Crossover: 2014
Chapter 181
Chapter 181
It sounds like Go has nothing to do with artificial intelligence.
Why does a man-machine battle in Go spark artificial intelligence?
This may have something to do with the mechanics of Go.
Although Go has always been considered as one of the most complicated board games in the world.
But the basic rules of Go are simple.
The Go board is square and consists of 19 vertical and horizontal lines.
19╳19 have formed 361 crossing points (hereinafter referred to as point), and chess piece is just placed on these points, can be placed at any point in limit, angle, middle abdomen.
When playing chess, the chess pieces must be placed on the intersection points of the chessboard, and the chess pieces cannot move after they are placed on the chessboard.
Black moves first, black moves next, white moves next, and until the end, the side that sees the most territory wins.
Of course, the rules of different countries are not exactly the same as to how to measure the amount of territory occupied.
Although the rules of Go are very simple, this does not prevent the ever-changing game of Go.
It is said that there are more possible changes in a game of Go than the number of atoms in the universe.
In this case, it is unrealistic for the computer to exhaustively obtain all possible changes in a game.
If the program wants to achieve higher efficiency, it can only make a fuss about the algorithm.
However, even if the algorithm is used, it involves Go:
It is much more difficult for a computer to win at Go than in games such as chess.
Because there are so many chess points in Go, the branching factor is far more than other games.
Moreover, each time the situation is good or bad, the situation is erratic.
In this case, traditional algorithms are difficult to work.
Not to mention traditional algorithms, even general artificial intelligence methods are difficult to work.
Traditional artificial intelligence methods such as brute force search, Alpha-beta pruning, and heuristic search are of little use in Go.
Because of the technical difficulties.
Although in the previous life in 97, artificial intelligence defeated the top human chess players at the chess level.
But in terms of Go, artificial intelligence has been falling into the sand.
Until 18 years after beating the top players in chess.
Artificial intelligence only defeated the nine-dan master of Go from the universe country for the first time.
This incident was also interpreted in the previous life as "in any single field, machines may be far ahead of humans."
Whether this statement is correct or not is yet to be judged.
But it is undeniable that the concept of "artificial intelligence" suddenly became popular after the man-machine battle between Li Shishi and AlphaGo.
The impact of this battle is not limited to the small circle that studies artificial intelligence.
Instead, it has aroused a great discussion on artificial intelligence in the whole society.
Anyway, Lin Hui remembered that in March 16 in his previous life, news and Weibo were full of AlphaGo and artificial intelligence.
Some discussed technology, some looked forward to the future, and some saw business opportunities and prepared to end...
Of course, the possibility of operation cannot be ruled out behind all this noise.
After all, as far as Lin Hui knows, Go is actually mainly circulated in East Asia, and it is not highly circulated in the world.
And even in places like China, island countries, and universe countries, where the circulation of Go is not bad.
The proportion of Go lovers among ordinary people is not too high.
Even if some people understand the rules a little bit, they can't explain clearly when it comes to slightly troublesome things such as robbery.
Grandpa Lin Hui is a fan of Go, and had even made a match before.
Under his influence, Lin Hui knows Go very well, probably at the level of Ye Wu.
Even so, Lin Hui never claimed to be good at Go.
After all, Ye Wu generally has to be conceded 2 to 6 pieces when facing the real professional [-]th dan.
In this case, the concept of "artificial intelligence" can become popular with the help of "Go".
It's hard to say that no one is behind it.
But these ins and outs are not what Lin Hui cares about.
Since this human-machine battle in Go in the previous life can become the explosive point of artificial intelligence.
Then this space-time forest gray can also come up with a program similar to AlphaGo and find a way to facilitate the human-machine battle.
Afterwards, it will be properly operated to make this event a breaking point for artificial intelligence.
It involves AlphaGo AlphaGo.
In the previous life, AlphaGo was launched by deepmind, a Chinese company.
Although the deepmind company also exists in this time and space.
But Lin Hui doesn't have to worry about crashing or anything.
Although the birth of AlphaGo in the previous life is inextricably linked to the company deepmind.
But the project involving AlphaGo was actually started after the deepmind company was acquired by Google/Google.
In short, the birth of AlphaGo in the previous life has a lot to do with the py transaction between deepmind and Google/Google.
But now in this time and space, Google/Google and deepmind have not cooperated on this project.
And there is a high probability that there will be no chance of cooperation in the future.
Lin Hui knew about it before.
A company named deepmind does exist in this time and space.
But because of the overall lag in the study of artificial intelligence in this time and space.
Although the company deepmind is also engaged in research on artificial intelligence.
But little progress has been made.
And deepmind is not a good company.
Not long ago, the company also tried to file for bankruptcy protection.
It is basically impossible for such a company to achieve the achievements of the previous life.
In the case of the overall lag in the research on spatio-temporal artificial intelligence.
If Lin Hui wants to carry AlphaGo, he basically doesn't have to worry about the risk of a technical crash.
Although there is no risk, the handling of AlphaGo is a little troublesome.
It's not that there is any trouble in technical theory.
Although people in this time and space haven't figured out the corresponding technology yet.
But for Lin Hui, the path of technical theory is very clear.
Classic AI applications like AlphaGo.
Basically, nine out of ten people who are engaged in artificial intelligence have studied what AlphaGo is all about.
Technology related to AlphaGo:
It is nothing more than a simple application of Monte Carlo tree search combined with two deep neural networks.
Monte Carlo tree search is a heuristic search algorithm used in certain decision-making processes, most notably in games.
Especially common in board games.
Specifically, there are two deep neural networks, one of which is a valuation network and the other is a chess network.
The former is used to evaluate a more suitable placement, and the chess network is used to adjust the best placement position.
Why use this design?
Largely inspired by humans playing chess.
When human beings play chess, first of all, chess players will roughly judge where to play without losing money through past experience and chess records.
After narrowing down the search area, the player will perform a detailed deduction on a certain local position.
As for deduction, chess players mainly think about how they make moves and how their opponents will react after making moves.
Generally speaking, good chess players should have this kind of deduction ability.
Only by taking one step and watching a dozen or even dozens of steps can one become a master of Go.
As for the purpose of the deduction, it is to find the most favorable landing point for oneself.
To sum up, a good chess player should have the following abilities:
First of all, it is possible to judge the possible way through the situation;
Then judge whether the situation is in your favor;
Then deduce the situation to find the best landing point.
Although artificial intelligence seems to be the knowledge of machines.
But it is actually researchers who are trying to make machines think like humans.
The logic of AlphaGo's operation is essentially close to the way of thinking of human chess players.
In short, the technical realization of AlphaGo is not very complicated.
The content related to technical aspects is very clear.
But it is still very troublesome to implement it concretely.
First of all, it involves a lot of underlying technology.
This space-time has short legs because of artificial intelligence.
Many theoretical things still need to be built from scratch.
In other words, Lin Hui wants to detonate the explosive point of artificial intelligence again.
There is a high probability that it will be necessary to move bricks in different time and space, and carry theoretical knowledge of artificial intelligence in various ways.
As for the specific handling, we need to figure out the technical route.
Although this job is a bit troublesome, fortunately, Lin Hui now has an academic tool person.
In addition to artificial intelligence at the technical level.
Some other technical aspects are also required.
In the previous life, in the first generation AlphaGo, in addition to the application of artificial intelligence achievements, Google/Google.
Some research results in distributed systems are also applied.
In computer science, distributed computing is also translated as distributed computing.
A distributed system is a system formed by a group of computers that are connected to each other through a network to transmit messages and communicate and coordinate their behavior.
Although programs like AlphaGo do not rely on distributed computing, they also have good performance.
But distributed computing is often more efficient than traditional computing.
It is a bit difficult to deal with distributed horses.
Lin Hui had never done anything similar in his previous life.
However, Lin Hui recently saw that Google/Google and the Department of Mathematics of Princeton University seem to have mentioned something related to distribution in the journal of collaborative abstract algorithm.
If this is the case, it is not that there is no chance to fool some things related to distributed technology.
In addition, AlphaGo AlphaGo also involves more troublesome training.
If only out of trouble.
There is no need for Lin Hui to keep staring at AlphaGo.
In the previous life, it wasn't just AlphaGo.
After AlphaGo, there is a master, and after the master, there is Alpha_Zero.
If it is said that AlphaGo has lost to humans.
Alpha_Zero is completely in the air every second of every day.
Lin Hui remembered a set of data he had seen in his previous life.
The Alpha_Zero algorithm only needs 8 hours of training to defeat Lee Sedol's version of "AlphaGo".
According to this statement, it means that the training cost of Alpha_Zero is much lower than that of AlphaGo.
Compared with its predecessor AlphaGo, Alpha_Zero has many unique features.
Although this technology is very powerful, Alpha_Zero and AlphaGo actually have a technical gap.
If you want to come up with Alpha_Zero, you still need to come up with AlphaGo first from a logical point of view.
In this case, Lin Hui feels that it is better for technology gods to respect the laws of objective development.
It may not be a good thing if you really want to get it right in one step.
It is already very good to think of AlphaGo, the explosive point of artificial intelligence.
Having said that, Lin Hui should have thought of Alpha Gou long ago.
Lin Hui remembered those two sentences he posted on Weibo when he first registered on Weibo:
——"Fine art is like a king, there are few in the world, and idlers are like me, there is nothing in the world"
It has a close relationship with Goose Factory's Go AI.
If Lin Hui thought of this earlier, he should be able to think of Alpha Gou soon.
Although these have been thought of.
But the actual reproduction of AlphaGo is still very difficult.
The biggest difficulty seems to be at the hardware level.
If the two technologies of AlphaGo and alphaZero want to come out, they need deep learning framework and hardware support.
Both AlphaGo and alphazZro involve the TensorFlow deep learning framework proposed by Google/Google in the previous life.
For this deep learning framework in the previous life, Google/Google also developed a tensor processor in 2016.
Tensor processors (TPUs) are Google/Google's custom-built chips for machine learning.
It's so outrageous, it's hard to describe domestic chips.
In foreign countries, this is a show of people and ghosts.
Those who seem to have nothing to do with chips are also making chips.
Speaking of the general parameters of the first-generation TPU specifications, Lin Hui remembers some.
Although I don't remember the whole thing.
But Lin Hui still vaguely remembers that the first-generation TPU was made with a 28nm process.
Although the 28nm process is a bit rough from Lin Hui's point of view.
But you must know that the chip manufacturing process on the iPhone5s is only 28nm at this time.
That sucks.
That is to say, even if Lin Hui can manufacture TPU, there is a high probability that the cost will remain high.
Although Lin Hui can directly use the computer running model brought from his previous life.
But personal computers will eventually limit the effectiveness of some AI programs.
Even if the full performance of AI can be brought into play on a personal computer, it is impossible for Lin Hui to face the world grandly with the technology from the next seven years.
Hey, it's hard.
Despite all the troubles of one kind or another.
But asking questions is more important than solving them.
As long as the thinking is not slippery, there are always more solutions than problems.
Compared with people in this era, they are still groping forward in the dark.
Lin Hui knows how to solve the problem and the difficulties faced in solving the problem.
On this point, I have the advantage!
This involves the use of the most advanced technological processes of the era.
It seems inevitable that it will involve cooperation with Waiguo.
A certain semiconductor seems to be looking at the face of the crooked nuts.
Why does the crooked fruit use this kind of technology as an "enemy"?
Speaking of it, it seems good to have a crooked endorsement company.
After all, there is a nest of snake rats with crooked nuts.
Faced with the same crooked fruit company, the chip maker does not seem to be too wary.
Crooked fruit company?
Lin Hui suddenly thought of deepmind.
Since the space-time of deepmind is so messed up.
It seems like a good idea to buy this company.
It shouldn't be very expensive to come to a company that is about to file for bankruptcy protection, right?
The more Lin Hui thought about it, the more reasonable it became.
The reason for such an idea is in addition to foreign cooperation.
There is another level of consideration.
To some extent, Lin Hui needs a spokesperson.
The advent of new technologies often faces huge controversy.
Take the innovation of Go by AlphaGo in the previous life as an example.
It is difficult for people who did not learn Go in their previous lives to understand why Go has been so impacted by artificial intelligence compared to other chess sports.
Because of the complex changes of Go, each player will have a very obvious style of chess when playing chess.
Different styles lead players to adopt different strategies at different stages, positions and shapes.
Compared with other chess games, Go is more obvious in this point.
The so-called "game" is not only a competition of brain power between two chess players, but also a confrontation of personal styles of chess players.
However, the emergence of artificial intelligence has led to the so-called "optimal solution" of Go, which is the most complex, most variable, and best reflects the fun of "playing games".
(End of this chapter)
It sounds like Go has nothing to do with artificial intelligence.
Why does a man-machine battle in Go spark artificial intelligence?
This may have something to do with the mechanics of Go.
Although Go has always been considered as one of the most complicated board games in the world.
But the basic rules of Go are simple.
The Go board is square and consists of 19 vertical and horizontal lines.
19╳19 have formed 361 crossing points (hereinafter referred to as point), and chess piece is just placed on these points, can be placed at any point in limit, angle, middle abdomen.
When playing chess, the chess pieces must be placed on the intersection points of the chessboard, and the chess pieces cannot move after they are placed on the chessboard.
Black moves first, black moves next, white moves next, and until the end, the side that sees the most territory wins.
Of course, the rules of different countries are not exactly the same as to how to measure the amount of territory occupied.
Although the rules of Go are very simple, this does not prevent the ever-changing game of Go.
It is said that there are more possible changes in a game of Go than the number of atoms in the universe.
In this case, it is unrealistic for the computer to exhaustively obtain all possible changes in a game.
If the program wants to achieve higher efficiency, it can only make a fuss about the algorithm.
However, even if the algorithm is used, it involves Go:
It is much more difficult for a computer to win at Go than in games such as chess.
Because there are so many chess points in Go, the branching factor is far more than other games.
Moreover, each time the situation is good or bad, the situation is erratic.
In this case, traditional algorithms are difficult to work.
Not to mention traditional algorithms, even general artificial intelligence methods are difficult to work.
Traditional artificial intelligence methods such as brute force search, Alpha-beta pruning, and heuristic search are of little use in Go.
Because of the technical difficulties.
Although in the previous life in 97, artificial intelligence defeated the top human chess players at the chess level.
But in terms of Go, artificial intelligence has been falling into the sand.
Until 18 years after beating the top players in chess.
Artificial intelligence only defeated the nine-dan master of Go from the universe country for the first time.
This incident was also interpreted in the previous life as "in any single field, machines may be far ahead of humans."
Whether this statement is correct or not is yet to be judged.
But it is undeniable that the concept of "artificial intelligence" suddenly became popular after the man-machine battle between Li Shishi and AlphaGo.
The impact of this battle is not limited to the small circle that studies artificial intelligence.
Instead, it has aroused a great discussion on artificial intelligence in the whole society.
Anyway, Lin Hui remembered that in March 16 in his previous life, news and Weibo were full of AlphaGo and artificial intelligence.
Some discussed technology, some looked forward to the future, and some saw business opportunities and prepared to end...
Of course, the possibility of operation cannot be ruled out behind all this noise.
After all, as far as Lin Hui knows, Go is actually mainly circulated in East Asia, and it is not highly circulated in the world.
And even in places like China, island countries, and universe countries, where the circulation of Go is not bad.
The proportion of Go lovers among ordinary people is not too high.
Even if some people understand the rules a little bit, they can't explain clearly when it comes to slightly troublesome things such as robbery.
Grandpa Lin Hui is a fan of Go, and had even made a match before.
Under his influence, Lin Hui knows Go very well, probably at the level of Ye Wu.
Even so, Lin Hui never claimed to be good at Go.
After all, Ye Wu generally has to be conceded 2 to 6 pieces when facing the real professional [-]th dan.
In this case, the concept of "artificial intelligence" can become popular with the help of "Go".
It's hard to say that no one is behind it.
But these ins and outs are not what Lin Hui cares about.
Since this human-machine battle in Go in the previous life can become the explosive point of artificial intelligence.
Then this space-time forest gray can also come up with a program similar to AlphaGo and find a way to facilitate the human-machine battle.
Afterwards, it will be properly operated to make this event a breaking point for artificial intelligence.
It involves AlphaGo AlphaGo.
In the previous life, AlphaGo was launched by deepmind, a Chinese company.
Although the deepmind company also exists in this time and space.
But Lin Hui doesn't have to worry about crashing or anything.
Although the birth of AlphaGo in the previous life is inextricably linked to the company deepmind.
But the project involving AlphaGo was actually started after the deepmind company was acquired by Google/Google.
In short, the birth of AlphaGo in the previous life has a lot to do with the py transaction between deepmind and Google/Google.
But now in this time and space, Google/Google and deepmind have not cooperated on this project.
And there is a high probability that there will be no chance of cooperation in the future.
Lin Hui knew about it before.
A company named deepmind does exist in this time and space.
But because of the overall lag in the study of artificial intelligence in this time and space.
Although the company deepmind is also engaged in research on artificial intelligence.
But little progress has been made.
And deepmind is not a good company.
Not long ago, the company also tried to file for bankruptcy protection.
It is basically impossible for such a company to achieve the achievements of the previous life.
In the case of the overall lag in the research on spatio-temporal artificial intelligence.
If Lin Hui wants to carry AlphaGo, he basically doesn't have to worry about the risk of a technical crash.
Although there is no risk, the handling of AlphaGo is a little troublesome.
It's not that there is any trouble in technical theory.
Although people in this time and space haven't figured out the corresponding technology yet.
But for Lin Hui, the path of technical theory is very clear.
Classic AI applications like AlphaGo.
Basically, nine out of ten people who are engaged in artificial intelligence have studied what AlphaGo is all about.
Technology related to AlphaGo:
It is nothing more than a simple application of Monte Carlo tree search combined with two deep neural networks.
Monte Carlo tree search is a heuristic search algorithm used in certain decision-making processes, most notably in games.
Especially common in board games.
Specifically, there are two deep neural networks, one of which is a valuation network and the other is a chess network.
The former is used to evaluate a more suitable placement, and the chess network is used to adjust the best placement position.
Why use this design?
Largely inspired by humans playing chess.
When human beings play chess, first of all, chess players will roughly judge where to play without losing money through past experience and chess records.
After narrowing down the search area, the player will perform a detailed deduction on a certain local position.
As for deduction, chess players mainly think about how they make moves and how their opponents will react after making moves.
Generally speaking, good chess players should have this kind of deduction ability.
Only by taking one step and watching a dozen or even dozens of steps can one become a master of Go.
As for the purpose of the deduction, it is to find the most favorable landing point for oneself.
To sum up, a good chess player should have the following abilities:
First of all, it is possible to judge the possible way through the situation;
Then judge whether the situation is in your favor;
Then deduce the situation to find the best landing point.
Although artificial intelligence seems to be the knowledge of machines.
But it is actually researchers who are trying to make machines think like humans.
The logic of AlphaGo's operation is essentially close to the way of thinking of human chess players.
In short, the technical realization of AlphaGo is not very complicated.
The content related to technical aspects is very clear.
But it is still very troublesome to implement it concretely.
First of all, it involves a lot of underlying technology.
This space-time has short legs because of artificial intelligence.
Many theoretical things still need to be built from scratch.
In other words, Lin Hui wants to detonate the explosive point of artificial intelligence again.
There is a high probability that it will be necessary to move bricks in different time and space, and carry theoretical knowledge of artificial intelligence in various ways.
As for the specific handling, we need to figure out the technical route.
Although this job is a bit troublesome, fortunately, Lin Hui now has an academic tool person.
In addition to artificial intelligence at the technical level.
Some other technical aspects are also required.
In the previous life, in the first generation AlphaGo, in addition to the application of artificial intelligence achievements, Google/Google.
Some research results in distributed systems are also applied.
In computer science, distributed computing is also translated as distributed computing.
A distributed system is a system formed by a group of computers that are connected to each other through a network to transmit messages and communicate and coordinate their behavior.
Although programs like AlphaGo do not rely on distributed computing, they also have good performance.
But distributed computing is often more efficient than traditional computing.
It is a bit difficult to deal with distributed horses.
Lin Hui had never done anything similar in his previous life.
However, Lin Hui recently saw that Google/Google and the Department of Mathematics of Princeton University seem to have mentioned something related to distribution in the journal of collaborative abstract algorithm.
If this is the case, it is not that there is no chance to fool some things related to distributed technology.
In addition, AlphaGo AlphaGo also involves more troublesome training.
If only out of trouble.
There is no need for Lin Hui to keep staring at AlphaGo.
In the previous life, it wasn't just AlphaGo.
After AlphaGo, there is a master, and after the master, there is Alpha_Zero.
If it is said that AlphaGo has lost to humans.
Alpha_Zero is completely in the air every second of every day.
Lin Hui remembered a set of data he had seen in his previous life.
The Alpha_Zero algorithm only needs 8 hours of training to defeat Lee Sedol's version of "AlphaGo".
According to this statement, it means that the training cost of Alpha_Zero is much lower than that of AlphaGo.
Compared with its predecessor AlphaGo, Alpha_Zero has many unique features.
Although this technology is very powerful, Alpha_Zero and AlphaGo actually have a technical gap.
If you want to come up with Alpha_Zero, you still need to come up with AlphaGo first from a logical point of view.
In this case, Lin Hui feels that it is better for technology gods to respect the laws of objective development.
It may not be a good thing if you really want to get it right in one step.
It is already very good to think of AlphaGo, the explosive point of artificial intelligence.
Having said that, Lin Hui should have thought of Alpha Gou long ago.
Lin Hui remembered those two sentences he posted on Weibo when he first registered on Weibo:
——"Fine art is like a king, there are few in the world, and idlers are like me, there is nothing in the world"
It has a close relationship with Goose Factory's Go AI.
If Lin Hui thought of this earlier, he should be able to think of Alpha Gou soon.
Although these have been thought of.
But the actual reproduction of AlphaGo is still very difficult.
The biggest difficulty seems to be at the hardware level.
If the two technologies of AlphaGo and alphaZero want to come out, they need deep learning framework and hardware support.
Both AlphaGo and alphazZro involve the TensorFlow deep learning framework proposed by Google/Google in the previous life.
For this deep learning framework in the previous life, Google/Google also developed a tensor processor in 2016.
Tensor processors (TPUs) are Google/Google's custom-built chips for machine learning.
It's so outrageous, it's hard to describe domestic chips.
In foreign countries, this is a show of people and ghosts.
Those who seem to have nothing to do with chips are also making chips.
Speaking of the general parameters of the first-generation TPU specifications, Lin Hui remembers some.
Although I don't remember the whole thing.
But Lin Hui still vaguely remembers that the first-generation TPU was made with a 28nm process.
Although the 28nm process is a bit rough from Lin Hui's point of view.
But you must know that the chip manufacturing process on the iPhone5s is only 28nm at this time.
That sucks.
That is to say, even if Lin Hui can manufacture TPU, there is a high probability that the cost will remain high.
Although Lin Hui can directly use the computer running model brought from his previous life.
But personal computers will eventually limit the effectiveness of some AI programs.
Even if the full performance of AI can be brought into play on a personal computer, it is impossible for Lin Hui to face the world grandly with the technology from the next seven years.
Hey, it's hard.
Despite all the troubles of one kind or another.
But asking questions is more important than solving them.
As long as the thinking is not slippery, there are always more solutions than problems.
Compared with people in this era, they are still groping forward in the dark.
Lin Hui knows how to solve the problem and the difficulties faced in solving the problem.
On this point, I have the advantage!
This involves the use of the most advanced technological processes of the era.
It seems inevitable that it will involve cooperation with Waiguo.
A certain semiconductor seems to be looking at the face of the crooked nuts.
Why does the crooked fruit use this kind of technology as an "enemy"?
Speaking of it, it seems good to have a crooked endorsement company.
After all, there is a nest of snake rats with crooked nuts.
Faced with the same crooked fruit company, the chip maker does not seem to be too wary.
Crooked fruit company?
Lin Hui suddenly thought of deepmind.
Since the space-time of deepmind is so messed up.
It seems like a good idea to buy this company.
It shouldn't be very expensive to come to a company that is about to file for bankruptcy protection, right?
The more Lin Hui thought about it, the more reasonable it became.
The reason for such an idea is in addition to foreign cooperation.
There is another level of consideration.
To some extent, Lin Hui needs a spokesperson.
The advent of new technologies often faces huge controversy.
Take the innovation of Go by AlphaGo in the previous life as an example.
It is difficult for people who did not learn Go in their previous lives to understand why Go has been so impacted by artificial intelligence compared to other chess sports.
Because of the complex changes of Go, each player will have a very obvious style of chess when playing chess.
Different styles lead players to adopt different strategies at different stages, positions and shapes.
Compared with other chess games, Go is more obvious in this point.
The so-called "game" is not only a competition of brain power between two chess players, but also a confrontation of personal styles of chess players.
However, the emergence of artificial intelligence has led to the so-called "optimal solution" of Go, which is the most complex, most variable, and best reflects the fun of "playing games".
(End of this chapter)
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