, and at the end one of the players turns out to be the winner.
Examples of definitely symmetrical games:
- checkers;
- chess;
- dominoes;
- any card games.
Does VirCities have examples of symmetrical play situations?
Almost, but not quite.
One could say that this could be the moment after the wipe, when all parameters are reset, but then we would be cheating. Because initially in the game there will already be a certain number of some companies, corporations and parties, which will already have some kind of owner-players. But who will be at the helm? The most active alpha testers, of course.
Also, symmetrical games could be called our sports competitions in three sports (athletics, weightlifting, gymnastics), in which all participants are also placed in the same conditions. However, this would not be entirely correct from the point of view of the definition of the game we have adopted - there is no decision making in competitions, these are mini-games for reaction.
Yes, we also have reaction mini-games presented in the form of sports disciplines. "Why?" - you ask. First, it allows the player to pass the time while waiting for something (for example, he placed a lot on the market and waits until it is bought). Secondly, try to become leaders in one of the disciplines - it's not so easy.
Cooperative and non-cooperative games
First, all players act “every man for himself”. Secondly, it implies the ability of players to cooperate in order to increase their chances of winning.
Zero-sum and non-zero-sum games
We assume that the size of the payoff is finite and cannot increase from the actions of the players, while the latter imply a change in the size of the payoff depending on the actions of the players.
The main interest in the above two categories, obviously, is their interaction with each other. If the players can cooperate with each other, and the payoff can increase indefinitely depending on the conditional "unity", then here we have a basis for very interesting game situations.
As a rule, the publisher is closely associated with one of the networks or several. For example, all our games receive priority placement in Mosigra (the largest domestic retail chain) and other partner networks. Specify exactly how the marketing of the game will be done - it's easy to publish, but selling a game for several thousand a month is very difficult. Note that in the domestic top sales at the beginning of 2013, 12 out of 20 games were released by us.
How rigorous is the selection?
To begin with, the games are tested. Considering that we are going to invest our funds and the team's time in the project, only the best games from the proposed ones are selected. We usually watch 150-300 games a year, and release less than a dozen of them.
If my game doesn't work, can I contact another publisher?
Yes, we usually even recommend a suitable option if the project is good, but it seems to us not entirely suitable for our market. Each has its own specifics. We love, for example, working with games that will sell from 500 pieces per month, or with really wonderful smart and complex projects.
Why are only less than a dozen domestic board games released a year?
Because any author competes with localizations. If you can take a ready-made and proven game from the West, where it has already shown its effectiveness, it is more logical to work with it than with something new. Nevertheless, we do our best to support the domestic market and regularly hold events for game authors.
What will Magellan do with my prototype, how will the development of the board game go?
- 1. You can not send a prototype as the first step, but simply send the rules and materials of the game. After reviewing them (if we like the game), we request a prototype.
- 2. After the tests, it is possible that recommendations will be given on changing a number of things in the mechanics, setting and rules. We give the vector to you or change it ourselves (by agreement).
- 3. An agreement is signed.
- 4. Then the work of the illustrators will begin. Good illustrators, the success of the game largely depends on the quality of the images.
- 5. Layout of maps, rules and other components.
- 6. At the same time, the "cover" is being made - the illustration for the box and the text on it. The name of the game is being clarified.
- 7. Components are then manufactured for each individual specification.
- 8. When everything is ready, your game is assembled in production.
Here are examples of stories from the publication of our board games:
In what form is it better to send a prototype?
It is desirable to be as finished as possible, that is, in the form of a box with components and rules. Cards must be cards (not pieces of paper that cannot be shuffled); if you are writing by hand, write in block letters. The box must be strong and clearly labeled. Everything inside should be as close to reality as possible - for example, it is good to use chips from other games or nuts instead of chips, bad - paper markers. The field can be drawn by hand, which is better than attaching a file. Etc.
If it is not possible to send it in the form of a box, then you need a description of the concept (2-3 paragraphs) and the rules of the game, as well as files for creating a prototype. Remember that there is no point in discussing an idea by itself. The test team needs to be able to sit down and play at least once.
The most important thing is what the game is called, who is it for, how many players, how old, how long the game is, what mechanics are used, what the most similar games are already there, what makes your product better.
If I just have an idea for a board game, what should I do?
Assemble the prototype. Better take your time: if you put it together in a hurry, it is quite possible that the game will be rated worse than if you think over the little things and write down the rules clearly and clearly. But don't be late - Perfectionists are the last to arrive. It is better to stop at a certain stage of readiness and listen to the opinion of the publisher than to work in the wrong direction for a year.
Are there any non-disclosure documents being signed?
At the prototype stage - no. Authors often fear that the publisher might use the files without their involvement. Note that due to the absence of at least some intelligible protection of game mechanics in Russian legislation, any agreements and documents at this stage can, of course, leave a feeling of security, but in practice they will be legally null and void. Therefore, you can only trust or not trust the publisher. Again, no one will risk their reputation, as well as releasing a game without an author is simply not economically feasible.
What games definitely don't need to be submitted?
- 1. Copies of already known games. "But I came up with Monopoly, only instead of cells there will be names of rock bands" - this is a bad idea.
- 2. Games your 14-year-old sister can't figure out. If the rules are 40 pages in small print, and you need to learn to play for several days, it may be worth simplifying. It will be quite difficult to sell this.
- 3. Games without implementation - that is, something that cannot be prototyped from.
- 4. Several versions of the same game with minor changes - one prototype is enough.
I already have illustrations. What then?
If they are good, we will publish it with them. But practice shows that it is better to bring a couple of samples of concept art - and then it will be clear before starting work whether an illustrator is suitable.
What's the money? Can you make money by creating a board game?
The author receives from 5 to 10% of royalties from each print run that has gone out of production. If a game costs 1000 rubles on a shelf in a store, then it costs 500 rubles in circulation and about 300 rubles in cost price. You receive deductions from the wholesale price, that is, in our example, from 500 rubles.
What is the average circulation?
The minimum circulation is 1000 pieces, the usual one is 3-5 thousand. We try to work with games that can sell more than 10 thousand pieces a year. Considering that once a game is published brings you income for at least another 3-4 years, you can independently calculate the profit. As a rule, the publication becomes a permanent job for very, very few who are ready to do several projects in a year, but as an addition to the main income, it is quite worthy.
What are the risks of the publisher?
- - If the game does not enter the market, the publisher will lose development funds and the first print run. You can only make money on the game - and at least receive deductions from the first batch.
- - If somewhere there is a marriage that causes a rework of the batch (a common occurrence for any publisher), everything will be decided at the expense of the publisher.
- - If the game is not delivered to the shelves on time and a network penalty is imposed for late payment, this is the publisher's problem, not yours.
Etc. Thus, you are in no way concerned with the traditional risks of publishing and any other things. You just get a deduction from each box - it doesn't matter what happened to it financially. These deductions remain unchanged, even if incredible adventures happened with the circulation.
What documents will need to be collected?
The main document is the author's agreement, in which you guarantee that you are the author of the game and have all rights to it, and the publisher describes in detail its obligations. In most cases, signing it is sufficient. An author's agreement can be signed both with a resident of the Russian Federation and with a non-resident of our country.
If you use third-party materials in the game, such as illustrations, you must have a transfer of rights from the illustrator or a contract with him. If we do the illustrations, you don't need to think about it.
We take care of the rest. Including certification of the game, for example.
What tests are done?
It is assumed that you send the finished game (by the way, if you have a protocol of at least 20 games, this is good). The game is tested not for balance, for example, but for playability. The tests are held in three stages: first, the developers watch, then experienced players, then, under supervision, random people "from the street". All three stages must be passed. The most important is the third.
What happens if the game doesn't work?
Typically 10% of games are good enough to be published. But less than 2% of board games sent to the publisher are released. The rest are simply put off in case they are needed. We let you know if your game is good, but won't be published yet - and we recommend other publishers. In this case, the game is queued for publication. In practice, over the past year, we have bought two games from such a "queue" of the reserve. The usual queue length is about 30 projects.
How long will the prototype be evaluated?
Usually about a month.
How long will the board game be released?
The cycle is 8-12 months from circulation to appearance on the shelf.
Please note again
Providing information or a prototype for review does not constitute a nondisclosure agreement. But, again, we promise that we will be very careful with your game.
We don't consider ideas - just prototypes. Magellan's consideration and assessment of your ideas does not constitute an acknowledgment of the idea's novelty, priority or originality, and does not prejudice the company's right to dispute or implement any existing or future ideas of a similar nature. However, if we consider the mechanics to be promising (but the game in the form of a specific implementation is not suitable for publication), we will tell you about it and suggest improvements.
You represent and warrant that you (or the team you represent) are the sole owners of the information disclosed, or that you have unlimited rights to disclose it. You also confirm that all third parties who may be interested in the disclosed information have been informed about the terms of the agreement and agree to its terms.
No prototype is returned.
We consider it undesirable to consider the project simultaneously with another publisher - in this case, we will wait for a response from another publisher. Please let us know before submitting your project if your project is already pending with another publisher. In the event that we request a prototype of a game from you, we mean that we are the only publisher considering your project, unless you have clearly agreed in advance with us to the contrary.
We can make significant changes to the game, which can lead to changes in the game mechanics, its theme and any other aspect to better adapt the game to the product line. And better sales.
The project may not be suitable for many reasons: we may think that the game is not profitable enough; that we will not be able to present the game in the best possible way; the game may be too similar to something that is already in our development; We didn't like the mechanics of the game and its execution, or for any other reason. We will provide details if something goes wrong.
We do not give feedback on sent games.
Types of board games
The number of board games that can be played today is simply enormous. Board games have always been popular - this is a kind of psychological aspect of human thinking that pushes us to this activity. But how, among all this diversity, to choose an occupation for your liking? To do this, you need to understand the question of what types of board games exist and to what classifications they are distributed.
All board games existing today, one way or another, are distributed according to four main criteria:
- on player interaction
- by subject
- on the inside of the game mechanism
- by genre
Each of these main points has its own subcategories and, accordingly, its own characteristics. If you delve deeper into them, then you can always find the ideal version of the game for yourself.
What type do you choose?
So, the first point concerns exclusively how the players will be positioned during the game and how they will have to interact in order to achieve victory. Therefore, this category can be divided into several types of relationships:
- Competitive type. This is a process where each player is solely responsible for themselves, trying to defeat their neighbors in the game. In this situation, all participants are rivals, and in the end only one will win.
- Team or cooperative type of game. Here, all participants are divided into teams, and each is trying to beat the other, or all participants are trying to beat the game itself. Here you can play with the whole team, alternately exposing one or the other player. Or you can choose a leader who will perform all the manipulations in the game on behalf of the entire team. A sufficiently large number of people can participate in such games and as a result, not one player wins, but the whole team.
- One against all. This is the type of game where all participants are fighting against one. He usually acts as a villain. There can be several such participants at once, but no more than three. In order to understand this kind of game principle, it is enough to recall the popular Mafia game today.
Themes of games
The theme of games also has its own varieties. It depends on the kind of world people who have decided to play this or that game plunge into. Different types of board games have different themes:
- Realism - proximity to our world, real life situations and game moments
- Classic fetasi - some elements of the fairytale or magical, special abilities for the players
- Science fiction - the complete opposite of realism, original characters and unique action that takes place during the game
The mechanism of the game itself is a very important point that should be considered more closely. It is the mechanics, or simply the rules of the game, that determines exactly how you will play it and who you will become in the process of this exciting action. The mechanism of the game implies the number of combinations in the game and is responsible for its level of difficulty. Here are some of the types of mechanisms that are most in demand and popular in various types of games:
- card mechanics (for example)
- mechanics on dice or dice
- social mechanics
- mechanics that places objects and characters in the space of the game
These mechanisms can exist both separately and interact with each other, making the game even more amazing and versatile.
Game genres
And finally, the types of board games have their own classification also by genre. The genre is responsible for the important moments in the game. This is the very meaning of the games, what sensations it gives and how it goes, and in addition, according to the genre classification, you can determine what goals this game pursues and what benefits it will bring you to your children or friends. What genres are found:
- Abstract games. This category is familiar to everyone and everyone. An example of such games is our favorite chess and checkers.
- Social games. This is a very broad category of games that simulates life situations and teaches you to find a way out of them. An example of such games is Mafia.
These are the categories of games that have been familiar to us since childhood. But board games do not stand still. They develop, like everything that is around us. That is why today there are several classes of games that have arisen in modern times:
- Wargames. These are games about war and strategy.
- Ameritresh. A variety of American games, which are mostly designed for luck and luck.
- Eurogamers. Games in which players oppose each other, showing skill, endurance and cunning. There is a certain percentage of luck in them, but most of this luck is based on mistakes made by other players.
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