Jul/Aug 2004  •   Fiction

Two-Player Infinitely Iterated Simultaneous Semi-Cooperative Game with Spite and Reputation

by Charles Yu


The highest score of all time was recorded on July 24, 2016.


On that date, Wally Kushner, age seven, of Eureka, CA, achieved a point total of 1,356,888, including all bonuses.


Using a modified Stupps-Kinsky approach (1973), Wally conducted a single session game lasting over 9,000 rounds. In total, he played for 11 days, six hours, 24 minutes and three seconds.


Wally's mother kept time. She also fed Wally and wiped down his face and neck with a damp washcloth. She did this twice a day, once in the morning and once in the evening.

At the conclusion of the game, Wally, then seated cross-legged on the floor of his bedroom, looked up at his mother. He asked her, "Are you proud of me?"

Wally's mother was very proud.


The game begins when a player walks into the room and announces a statement. The statement can be a truth or a falsehood. If another player is in the vicinity and hears the announcement, and if such other player has his setting switched on to Accept Truths, then the program will engage. The subroutines will be loaded. This is the beginning of a game, and this is how a game always begins.


During his marathon effort, Wally consumed 16 bologna and cheese sandwiches, six gallons of orange juice, and 191 Oreos. His average pulse during the game was a placid 64 beats per minute. Doctors monitoring Wally noted his almost total lack of perspiration.


The program run-time summary from Wally's record session reported that Player 1, controlled by Wally, made exactly 9,072 statements. Of these, 5,000 were statements about the world, 4,000 were statements about other players, 30 were statements about himself, ten were statements about all of the above.

7,500 statements Wally made were true; 1,500 were false; 60 statements were both true and false; ten statements were neither true nor false; one statement was false and beautiful; one statement was neither true nor false nor beautiful, but it was funny and sad and sweet, and on top of it all, grammatically correct.


The basic tool in the game is the eye-looking vector. Each player has one. The eye-looking vector starts from the center of the player's head and extends forward, parallel to the sagittal plane and orthogonally to the coronal plane of the player's body. Players can point their eye-looking vectors in a 90-degree peripheral field of vision from their line of forward orientation.


Another important tool in the game is the vector-accepting eye. A vector-accepting eye is the same as an eye-looking vector. They are two names for the same thing, but they are described with different terms, depending on the current polarization of the players.


A general rule of thumb is this: when a player is announcing the truth, he looks with an eye-looking vector. When a player is accepting the truth, he accepts with a vector-accepting eye.


The average eye-looking vector is three yards long. Within the range of the eye-looking vectors, a player can absorb data and make true statements about the world. The length and spatial orientation of the eye-looking vector determine the statements about the world that can be made. The longer the eye-looking vector, the more statements a player can make about the world. These might be true or false, beautiful or not beautiful, but these are the only statements that can be made.

Note, however, that even a very long eye-looking vector cannot help a player make statements about other players. More about this later.


Wally began his game by choosing Player 1.


Each player must assume certain things about himself.


Wally chose the Husband-Wife module.

He assumed the following:

"I am 37 years old."

"I make more than I deserve."

"I have a beautiful wife. I know this because everyone tells me so."

"As far as I can tell, I have no attachments to anyone or anything in the entire world."


Other modules include Brother-Brother, Father-Son and Total Strangers.


Mirrors are an interesting feature of the game. A mirror will turn the vector in a different direction. Mirrors can confuse the difference between eye-looking vectors and vector-accepting eyes. Another feature is the black box. Not much is known about the black box.


The Sorry Feature has been updated for more realistic game play, especially between lovers or strangers.


Another updated feature of the game is Common Knowledge. Common Knowledge is activated in the following situation. If Player 1 walks into the room and makes a true statement, and Player 2 is within range and hears the truth of the statement, Common Knowledge may be attained. What has to happen is that Player 1 must utter the true statement while pointing his eye-looking vector in the direction of Player 2's vector-accepting eye. Player 2 hears the truth and knows it. Because Player 1 is eye-looking, Player 1 knows that Player 2 knows the truth. Because Player 2 is eye-looking, Player 2 knows that Player 1 knows that Player 2 knows the truth. Likewise, Player 1 knows that Player 2 knows that Player 1 knows that Player 2 knows the truth. An infinite hierarchy of knowledge is created. This can be depicted as a spiral between the players, each one knowing an infinite number of truths about the other.


Wally writes:

A lot of people spend too much time deciding between Player 1 versus Player 2. This is the first mistake, in my estimation.

Everyone I talk to wants to know how I got my high score, but when I tell them, they refuse to believe. Most readers of your magazine will not believe it, either, I'm afraid, but I'll say it again anyway, in case anyone out there is open-minded.


Wally also notes:

Sorry is not what it seems to be. This is the main thing that makes me different form your average player.

Your average weekend player thinks that Sorry is used as a defensive measure, to block eye-looking vectors

The professional uses Sorry as a neutral move.


Wally concludes:

When the amateur says Sorry, he means: I wish that had not happened, but the world is what the world is.

When the player of strength says Sorry, he means: that happened.


Neat Trick

Also, thanks to Wayne Garza of Grand Rapids, MI, for the Trick of the Month.

Wayne writes:

Common Knowledge works in the mirror, too.

To use it, go into Player 1's house. This is at the very beginning of the game. The program will place you in the town square. Walk two units south and one unit west. Find the white house with a blue roof. Go in. (The door will be locked. The key is under the mat.)


Our staffers have verified that Wayne's tip works. To try it for yourself, follow these directions:

A. From the entrance, go down the main hall to the second door on the right. This is the guest bathroom. Turn on the shower. Make sure the water is very hot. Close the door and let the bathroom fill with steam.

B. When the mirror is cloudy and opaque with the condensation from water vapor, stand in front of the mirror, about a foot to 18 inches away. This is the optimal length for all eye-looking vectors. At this length, an eye-looking vector has unique properties. Use your hand to wipe off a small area, maybe six inches by three inches from the glass, so that the mirror can reflect your eye-looking vector. Now look at yourself. Keep looking. Do not look away. Stand still. Do not look away. The game will ask you over and over again if you want to look away. Resist the temptation. Note what is happening. Your eye-looking vector will begin bouncing off the mirror and into your reflection's vector-accepting eye, and then back out again. The vector will keep bouncing off the mirror, back and forth, into the mirror and then out and back into your own head.

C. After a while, small windows will pop-up and the game will ask you over and over again: Are you sure Are you sure Are you sure Are you sure? Click away all of these little boxes. New windows will spring forth, asking if you want to terminate the subroutine. The game will assume there has been some kind of error. Keep clicking these closed, too. Stand still, and whatever you do, do not look away.

D. If you wait long enough, the game will give up and override the defaults. It will recognize your reflection in the mirror as a different player, Player 2. Now you are Player 1 and your reflection is Player 2. Now, say you are sorry. Say a true thing. You will know it and you will know you know it and you will know you know you know you know you know you know you know you know you know it. You will know a infinite number of things about yourself, an infinite regress, telescoping up to a vanishing point, a hierarchy of statements, longer and longer, more and more abstract, receding into the distance, farther and farther from the world, none of them beautiful, all of them true.