How many non-repeating games in chess. Chess clock - to stay awake
Shannon's number
Shannon's number- the approximate minimum number of non-repeating chess games, calculated in 1950 by the American mathematician Claude Shannon, is approximately 10 120. The calculation is described in the work "Programming a computer for playing chess" (eng. "Programming a Computer for Playing Chess" ), published in March 1950 in the Philosophical Magazine and became one of the fundamental works in the development of computer chess as a discipline. The calculations were based on the assumption that each game lasts on average 40 moves and on each move the player makes a choice on average out of 30 options. For comparison, the number of atoms in the observable Universe is, according to various estimates, from to, that is, 10 40 times less than the Shannon number.
In addition, Shannon also calculated the number of possible positions, which is approximately
This number, however, also includes situations that are excluded by the rules of the game, and therefore inaccessible in the tree of possible moves. Currently, a number of works have appeared that clarify or even refute this number.
Notes (edit)
Literature
- Claude shannon Programming a Computer for Playing Chess // Philosophical Magazine... - 1950 .-- T. 7/41. - No. 314. - S. 256-275.
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Every time we sit down to play chess the game is on in a new way and almost never repeats itself. And it really never repeats itself - this was proved by the American mathematician Claude Shannon. He calculated the minimum number of non-repeating chess games.
This number equals ...
... ten to the one hundred and twentieth power, and it is named after its discoverer "Shannon's number."
Claude Elwood Shannon (1916-2001) - famous engineer and mathematician, is the "father of information theory". He was fascinated by chess and is the first to recalculate the complex game tree with great precision, i.e. the number of possible chess games. The basis of his calculations is the theory that any game contains on average 40 moves and on each move the players choose from about 30 possibilities. This equates to approximately 10,120 possible batches. In the end, it turns out that the approximate number of non-repeating chess games is these ten to the one hundred and twentieth power. This is more than the total number of atoms in the observable Universe:
This number is known as the Shannon number.
Shannon also calculated the number of possible positions on the chessboard - it is ten to the forty-third power.
Peterson came to the same conclusion in 1996. An interesting comparison with Shannon's number is that the total number of atoms in the universe is 1081. But Peterson sets the limits of calculations and determines the real moves in chess at 1050.
All these calculations will change when new rules of chess are applied, such as the Sophia rule. The numbers are close enough to real ones to show the deep meaning and diversity of chess.
And a dozen more interesting things about chess:
1. Origin of the name
Chess evolved from the 6th century ancient Indian game "chaturanga", whose name translates from Sanskrit as "four divisions of the army", which includes infantry, cavalry, elephants and chariots, which are represented in chess by pawn, knight, bishop and rook.
In the 7th century, the game came to Persia and was renamed shatranj. It is from the Persian language that the name chess comes from. The players said "Shah" (from the Persian "king") attacking the opponent's king, and "Shah mat" (from Persian - "the king is dead").
2. The chess machine that cheated everyone
In 1770, the Hungarian inventor Wolfgang von Kempelen created a chess machine. The car was a human-sized figure of a "Turk", who was sitting behind a huge wooden cabinet, whose doors opened, showing the public the complex mechanisms.
The mechanical arm moved the pieces across the field, and beat such famous opponents as Napoleon Bonaparte and Benjamin Franklin.
As it turned out many years later, the chess machine was not a machine. Inside the machine was a chess player who moved inside and hid when the audience was shown the complex mechanisms of the clever "machine".
3. The shortest and longest chess game
The shortest chess game is called a stupid checkmate, which consists of two moves: 1. f3 e5 and 2. g4 Qh4 ++. A draw or a loss can also occur before the players start making moves, both in the case of a certain scenario in the standings, and as a result of the player not coming to the game.
The longest chess game was played between Ivan Nikolic and Goran Arsovic in Belgrade in 1989. It lasted 20 hours 15 minutes, 269 moves were made during the game, and it ended in a draw. In theory, the game can last even longer, but after the introduction of the 50-move rule, this number can be somehow limited.
4. Checkbox
Garry Kasparov once said that "chess is a torment of the mind." Apparently that's why someone decided to combine chess with physical challenges by creating a chessbox. Dutch artist Ipe Rubing became the founder of chess after seeing the idea of combining chess and boxing in one comic book.
In chess boxing, rounds of chess and boxing alternate and its motto is "Battles take place in the ring, and wars are fought on the board."
Chessboxing is gaining more and more popularity and is administered by the World Chessboxing Organization.
5. Dynamic queen
Chess figure The queen or queen has undergone many changes throughout the history of chess. It all started with the fact that she could walk only one square diagonally, then she moved two squares, and then farther and farther, like a horse.
Now this figure can move both diagonally and horizontally and vertically. At first she was the advisor or prime minister of the king.
But later she became the strongest chess figure.
6. Blind Chess
Blind Chess is a variation of the game in which the player makes all moves without looking at the chessboard. As a rule, there is an intermediary in the game who moves the pieces.
Blind Chess is an impressive ability that many of the strongest chess players have. One of the record holders in blind chess was the Hungarian chess player Janos Flesch, who played with 52 opponents at the same time blindfolded and won 32 games.
7. Endless possibilities
After three moves, there are over nine million possible positions on each side. The American mathematician calculated the minimum number of non-repeating chess games and deduced the Shannon number.
According to this number, the number of possible unique parties exceeds the number of atoms in the visible universe. The number of atoms is estimated to be 10 ^ 79, and the number of unique chess games is 10 ^ 120.
8. The power of chess computers
Chess computers are now an important part of chess. World champion Garry Kasparov, considered the strongest player in the history of chess, lost to the Deep Blue computer in 1997, and it came as a real shock to the entire world of chess.
In 2006, world champion Vladimir Kramnik was defeated by the Deep Fritz computer, further emphasizing the power of chess computers... Today chess programs are often used by players to analyze and improve the game, and are often placed on a par with grandmasters.
9. Chess clock - to stay awake
initially chess games played without a watch. At the same time, the players could play for many hours, or even days in a row, bringing each other to exhaustion. In 1851, during a chess tournament, an assistant referee recorded that "the game was not completed because the players finally fell asleep."
After that, a year later, international tournament introduced time control in the form hourglass, and in 1883 the first mechanical chess clock appeared, created by the Briton Thomas Wilson.
10. Chess and our brain
Psychologists often refer to chess as effective method improve your memory. It also allows you to decide challenging tasks and think through ideas.
Many people believe that chess is a game for those who are naturally highly intelligent. This is partly true, but you can also significantly increase your intelligence by playing chess. What's more, research has shown that chess activates both hemispheres of the brain, improving creativity, concentration, critical thinking and reading skills.
Every time we sit down to play chess, the game goes on in a new way and almost never repeats itself. And it really never repeats itself - this was proved by the American mathematician Claude Shannon. He calculated the minimum number of non-repeating chess games.
This number equals ...
... ten to the one hundred and twentieth power, and it is named after its discoverer "Shannon's number."
Claude Elwood Shannon (1916-2001) - famous engineer and mathematician, is the "father of information theory". He was fascinated by chess and is the first to recalculate the complex game tree with great precision, i.e. the number of possible chess games. The basis of his calculations is the theory that any game contains on average 40 moves and on each move the players choose from about 30 possibilities. This equates to approximately 10,120 possible batches. In the end, it turns out that the approximate number of non-repeating chess games is these ten to the one hundred and twentieth power. This is more than the total number of atoms in the observable Universe:
This number is known as the Shannon number.
Shannon also calculated the number of possible positions on the chessboard - it is ten to the forty-third power.
Peterson came to the same conclusion in 1996. An interesting comparison with Shannon's number is that the total number of atoms in the universe is 10 to 81. But Peterson sets limits on calculations and determines the real moves in chess at 1050.
All these calculations will change when new rules of chess are applied, such as the Sophia rule. The numbers are close enough to real ones to show the deep meaning and diversity of chess.
And a dozen more interesting things about chess:
1. Origin of the name
Chess evolved from the 6th century ancient Indian game "chaturanga", whose name translates from Sanskrit as "four divisions of the army", which includes infantry, cavalry, elephants and chariots, which are represented in chess by pawn, knight, bishop and rook.
In the 7th century, the game came to Persia and was renamed shatranj. It is from the Persian language that the name chess comes from. The players said "Shah" (from the Persian "king") attacking the opponent's king, and "Shah mat" (from Persian - "the king is dead").
2. The chess machine that cheated everyone
In 1770, the Hungarian inventor Wolfgang von Kempelen created a chess machine. The car was a human-sized figure of a "Turk", who was sitting behind a huge wooden cabinet, whose doors opened, showing the public the complex mechanisms.
The mechanical arm moved the pieces across the field, and beat such famous opponents as Napoleon Bonaparte and Benjamin Franklin.
As it turned out many years later, the chess machine was not a machine. Inside the machine was a chess player who moved inside and hid when the audience was shown the complex mechanisms of the clever "machine".
3. The shortest and longest chess game
The shortest chess game is called a stupid checkmate, which consists of two moves: 1. f3 e5 and 2. g4 Qh4 ++. A draw or a loss can also occur before the players start making moves, both in the case of a certain scenario in the standings, and as a result of the player not coming to the game.
The longest chess game was played between Ivan Nikolic and Goran Arsovic in Belgrade in 1989. It lasted 20 hours 15 minutes, 269 moves were made during the game, and it ended in a draw. In theory, the game can last even longer, but after the introduction of the 50-move rule, this number can be somehow limited.
4. Checkbox
Garry Kasparov once said that "chess is a torment of the mind." Apparently that's why someone decided to combine chess with physical challenges by creating a chessbox. Dutch artist Ipe Rubing became the founder of chess after seeing the idea of combining chess and boxing in one comic book.
In chess boxing, rounds of chess and boxing alternate and its motto is "Battles take place in the ring, and wars are fought on the board."
Chessboxing is gaining more and more popularity and is administered by the World Chessboxing Organization.
5. Dynamic queen
The Queen or Queen chess piece has undergone many changes throughout the history of chess. It all started with the fact that she could only walk one square diagonally, then she moved two squares, and then farther and farther, like a horse.
Now this figure can move both diagonally and horizontally and vertically. At first she was the advisor or prime minister of the king.
But later she became the strongest chess figure.
6. Blind Chess
Blind Chess is a variation of the game in which the player makes all moves without looking at the chessboard. As a rule, there is an intermediary in the game who moves the pieces.
Blind Chess is an impressive ability that many of the strongest chess players have. One of the record holders in blind chess was the Hungarian chess player Janos Flesch, who played with 52 opponents at the same time blindfolded and won 32 games.
7. Endless possibilities
After three moves, there are over nine million possible positions on each side. The American mathematician calculated the minimum number of non-repeating chess games and deduced the Shannon number.
According to this number, the number of possible unique parties exceeds the number of atoms in the visible universe. The number of atoms is estimated to be 10 ^ 79, and the number of unique chess games is 10 ^ 120.
8. The power of chess computers
Chess computers are now an important part of chess. World champion Garry Kasparov, considered the strongest player in the history of chess, lost to the Deep Blue computer in 1997, and it came as a real shock to the entire world of chess.
In 2006, World Champion Vladimir Kramnik was defeated by the Deep Fritz computer, further highlighting the power of chess computers. Today chess programs are often used by players to analyze and improve the game, and they are often placed on a par with grandmasters.
9. Chess clock - to stay awake
In the beginning, chess games were played without a clock. At the same time, the players could play for many hours, or even days in a row, bringing each other to exhaustion. In 1851, during a chess tournament, an assistant referee noted that "the game was not completed because the players eventually fell asleep."
After that, a year later, the time control in the form of an hourglass was introduced at the international tournament, and in 1883 the first mechanical chess clock appeared, created by the Briton Thomas Wilson.
10. Chess and our brain
Psychologists often cite chess as an effective way to improve your memory. It also allows you to solve complex problems and think through ideas.
Many people believe that chess is a game for those who are naturally highly intelligent. This is partly true, but you can also significantly increase your intelligence by playing chess. What's more, research has shown that chess activates both hemispheres of the brain, improving creativity, concentration, critical thinking and reading skills.
sources
http://www.factroom.ru/facts/20867
https://ru.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%BB%D0%BE_%D0%A8%D0%B5%D0%BD%D0%BD%D0 % BE% D0% BD% D0% B0
Here's what else you might be interested in about chess: there are some, but unusual game... Well, if you do not have chess at hand, then here The original article is on the site InfoGlaz.rf The link to the article this copy was made from is
