In the Pippi video studio, Zhan Jun, Huang Feixiang and others were as excited as chickens, because they finally met the first world-class star in the history of Chinese football although they had changed their nationality, and this star was still so young and had unlimited potential.

Accepted the invitation of Pi Phi Video and became a special guest for tonight's battle between the Chinese team and Uzbekistan, this news also made the audience who originally watched the CCTV live broadcast open the Pi Phi video through computers and mobile phones at once, and the huge traffic almost paralyzed the live broadcast room.

CCTV wanted to cry without tears, it was expected to break the ratings of the three, but it was defeated by one person, and I beat my chest with regret Why didn't I think of this.

The commentators of Pi Phi Video are like idols, taking photos with Zhang Zhetian and asking for autographs, and even have a friendly match with him, wanting to experience the strength of this world-class goalkeeper.

Zhang Zhetian readily agreed, which also made them see the affinity of this young star's good dealing, and made them firmly believe that Zhang Zhetian was "persecuted" out of the national team.

For the sake of fairness, Zhang Zhetian represented the commentary team in the first half and the Suns executive team in the second half, and played a friendly match at the training base of the Sun Club, a team in China.

The players of the big coffee team said that the ball is top-notch, and the football is not far behind. Former international players, who can be regarded as Zhang Zhetian's former senior brothers Liu Xiaoyue and Li Yanlong, plus a group of well-known commentators, as well as Zhang Zhetian, the lineup can be called super luxurious.

The Suns executive team is dominated by former international player Li Jinyu, and the strength should not be underestimated, and the players of the commentary team specially wore the red uniforms of the Chinese national team to help tonight's life-and-death battle.

The game is divided into three quarters of 30 minutes each. At the beginning of the game, the big coffee team was obviously slow to heat up, and the Sun executives team used effective counterattacks to create many must-win opportunities, all of which were easily resolved by Zhang Zhetian, who was tens of thousands of times stronger than the team, and the surrounding audience was even more excited to shout "The world's first door god!" ”

Because of the existence of Zhang Zhetian, the big coffee team defended without worry in the first half, and scored three goals against the opponent with all their might. But in the second half, it became the defense of the executive team to be solid, but pulled back three goals, and finally the penalty shootout, the two sides argued endlessly for Zhang Zhetian to defend the goal, and in the end, Zhang Zhetian actually represented both sides at the same time to guard the goal.

As a result, everyone was punished once, and no one broke the ten fingers of Zhangzhetian, even if the persuasion and "bribery" of both sides could not persuade the professional Zhangzhetian to release water, in order to avoid kicking until dark, and finally canceled the penalty for the first time, the two sides shook hands and made peace, and they were all happy.

"Mr. Zhang, seeing your strength, we finally believe that you are not only worth 110 million euros, but also worth the money, and Neymar is not as good as you."

"We can't play footwork well, after all, we play football as an amateur and enjoy football. But Da Yu and Brother Liu are both former internationals, and they can't score penalties, how did you do it? ”

Zhang Zhetian smiled slightly, and said modestly: "Luck, luck." ”

What I said in my heart is, it's not that I'm arrogant, you people are all spicy chickens.

Every penalty is a choice – both for the goalkeeper and for the penalty taker.

The penalty taker needs to decide whether to kick the ball to the right, left or centre, and conversely, the goalkeeper needs to decide whether to pounce on the right, to the left or to stay put.

Soccer is a game in which two teams of 11 players compete for a ball.

But the question is, each player on both sides has their own position on the field, which one is the most eye-catching?

The two players who have rotated in the Ballon d'Or over the past nine years seem to confirm that strikers will always be the stars of football, but we think it's much more than that.

A columnist once wrote in an article: "When I first started dabbling in film and television, football was no longer just a competitive game for me, for me, football became a medium for me to understand historical and philosophical ideas, and I was fascinated by the role of goalkeeper." Seriously, do you know the goalkeeper? Do you know how a goalkeeper thinks before he makes a save? Is a goalkeeper a true footballer? Or are they just spectators of the game, a postmodernist sports practitioner? Or Joseph K. in football. (the character of the Austrian writer Kafka), who has to go through an unfair trial after every game? ”

He then referred to the existential masterpiece by German director Wim Wenders, "The Goalkeeper Fears a Penalty" (1971, 26-year-old Wim Wenders directed the non-episodic, non-expressive sports film "The Goalkeeper is Afraid of Penalty Kicks"), in which the protagonist is a goalkeeper who kicks the ball into the goal while he is talking to someone outside the touchline, and after the goal is ruled valid, he angrily pushes the referee, resulting in a red card, which is the scene at the beginning of the movie. This is the end of Banerjee's reference to the film, and he thinks it's a good time to ask the question he just asked: "What kind of role is a goalkeeper?" ”

This is indeed a question worth exploring.

But in penalty kicks, the goalkeeper is the absolute protagonist and they have to decide again and again – whether to throw to the side or keep the middle.

Although there is no shortage of cases in history where goalkeepers have struggled to defuse penalties and make a name for themselves, the history of penalty kicks is nothing more than the history of goalkeeper choices.

Of course, a history of goalkeeper choices is also a history of penalty maker choices.

In the 1994 FA Cup final between Manchester United and Chelsea, French star Eric Cantona scored two penalties to help the Red Devils win 4-0.

In response to a question from a reporter at the post-match press conference about his state of mind when he took the second penalty, Cantona said: "At first I was going to kick [to the other side of the goal], but I think he had guessed it, so I decided to go to the same side. But then I thought about it, and he might have guessed what I was thinking, so I decided to kick the ball to the other side. But I thought about it again, and he probably had guessed what he was thinking, so I still chose to kick the ball to the same side......" At this point, the Frenchman stopped, as if he realized that he was in an endless loop, and simply said, "So I didn't think much about it and just kicked it out." ”

Many of the team's regular penalty takers have said that even though they have started running, they still haven't decided which side of the goal to kick the ball towards.

During the penalty shootout in the 2016 Centennial Copa America final, Leo Messi, who was Argentina's first penalty, had an impressive nervous and complicated facial expression as he walked to the penalty spot.

In the Copa America final a year ago, he kicked the ball into the bottom left corner of the goal.

Chilean goalkeeper Claudio Bravo has been teammates with Messi for two years, and he must have some knowledge of Messi's mental activities at this time.

At that moment, I believed it was a typical two-player situation.

Messi kicked the ball to his right again, but unfortunately the ball hit the lintel and Argentina missed out on the title for the third time in three years.

If Messi has never been able to lead Argentina to the international championship, and whether he can be called the best in history, it is up for debate whether this Argentina team does not deserve to be called the uncrowned king of world football.

Hungary in 1954 was fully worthy of the title of uncrowned king – but the 1954 World Cup final in Switzerland did not go to a penalty shoot-out.

Then there was the Dutch team led by Johan Cruyff in 1974.

Another Hungarian, von Neumann, is one of the most important mathematicians of the 20th century, a great scientist with outstanding achievements in many fields such as modern computers, game theory, nuclear weapons, and biological and chemical weapons, and is known as the "father of computers" and "the father of game theory". Game Theory and Economic Behavior (1944) with Morgan Stern, the foundational work of the discipline of game theory) may well have had no interest in football, but he certainly realized what a successful team the Hungarian team was.

But it is not known whether he took penalty kicks into account when working on the "min/max theorem".

In 1928, Neumann published a paper entitled "The Theory of Parlor Games", which is regarded as the pioneering work of game theory.

The general meaning of this theory is that in a zero-sum game, it is a concept of game theory, which is a non-cooperative game. Refers to the parties involved in the game, under strict competition, the gain of one party must mean the loss of the other party, the sum of the gains and losses of the parties to the game is always "zero", there is no possibility of cooperation between the two sides), the two sides have perfect information (the so-called perfect information refers to the turn of the player in the action knows what strategy the other players in the previous action have taken, such as in the 2016 Centennial Copa America final, Bravo knew Messi's previous decision), Both parties can take corresponding countermeasures to minimize their losses.

When considering every strategy they can employ, one must consider all the possible responses that the other party might have if they adopted a strategy themselves.

What both sides need to consider is "the best result that can be obtained under the worst conditions", that is, in the process of the game, see what their minimum return is after the other party puts forward a decision; Then find the biggest one among these lowest returns.

It is very difficult to test such a theorem empirically, but the penalty case is an ideal material for studying the minimum maximum theorem.

The penalty game is a typical zero-sum game, and the benefit of the penalty taker and the goalkeeper must be relative (that is, there is no possibility that the penalty taker and the opposing goalkeeper will win).

Ignacio Virta, professor of management strategy at the London School of Economics and head of the Talent Screening Centre at Athletic Bilbao Football Club, has conducted a valuable study on this.

The penalty game model can be analysed like this: in a penalty game, both sides win the game – the penalty taker needs to score the penalty and the goalkeeper needs to save the penalty. We assume that the penalty taker can kick the ball to the left or right, and conversely, the goalkeeper can make a save to the left or right. Another option for both sides is for the penalty taker to kick the ball to the middle and the goalkeeper to stay in the middle, but we will later analyze that this situation is not statistically significant, so we maintain the assumption of left or right. Of course, it's entirely possible for the penalty taker to kick the ball out of goal, but we don't consider it here.

π represents a specific event here, πLR represents the situation where the penalty kicks the ball to his left and the goalkeeper pounces on the right side of the penalty taker. At the factual level, it is manifested as the goalkeeper is completely wrong in the wrong direction.

Let's be clear: both sides move at the same time – studies have shown that it only takes about 0.3 seconds for the ball to get from the kicker's feet to the goal line, which means that the goalkeeper can't wait until the ball is kicked out and sees the ball's trajectory before making a successful save.

This means that both the penalty and the goalkeeper must choose their strategy at the same time.

Professor Wilta has shown that penalty kick games can achieve a distinctive Nash equilibrium when they are called non-cooperative equilibriums, named after John Nash, and a combination of strategies called Nash equilibrium if none of the participants can act alone in a given situation.

In the above model, to achieve Nash equilibrium, the penalty maker and goalkeeper need to adopt a combination of strategies.

The above equilibrium yields two predictable experimental results. We came up with the concept of a "success rate" – the penalty taker and the goalkeeper should have the same probability of success.

The choice of the penalty taker and the goalkeeper in the penalty process must be independent of each other.

In short, both sides must only care about the benefits at the time and not about past penalty experiences – and the choice must be based on no memory.

In other words, neither side can be influenced by previous experience in the decision-making process for a current penalty.

In fact, the reason is very simple, as a penalty taker or goalkeeper, if the opponent knows your options in advance, then the situation will be quite unfavorable for you. Therefore, the ideal situation for both parties is that they each randomly pick their own strategy combinations and cannot profit from each other's strategy combinations.

Professor Vieta used classical hypothesis methods and real data to verify the validity of the above two hypotheses. Data comes from Spain, England, Italy and a number of international competitions, from September 1995 to June 2012.

The data was recorded on a total of 9,017 penalties and was recorded as follows: the names of the players (including the names of the penalty taker and goalkeeper), the names of the teams on both sides of the match, the date of the match, the direction in which the penalty taker kicked the ball (to their left, right or centre), the time of the penalty, the score before the penalty, the final result of the match, whether the penalty was scored (if not scored, it was saved by the goalkeeper, missed or hit the post or crossbar), Each of these items is clearly categorized.