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120-627: The elite tournament was usually played in a round-robin or double round-robin format. However, it took the form of a series of heads-up matches in 2002 and 2004. The 2002 Dortmund event was also notable in that it served as the Candidates Tournament for the Classical World Chess Championship 2004 . Péter Lékó won, defeating Veselin Topalov in the finals. A flagship event of the newer incarnation

240-463: A bye . The schedule can therefore be computed as though the dummy were an ordinary player, either fixed or rotating. Instead of rotating one position, any number relatively prime to ( n − 1 ) {\displaystyle (n-1)} will generate a complete schedule. The upper and lower rows can indicate home/away in sports, white/black in chess , etc.; to ensure fairness, this must alternate between rounds since competitor 1

360-585: A communist-led revolution in Afghanistan, Soviet forces invaded the country, ultimately starting the Soviet–Afghan War . In May 1988, the Soviets started to withdraw from Afghanistan , due to international opposition, persistent anti-Soviet guerrilla warfare, and a lack of support by Soviet citizens. From 1985 onwards, the last Soviet leader Mikhail Gorbachev , who sought to enact liberal reforms in

480-653: A troika was designated to take charge. Eventually Joseph Stalin , the General Secretary of the Communist Party , managed to suppress all opposition factions and consolidate power in his hands to become the country's dictator by the 1930s. Leon Trotsky , the main proponent of world revolution , was exiled from the Soviet Union in 1929, and Stalin's idea of Socialism in One Country became

600-611: A Varangian from the Rus' people , named Rurik , was elected ruler of Novgorod in 862. In 882, his successor Oleg ventured south and conquered Kiev , which had been previously paying tribute to the Khazars . Rurik's son Igor and Igor's son Sviatoslav subsequently subdued all local East Slavic tribes to Kievan rule, destroyed the Khazar Khaganate, and launched several military expeditions to Byzantium and Persia . In

720-464: A bye. If the number is even, an added player (ω) becomes the opponent. For an even number n {\displaystyle n} or an odd number n − 1 {\displaystyle n-1} of competitors, Schurig builds a table with n / 2 {\displaystyle n/2} vertical rows and n − 1 {\displaystyle n-1} horizontal rows. Then he populates it starting from

840-489: A certain number of wins or losses. The term round-robin is derived from the French term ruban ('ribbon'). Over time, the term became idiomized to robin . In a single round-robin schedule, each participant plays every other participant once. If each participant plays all others twice, this is frequently called a double round-robin . The term is rarely used when all participants play one another more than twice, and

960-411: A competitor to play the strongest opponents in a round robin in quick succession while others play them intermittently with weaker opposition. This asymmetry means that playing the same opponents is not necessarily completely equitable. There is also no scheduled showcase final match unless (by coincidence) two competitors meet in the last match of the tournament, with the result of that match determining

1080-477: A competitor's chance of ultimate victory. Final records of participants are more accurate, in the sense that they represent the results over a longer period against the same opposition. The system is also better for ranking all participants, not just determining the winner. This is helpful to determine the final rank of all competitors, from strongest to weakest, for purposes of qualification for another stage or competition as well as for prize money. In team sports,

1200-510: A crisis. By 1991, economic and political turmoil began to boil over as the Baltic states chose to secede from the Soviet Union. On 17 March, a referendum was held, in which the vast majority of participating citizens voted in favour of changing the Soviet Union into a renewed federation . In June 1991, Boris Yeltsin became the first directly elected President in Russian history when he

1320-664: A global superpower. After World War II, according to the Potsdam Conference , the Red Army occupied parts of Eastern and Central Europe, including East Germany and the eastern regions of Austria . Dependent communist governments were installed in the Eastern Bloc satellite states. After becoming the world's second nuclear power , the Soviet Union established the Warsaw Pact alliance, and entered into

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1440-800: A large confederacy, which was subsequently taken over by the Cumans and the Kipchaks . The ancestors of Russians are among the Slavic tribes that separated from the Proto-Indo-Europeans, who appeared in the northeastern part of Europe c.  1500  years ago. The East Slavs gradually settled western Russia (approximately between modern Moscow and Saint-Petersburg ) in two waves: one moving from Kiev towards present-day Suzdal and Murom and another from Polotsk towards Novgorod and Rostov . Prior to Slavic migration, that territory

1560-489: A lower-placed qualifier is perceived to be easier than for a higher-placed one). Four pairs in the 2012 Olympics Women's doubles badminton , having qualified for the next round, were ejected from the competition for attempting to lose in the round robin stage to avoid compatriots and better ranked opponents. The round robin stage at the Olympics was a new introduction, and these potential problems were readily known prior to

1680-437: A round in which players meets each other. For example, player 7 plays against player 11 in round 4. If a player meets itself, then this shows a bye or a game against player n. All games in a round constitutes a diagonal in the table. The above schedule can also be represented by a graph, as shown below: Both the graph and the schedule were reported by Édouard Lucas in as a recreational mathematics puzzle. Lucas, who describes

1800-497: A round, a non-leftmost position (not including 1 {\displaystyle 1} ) can only be taken by competitors of a fixed distance. In round 1 {\displaystyle 1} of the example, in the second position competitor 2 {\displaystyle 2} plays against 13 {\displaystyle 13} , their distance is 2 {\displaystyle 2} . In round 2 {\displaystyle 2} , this position

1920-540: A schedule where player 14 has a fixed position, and all other players are rotated counterclockwise n 2 {\displaystyle {\frac {n}{2}}} positions. This schedule is easily generated manually. To construct the next round, the last player, number 8 in the first round, moves to the head of the table, followed by player 9 against player 7, player 10 against 6, until player 1 against player 2. Arithmetically, this equates to adding n 2 {\displaystyle {\frac {n}{2}}} to

2040-633: A secret protocol within the Molotov–Ribbentrop Pact with Nazi Germany . The Soviet Union later invaded Finland , and occupied and annexed the Baltic states , as well as parts of Romania . On 22 June 1941, Germany invaded the Soviet Union , opening the Eastern Front , the largest theater of World War II. Eventually, some 5 million Red Army troops were captured by the Nazis;

2160-619: A straight knockout system. The top one, two, or occasionally three teams in these groups then proceed to a straight knockout stage for the remainder of the tournament. In the circle of death it is possible that no champion emerges from a round-robin tournament, even if there is no draw, but most sports have tie-breaker systems which resolve this. Round-robins can suffer from being too long compared to other tournament types, and with later scheduled games potentially not having any substantial meaning. They may also require tie-breaking procedures. Swiss system tournaments attempt to combine elements of

2280-517: A struggle for global dominance, known as the Cold War , with the rivalling United States and NATO . After Stalin's death in 1953 and a short period of collective rule , the new leader Nikita Khrushchev denounced Stalin and launched the policy of de-Stalinization , releasing many political prisoners from the Gulag labour camps. The general easement of repressive policies became known later as

2400-526: A table. In France this is called the Carousel -Berger system (Système Rutch-Berger). The schedule can also be used for "asynchronous" round-robin tournaments where all games take place at different times (for example, because there is only one venue). The games are played from left to right in each round, and from the first round to the last. When the number of competitors is even, this schedule performs well with respect to quality and fairness measures such as

2520-416: A tournament of 16 teams can be completed in just 4 rounds (i.e. 15 matches) in a knockout format; a double elimination tournament format requires 30 (or 31) matches, but a round-robin would require 15 rounds (i.e. 120 matches) to finish if each competitor faces each other once. Other issues stem from the difference between the theoretical fairness of the round robin format and practice in a real event. Since

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2640-571: A variety of tiebreaker criteria. Frequently, pool stages within a wider tournament are conducted on a round-robin basis. Examples with single round-robin scheduling include the FIFA World Cup , UEFA European Football Championship , and UEFA Cup (2004–2009) in football, Super Rugby ( rugby union ) in the Southern Hemisphere during its past iterations as Super 12 and Super 14 (but not in its later 15- and 18-team formats),

2760-651: Is a permanent member of the United Nations Security Council ; a member state of the G20 , SCO , BRICS , APEC , OSCE , and WTO ; and the leading member state of post-Soviet organisations such as CIS , CSTO , and EAEU/EEU . It possesses the largest stockpile of nuclear weapons and has the third-highest military expenditure . Russia is generally considered a great power and is a regional power . Internationally, Russia ranks very low in measurements of democracy , human rights and freedom of

2880-613: Is a simple algorithm to create a schedule for a round-robin tournament. All competitors are assigned to numbers, and then paired in the first round: Next, one of the competitors in the first or last column of the table is fixed (number one in this example) and the others rotated clockwise one position: This is repeated until when the next iteration would lead back to the initial pairings: With an even number n {\displaystyle n} of competitors this algorithm realizes every possible combination of them (equivalently, that all pairs realized are pairwise different). First,

3000-435: Is always on the first row. If, say, competitors 3 and 8 were unable to fulfil their fixture in the third round, it would need to be rescheduled outside the other rounds, since both competitors would already be facing other opponents in those rounds. More complex scheduling constraints may require more complex algorithms. This schedule is applied in chess and draughts tournaments of rapid games, where players physically move round

3120-691: Is even, then in each of ( n − 1 ) {\displaystyle (n-1)} rounds, n 2 {\displaystyle {\begin{matrix}{\frac {n}{2}}\end{matrix}}} games can be run concurrently, provided there exist sufficient resources (e.g. courts for a tennis tournament). If n {\displaystyle n} is odd, there will be n {\displaystyle n} rounds, each with n − 1 2 {\displaystyle {\begin{matrix}{\frac {n-1}{2}}\end{matrix}}} games, and one competitor having no game in that round. The circle method

3240-1054: Is held by competitors 14 {\displaystyle 14} and 12 {\displaystyle 12} , also having distance 2 {\displaystyle 2} , etc. Similarly, the next position ( 3 {\displaystyle 3} against 12 {\displaystyle 12} in round 1 {\displaystyle 1} , 2 {\displaystyle 2} against 11 {\displaystyle 11} in round 2 {\displaystyle 2} , etc.) can only hold distance- 4 {\displaystyle 4} competitors. For every k < n 2 {\displaystyle k<{\frac {n}{2}}} , there are exactly n − 1 {\displaystyle n-1} pairs of distance k {\displaystyle k} . There are n − 1 {\displaystyle n-1} rounds and they all realize one distance- k {\displaystyle k} pair at

3360-504: Is never used when one participant plays others an unequal number of times, as is the case in almost all of the major North American professional sports leagues. In the United Kingdom , a round-robin tournament has been called an American tournament in sports such as tennis or billiards which usually have single-elimination (or "knockout") tournaments, although this is now rarely done. A round-robin tournament with four players

3480-413: Is sometimes called "quad" or "foursome". In sports with a large number of competitive matches per season, double round-robins are common. Most association football leagues in the world are organized on a double round-robin basis, in which every team plays all others in its league once at home and once away. This system is also used in qualification for major tournaments such as the FIFA World Cup and

3600-706: Is the No Castling Masters (see No Castling Chess ). It is accompanied by large open events and invite-only cup competitions. The title sponsor is Sparkasse Dortmund, the local public savings bank. [REDACTED] GM Romuald Mainka won Open A tournament with the result 7½ out of 9. 17-year-old [REDACTED] Olaf Wegener won Open A Swiss-system tournament with the score 8/10. [REDACTED] IM Arkadij Naiditsch ( 2524 ) defeated [REDACTED] IM Almira Skripchenko-Lautier ( 2494 ) in Dortmund Sparkassen Match with

3720-408: Is the fairest way to determine the champion from among a known and fixed number of contestants. Each contestant, whether player or team, has equal chances against all other opponents because there is no prior seeding of contestants that will preclude a match between any given pair. The element of luck is seen to be reduced as compared to a knockout system since one or two bad performances need not ruin

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3840-510: Is the world's ninth-most populous country and Europe's most populous country . Russia is a highly urbanised country including 16 population centres with over a million inhabitants. Its capital and largest city is Moscow . Saint Petersburg is Russia's second-largest city and its cultural capital . The East Slavs emerged as a recognised group in Europe between the 3rd and 8th centuries CE. The first East Slavic state, Kievan Rus' , arose in

3960-628: The Oxford English Dictionary , the English name Russia first appeared in the 14th century, borrowed from Medieval Latin : Russia , used in the 11th century and frequently in 12th-century British sources, in turn derived from Russi , 'the Russians'; and the suffix -ia . In modern historiography, this state is usually denoted as Kievan Rus' after its capital city. Another Medieval Latin name for Rus'

4080-574: The 2025 ICC Champions Trophy . In a more extreme example, the KBO League in baseball plays a 16-fold round robin, with each of the 10 teams playing each other 16 times for a total of 144 games per team. LIDOM (Baseball Winter League in the Dominican Republic) plays an 18-fold round robin as a semi final tournament between four classified teams. Group tournaments rankings usually go by number of matches won and drawn, with any of

4200-554: The Battle of Kursk in the summer of 1943. Another German failure was the Siege of Leningrad , in which the city was fully blockaded on land between 1941 and 1944 by German and Finnish forces, and suffered starvation and more than a million deaths, but never surrendered. Soviet forces steamrolled through Eastern and Central Europe in 1944–1945 and captured Berlin in May 1945. In August 1945,

4320-765: The Brusilov Offensive of the Imperial Russian Army almost completely destroyed the Austro-Hungarian Army . However, the already-existing public distrust of the regime was deepened by the rising costs of war, high casualties , and rumors of corruption and treason. All this formed the climate for the Russian Revolution of 1917, carried out in two major acts. In early 1917, Nicholas II was forced to abdicate ; he and his family were imprisoned and later executed during

4440-475: The Congress of Vienna , which defined the map of post-Napoleonic Europe. The officers who pursued Napoleon into Western Europe brought ideas of liberalism back to Russia, and attempted to curtail the tsar's powers during the abortive Decembrist revolt of 1825. At the end of the conservative reign of Nicholas I (1825–1855), a zenith period of Russia's power and influence in Europe, was disrupted by defeat in

4560-656: The Cricket World Cup along with Indian Premier League , major Twenty-20 Cricket tournament, and many American football college conferences , such as the Conference USA (which currently has 9 members). The group phases of the UEFA club competitions and Copa Libertadores are contested as a double round-robin, as are most basketball leagues outside the United States, including the regular season of

4680-693: The Crimean War . Nicholas's successor Alexander II (1855–1881) enacted significant changes throughout the country, including the emancipation reform of 1861 . These reforms spurred industrialisation, and modernised the Imperial Russian Army, which liberated much of the Balkans from Ottoman rule in the aftermath of the 1877–1878 Russo-Turkish War . During most of the 19th and early 20th century, Russia and Britain colluded over Afghanistan and its neighbouring territories in Central and South Asia;

4800-536: The EuroLeague (as well as its former Top 16 phase); the United Football League has used a double round-robin for both its 2009 and 2010 seasons. Season ending tennis tournaments also use a round robin format prior to the semi on stages. The champion in a round-robin tournament is the contestant that wins the most games, except when draws are possible. In theory, a round-robin tournament

4920-614: The Great Northern War (1700–1721), securing Russia's access to the sea and sea trade. In 1703, on the Baltic Sea, Peter founded Saint Petersburg as Russia's new capital. Throughout his rule, sweeping reforms were made , which brought significant Western European cultural influences to Russia. He was succeeded by Catherine I (1725–1727), followed by Peter II (1727–1730), and Anna . The reign of Peter I's daughter Elizabeth in 1741–1762 saw Russia's participation in

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5040-701: The Khrushchev Thaw . At the same time, Cold War tensions reached its peak when the two rivals clashed over the deployment of the United States Jupiter missiles in Turkey and Soviet missiles in Cuba . In 1957, the Soviet Union launched the world's first artificial satellite , Sputnik 1 , thus starting the Space Age . Russian cosmonaut Yuri Gagarin became the first human to orbit

5160-707: The Oldowan period in the early Lower Paleolithic . About 2 million years ago, representatives of Homo erectus migrated to the Taman Peninsula in southern Russia. Flint tools, some 1.5 million years old, have been discovered in the North Caucasus . Radiocarbon dated specimens from Denisova Cave in the Altai Mountains estimate the oldest Denisovan specimen lived 195–122,700 years ago. Fossils of Denny , an archaic human hybrid that

5280-568: The Rurik dynasty that ruled Kievan Rus' collectively. Kiev's dominance waned, to the benefit of Vladimir-Suzdal in the north-east, the Novgorod Republic in the north, and Galicia-Volhynia in the south-west. By the 12th century, Kiev lost its pre-eminence and Kievan Rus' had fragmented into different principalities. Prince Andrey Bogolyubsky sacked Kiev in 1169 and made Vladimir his base, leading to political power being shifted to

5400-843: The Russian Civil War . The monarchy was replaced by a shaky coalition of political parties that declared itself the Provisional Government , and proclaimed the Russian Republic . On 19 January [ O.S. 6 January], 1918, the Russian Constituent Assembly declared Russia a democratic federal republic (thus ratifying the Provisional Government's decision). The next day the Constituent Assembly

5520-646: The Russian Empire , which remains the third-largest empire in history . However, with the Russian Revolution in 1917, Russia's monarchic rule was abolished and eventually replaced by the Russian SFSR —the world's first constitutionally socialist state . Following the Russian Civil War , the Russian SFSR established the Soviet Union with three other Soviet republics , within which it was

5640-632: The Seven Years' War (1756–1763). During the conflict, Russian troops overran East Prussia , reaching Berlin. However, upon Elizabeth's death, all these conquests were returned to the Kingdom of Prussia by pro-Prussian Peter III of Russia . Catherine II ("the Great"), who ruled in 1762–1796, presided over the Russian Age of Enlightenment . She extended Russian political control over

5760-852: The Siberian River Routes , and by the mid-17th century, there were Russian settlements in eastern Siberia, on the Chukchi Peninsula , along the Amur River , and on the coast of the Pacific Ocean. In 1648, Semyon Dezhnyov became the first European to navigate through the Bering Strait . Under Peter the Great , Russia was proclaimed an empire in 1721, and established itself as one of the European great powers. Ruling from 1682 to 1725, Peter defeated Sweden in

5880-472: The Soviet Union , by joining the Russian SFSR into a single state with the Byelorussian , Transcaucasian , and Ukrainian republics. Eventually internal border changes and annexations during World War II created a union of 15 republics ; the largest in size and population being the Russian SFSR, which dominated the union politically, culturally, and economically. Following Lenin's death in 1924,

6000-666: The 10th to 11th centuries, Kievan Rus' became one of the largest and most prosperous states in Europe. The reigns of Vladimir the Great (980–1015) and his son Yaroslav the Wise (1019–1054) constitute the Golden Age of Kiev, which saw the acceptance of Orthodox Christianity from Byzantium , and the creation of the first East Slavic written legal code , the Russkaya Pravda . The age of feudalism and decentralisation had come, marked by constant in-fighting between members of

6120-625: The 16th century, Russia expanded east of the Ural Mountains . However, the Tsardom was weakened by the long and unsuccessful Livonian War against the coalition of the Kingdom of Poland and the Grand Duchy of Lithuania (later the united Polish–Lithuanian Commonwealth ), the Kingdom of Sweden , and Denmark–Norway for access to the Baltic coast and sea trade. In 1572, an invading army of Crimean Tatars were thoroughly defeated in

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6240-488: The 20th century saw some of the most significant Russian technological achievements , including the first human-made satellite and the first human expedition into outer space . In 1991, the Russian SFSR emerged from the dissolution of the Soviet Union as the Russian Federation. A new constitution was adopted, which established a federal semi-presidential system . Since the turn of the century, Russia's political system has been dominated by Vladimir Putin , under whom

6360-400: The 9th century, and in 988, it adopted Orthodox Christianity from the Byzantine Empire . Kievan Rus' ultimately disintegrated; the Grand Duchy of Moscow led the unification of Russian lands, leading to the proclamation of the Tsardom of Russia in 1547. By the early 18th century, Russia had vastly expanded through conquest, annexation, and the efforts of Russian explorers , developing into

6480-428: The Byzantine double-headed eagle his own, and eventually Russia's, coat-of-arms. Vasili III united all of Russia by annexing the last few independent Russian states in the early 16th century. In development of the Third Rome ideas, the grand duke Ivan IV ("the Terrible") was officially crowned the first tsar of Russia in 1547. The tsar promulgated a new code of laws ( Sudebnik of 1550 ), established

6600-406: The Earth, aboard the Vostok 1 crewed spacecraft on 12 April 1961 . Following the ousting of Khrushchev in 1964, another period of collective rule ensued, until Leonid Brezhnev became the leader. The era of the 1970s and the early 1980s was later designated as the Era of Stagnation . The 1965 Kosygin reform aimed for partial decentralisation of the Soviet economy . In 1979, after

6720-415: The Polish–Lithuanian Commonwealth and annexed most of its territories into Russia , making it the most populous country in Europe. In the south, after the successful Russo-Turkish Wars against the Ottoman Empire , Catherine advanced Russia's boundary to the Black Sea, by dissolving the Crimean Khanate , and annexing Crimea . As a result of victories over Qajar Iran through the Russo-Persian Wars , by

6840-692: The Provisional Government and gave full governing power to the soviets, leading to the creation of the world's first socialist state . The Russian Civil War broke out between the anti-communist White movement and the Bolsheviks with its Red Army . In the aftermath of signing the Treaty of Brest-Litovsk that concluded hostilities with the Central Powers of World War I ; Bolshevist Russia surrendered most of its western territories, which hosted 34% of its population, 54% of its industries, 32% of its agricultural land, and roughly 90% of its coal mines. The Allied powers launched an unsuccessful military intervention in support of anti-communist forces. In

6960-406: The Red Army invaded Manchuria and ousted the Japanese from Northeast Asia, contributing to the Allied victory over Japan. The 1941–1945 period of World War II is known in Russia as the Great Patriotic War . The Soviet Union, along with the United States, the United Kingdom and China were considered the Big Four of Allied powers in World War II, and later became the Four Policemen , which

7080-403: The Russian autocratic state. The destruction of Kievan Rus' saw the eventual rise of the Grand Duchy of Moscow , initially a part of Vladimir-Suzdal . While still under the domain of the Mongol - Tatars and with their connivance, Moscow began to assert its influence in the region in the early 14th century, gradually becoming the leading force in the "gathering of the Russian lands". When

7200-476: The Russian parliament culminated in a constitutional crisis which ended violently through military force. During the crisis, Yeltsin was backed by Western governments, and over 100 people were killed. In December, a referendum was held and approved, which introduced a new constitution, giving the president enormous powers. The 1990s were plagued by armed conflicts in the North Caucasus , both local ethnic skirmishes and separatist Islamist insurrections. From

7320-408: The Soviet Union led Russia into a deep and prolonged depression. During and after the disintegration of the Soviet Union, wide-ranging reforms including privatisation and market and trade liberalisation were undertaken, including radical changes along the lines of " shock therapy ". The privatisation largely shifted control of enterprises from state agencies to individuals with inside connections in

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7440-523: The Soviet Union. The transitional disorganisation of the country's agriculture, combined with the harsh state policies and a drought, led to the Soviet famine of 1932–1933 ; which killed 5.7 to 8.7 million, 3.3 million of them in the Russian SFSR. The Soviet Union, ultimately, made the costly transformation from a largely agrarian economy to a major industrial powerhouse within a short span of time. The Soviet Union entered World War II on 17 September 1939 with its invasion of Poland , in accordance with

7560-406: The Soviet system, introduced the policies of glasnost (openness) and perestroika (restructuring) in an attempt to end the period of economic stagnation and to democratise the government . This, however, led to the rise of strong nationalist and separatist movements across the country. Prior to 1991, the Soviet economy was the world's second-largest, but during its final years, it went into

7680-493: The Ukrainian leader, Bohdan Khmelnytsky , offered to place Ukraine under the protection of the Russian tsar, Alexis ; whose acceptance of this offer led to another Russo-Polish War . Ultimately, Ukraine was split along the Dnieper , leaving the eastern part, ( Left-bank Ukraine and Kiev ) under Russian rule. In the east, the rapid Russian exploration and colonisation of vast Siberia continued, hunting for valuable furs and ivory. Russian explorers pushed eastward primarily along

7800-516: The Volga-Dnieper region of southern Russia and Ukraine as the urheimat of the Proto-Indo-Europeans . Early Indo-European migrations from the Pontic–Caspian steppe of Ukraine and Russia spread Yamnaya ancestry and Indo-European languages across large parts of Eurasia. Nomadic pastoralism developed in the Pontic–Caspian steppe beginning in the Chalcolithic . Remnants of these steppe civilizations were discovered in places such as Ipatovo , Sintashta , Arkaim , and Pazyryk , which bear

7920-446: The algorithm obviously realizes every pair of competitors if one of them equals 1 {\displaystyle 1} (the non-moving competitor). Next, for pairs of non- 1 {\displaystyle 1} competitors, let their distance be the number k < n 2 {\displaystyle k<{\frac {n}{2}}} of times the rotation has to be carried out in order that one competitor arrives at

8040-485: The amount of rest between games. On the other hand, when the number of competitors is odd, it does not perform so well and a different schedule is superior with respect to these measures. Alternatively Berger tables, named after the Austrian chess master Johann Berger , are widely used in the planning of tournaments. Berger published the pairing tables in his two Schach-Jahrbücher (Chess Annals), with due reference to its inventor Richard Schurig. This constitutes

8160-423: The capital Moscow. In 1612, the Poles were forced to retreat by the Russian volunteer corps, led by merchant Kuzma Minin and prince Dmitry Pozharsky . The Romanov dynasty acceded to the throne in 1613 by the decision of the Zemsky Sobor, and the country started its gradual recovery from the crisis. Russia continued its territorial growth through the 17th century, which was the age of the Cossacks . In 1654,

8280-435: The championship. A notable instance of such an event was the 1950 FIFA World Cup match between Uruguay and Brazil . Further issues arise where a round-robin is used as a qualifying round within a larger tournament. A competitor already qualified for the next stage before its last game may either not try hard (in order to conserve resources for the next phase) or even deliberately lose (if the scheduled next-phase opponent for

8400-581: The continental tournaments (e.g. UEFA European Championship , CONCACAF Gold Cup , AFC Asian Cup , CONMEBOL Copa América and CAF Cup of Nations ). There are also round-robin cricket , bridge , chess , draughts , go , ice hockey , curling , and Scrabble tournaments. The World Chess Championship decided in 2005 and in 2007 on an eight-player double round-robin tournament where each player faces every other player once as white and once as black. There has been several major international cricket tournaments held in this format including ICC events, including

8520-414: The control of the Golden Horde and consolidated the whole of northern Rus' under Moscow's dominion, and was the first Russian ruler to take the title "Grand Duke of all Rus'". After the fall of Constantinople in 1453, Moscow claimed succession to the legacy of the Eastern Roman Empire . Ivan III married Sophia Palaiologina , the niece of the last Byzantine emperor Constantine XI , and made

8640-476: The country has experienced democratic backsliding and become an authoritarian dictatorship . Russia has been militarily involved in a number of conflicts in former Soviet states and other countries , including its war with Georgia in 2008 and its war with Ukraine since 2014, which has involved the internationally unrecognised annexations of Ukrainian territory including Crimea in 2014 and four other regions in 2022 during an ongoing invasion . Russia

8760-839: The country was more often referred to by its inhabitants as Rus ' , the Russian land ( Russkaia zemlia ), or the Muscovite state ( Moskovskoe gosudarstvo ), among other variations. In 1721, Peter the Great changed the name of the state from Tsardom of Russia ( Russian : Русское царство , romanized :  Russkoye tsarstvo ) or Tsardom of Muscovy ( Russian : Московское царство , romanized :  Moskovskoye tsarstvo ) to Russian Empire ( Rossiiskaia imperiia ). There are several words in Russian which translate to "Russians" in English. The noun and adjective русский , russkiy refers to ethnic Russians . The adjective российский , rossiiskiy denotes Russian citizens regardless of ethnicity. The same applies to

8880-450: The crucial Battle of Molodi . The death of Ivan's sons marked the end of the ancient Rurik dynasty in 1598, and in combination with the disastrous famine of 1601–1603 , led to a civil war, the rule of pretenders, and foreign intervention during the Time of Troubles in the early 17th century. The Polish–Lithuanian Commonwealth , taking advantage, occupied parts of Russia, extending into

9000-575: The earliest known traces of horses in warfare . The genetic makeup of speakers of the Uralic language family in northern Europe was shaped by migration from Siberia that began at least 3,500 years ago. In the 3rd to 4th centuries CE, the Gothic kingdom of Oium existed in southern Russia, which was later overrun by Huns . Between the 3rd and 6th centuries CE, the Bosporan Kingdom , which

9120-481: The first Europeans to reach and colonise Alaska . In 1803–1806, the first Russian circumnavigation was made. In 1820, a Russian expedition discovered the continent of Antarctica . During the Napoleonic Wars , Russia joined alliances with various European powers, and fought against France. The French invasion of Russia at the height of Napoleon's power in 1812 reached Moscow, but eventually failed as

9240-564: The first Russian feudal representative body (the Zemsky Sobor ), revamped the military, curbed the influence of the clergy, and reorganised local government. During his long reign, Ivan nearly doubled the already large Russian territory by annexing the three Tatar khanates: Kazan and Astrakhan along the Volga , and the Khanate of Sibir in southwestern Siberia. Ultimately, by the end of

9360-586: The first half of the 19th century, Russia also conquered the Caucasus . Catherine's successor, her son Paul , was unstable and focused predominantly on domestic issues . Following his short reign, Catherine's strategy was continued with Alexander I's (1801–1825) wresting of Finland from the weakened Sweden in 1809, and of Bessarabia from the Ottomans in 1812. In North America, the Russians became

9480-485: The government, which led to the rise of Russian oligarchs . Many of the newly rich moved billions in cash and assets outside of the country in an enormous capital flight . The depression of the economy led to the collapse of social services—the birth rate plummeted while the death rate skyrocketed, and millions plunged into poverty; while extreme corruption, as well as criminal gangs and organised crime rose significantly. In late 1993, tensions between Yeltsin and

9600-587: The largest and principal constituent. At the expense of millions of lives , the Soviet Union underwent rapid industrialisation in the 1930s and later played a decisive role for the Allies in World War II by leading large-scale efforts on the Eastern Front . With the onset of the Cold War , it competed with the United States for ideological dominance and international influence . The Soviet era of

9720-535: The latter deliberately starved to death or otherwise killed 3.3 million Soviet POWs , and a vast number of civilians, as the " Hunger Plan " sought to fulfil Generalplan Ost . Although the Wehrmacht had considerable early success, their attack was halted in the Battle of Moscow . Subsequently, the Germans were dealt major defeats first at the Battle of Stalingrad in the winter of 1942–1943, and then in

9840-686: The meantime, both the Bolsheviks and White movement carried out campaigns of deportations and executions against each other, known respectively as the Red Terror and White Terror . By the end of the violent civil war, Russia's economy and infrastructure were heavily damaged, and as many as 10 million perished during the war, mostly civilians. Millions became White émigrés , and the Russian famine of 1921–1922 claimed up to five million victims. On 30 December 1922, Lenin and his aides formed

9960-403: The method as simple and ingenious , attributes the solution to Felix Walecki, a teacher at Lycée Condorcet . Lucas also included an alternative solution by means of a sliding puzzle . To easily remember this method, the following mnemonic can be used. Starting from the first round, the next round is constructed: and then, If the number of players is odd, the player in the first venue gets

10080-609: The more recently coined noun россиянин , rossiianyn , "Russian" in the sense of citizen of the Russian state. According to the Primary Chronicle , the word Rus' is derived from the Rus' people , who were a Swedish tribe, and where the three original members of the Rurikid dynasty came from. The Finnish word for Swedes, ruotsi , has the same origin. Later archeological studies mostly confirmed this theory. The first human settlement on Russia dates back to

10200-641: The north-east. Led by Prince Alexander Nevsky , Novgorodians repelled the invading Swedes in the Battle of the Neva in 1240, as well as the Germanic crusaders in the Battle on the Ice in 1242. Kievan Rus' finally fell to the Mongol invasion of 1237–1240, which resulted in the sacking of Kiev and other cities, as well as the death of a major part of the population. The invaders, later known as Tatars , formed

10320-620: The obstinate resistance in combination with the bitterly cold Russian winter led to a disastrous defeat of invaders, in which the pan-European Grande Armée faced utter destruction. Led by Mikhail Kutuzov and Michael Andreas Barclay de Tolly , the Imperial Russian Army ousted Napoleon and drove throughout Europe in the War of the Sixth Coalition , ultimately entering Paris. Alexander I controlled Russia's delegation at

10440-654: The official line. The continued internal struggle in the Bolshevik party culminated in the Great Purge . Under Stalin's leadership, the government launched a command economy , industrialisation of the largely rural country , and collectivisation of its agriculture . During this period of rapid economic and social change, millions of people were sent to penal labour camps , including many political convicts for their suspected or real opposition to Stalin's rule; and millions were deported and exiled to remote areas of

10560-496: The position the other had. In the example given ( n = 14 {\displaystyle n=14} ), 2 {\displaystyle 2} has distance 1 {\displaystyle 1} to 3 {\displaystyle 3} and to 14 {\displaystyle 14} and it has distance 6 {\displaystyle 6} to 8 {\displaystyle 8} and to 9 {\displaystyle 9} . In

10680-407: The press ; the country also has high levels of perceived corruption . As of 2024, Russia has a high-income economy which ranks eleventh in the world by nominal GDP and fourth at purchasing power parity , relying on its vast mineral and energy resources ; the world's second-largest for oil production and natural gas production . Russia is home to 32 UNESCO World Heritage Sites . According to

10800-400: The previous row, with the exception of player n {\displaystyle n} . When the result of the addition is greater than ( n − 1 ) {\displaystyle (n-1)} , then subtract ( n − 1 ) {\displaystyle (n-1)} from the sum. This schedule can also be represented as a (n-1, n-1) table, expressing

10920-536: The rest of the game plus 30 seconds per move starting from move one. The 43rd Dortmund Sparkassen Chess Meeting took place between June 27 to July 5 in the "Orchesterzentrum NRW" in Dortmund, Germany. The eight-player round-robin tournament consisted of 7 games of Classical Chess. The field was led by Vladimir Kramnik, Fabiano Caruana, and Wesley So. Players received 100 minutes for 40 moves, then an additional 50 minutes for 20 additional moves, and finally 15 minutes for

11040-602: The rest of the game plus 30 seconds per move starting from move one. The tournament was also the final Dortmund appearance for Arkadij Naiditsch before his transfer to the Azerbaijan Chess Federation. [REDACTED] GM Ian Nepomniachtchi qualified as the winner of Aeroflot Open 2015. The 44th Dortmund Sparkassen Chess Meeting took place between July 9 to 17 in the "Orchesterzentrum NRW" in Dortmund, Germany. The eight-player round-robin tournament consisted of 7 games of Classical Chess. The field

11160-589: The rivalry between the two major European empires came to be known as the Great Game . The late 19th century saw the rise of various socialist movements in Russia. Alexander II was assassinated in 1881 by revolutionary terrorists. The reign of his son Alexander III (1881–1894) was less liberal but more peaceful. Under last Russian emperor, Nicholas II (1894–1917), the Revolution of 1905

11280-406: The round-robin and elimination formats, to provide a worthy champion using fewer rounds than a round-robin, while allowing draws and losses. The main disadvantage of a round robin tournament is the time needed to complete it. Unlike a knockout tournament where half of the participants are eliminated after each round, a round robin requires one round less than the number of participants. For instance,

11400-525: The round-robin major league champions are generally regarded as the "best" team in the land, rather than the cup winners, whose tournaments usually follow a single-elimination format. Moreover, in tournaments such as the FIFA or ICC World Cups, a first round stage consisting of a number of mini round robins between groups of 4 teams guards against the possibility of a team travelling possibly thousands of miles only to be eliminated after just one poor performance in

11520-408: The same position. Clearly, these pairs are pairwise different. The conclusion is that every distance- k {\displaystyle k} pair is realized. This holds for every k {\displaystyle k} , hence, every pair is realized. If there are an odd number of competitors, a dummy competitor can be added, whose scheduled opponent in a given round does not play and has

11640-497: The score 7:3. The Dortmund Sparkassen Man-Machine Match between [REDACTED] GM Robert Hübner ( 2612 ) and Deep Fritz ended in a draw with the score 3:3 (all the games were drawn). The main event was a Candidates Tournament to determine a challenger for Vladimir Kramnik 's Einstein Group World Chess title. [REDACTED] IM Tigran Nalbandian ( 2458 ) won Dortmund Open Swiss-system tournament with

11760-565: The score 7½/9 and performance rating 2533. The 2024 edition features a 6-games standard rules match between the top 2 German women, GM Elisabeth Pähtz versus IM Dinara Wagner , alongside open tournaments. The Open A tournament is included in the 2024 FIDE Circuit . Round-robin tournament A round-robin tournament or all-play-all tournament is a competition format in which each contestant meets every other participant, usually in turn. A round-robin contrasts with an elimination tournament , wherein participants are eliminated after

11880-495: The score 8/9 and performance rating 2616. [REDACTED] GM Vladimir Belikov ( 2499 ) defeated [REDACTED] IM David Baramidze ( 2470 ) in Dortmund Match with the score 6:4. [REDACTED] GM Sergei Rublevsky qualified as the winner of Aeroflot Open 2004. [REDACTED] GM Emil Sutovsky qualified as the winner of Aeroflot Open 2005. [REDACTED] GM Baadur Jobava qualified as

12000-516: The score 9/11. The match between [REDACTED] GM Arkadij Naiditsch ( 2581 ) and [REDACTED] GM Jan Timman ( 2623 ) ended in a draw with the score 4:4. [REDACTED] David Baramidze ( 2351 ) defeated [REDACTED] IM Alisa Marić ( 2470 ) in Dortmund Sparkassen Match with the score 4½:3½. [REDACTED] GM Victor Bologan qualified as the winner of Aeroflot Open 2003. [REDACTED] IM Yuri Boidman ( 2407 ) won Dortmund Open A Swiss-system tournament with

12120-876: The seat of the Metropolitan of the Russian Orthodox Church moved to Moscow in 1325, its influence increased. Moscow's last rival, the Novgorod Republic , prospered as the chief fur trade centre and the easternmost port of the Hanseatic League . Led by Prince Dmitry Donskoy of Moscow, the united army of Russian principalities inflicted a milestone defeat on the Mongol-Tatars in the Battle of Kulikovo in 1380. Moscow gradually absorbed its parent duchy and surrounding principalities, including formerly strong rivals such as Tver and Novgorod . Ivan III ("the Great") threw off

12240-656: The state of the Golden Horde , which ruled over Russia for the next two centuries. Only the Novgorod Republic escaped foreign occupation after it agreed to pay tribute to the Mongols. Galicia-Volhynia would later be absorbed by Lithuania and Poland , while the Novgorod Republic continued to prosper in the north. In the northeast, the Byzantine-Slavic traditions of Kievan Rus' were adapted to form

12360-608: The teams. This famously happened during the 1994 FIFA World Cup Group E , where all four teams finished with a record of one win, one draw, and one loss. This phenomenon is analogous to the Condorcet paradox in voting theory. If n {\displaystyle n} is the number of competitors, a pure round robin tournament requires n 2 ( n − 1 ) {\displaystyle {\begin{matrix}{\frac {n}{2}}\end{matrix}}(n-1)} games. If n {\displaystyle n}

12480-523: The time Chechen separatists declared independence in the early 1990s, an intermittent guerrilla war was fought between the rebel groups and Russian forces. Terrorist attacks against civilians were carried out by Chechen separatists, claiming the lives of thousands of Russian civilians. After the dissolution of the Soviet Union, Russia assumed responsibility for settling the latter's external debts. In 1992, most consumer price controls were eliminated, causing extreme inflation and significantly devaluing

12600-515: The top left corner by repeating the sequence of numbers from 1 up to n − 1 {\displaystyle n-1} . Here is an example table for 7 or 8 competitors: Russia Russia , or the Russian Federation , is a country spanning Eastern Europe and North Asia . It is the largest country in the world by area , extending across eleven time zones and sharing land borders with fourteen countries . It

12720-435: The tournament; changes were made prior to the next Olympics to prevent a repeat of these events. Another disadvantage, especially in smaller round-robins, is the "circle of death", where teams cannot be separated on a head-to-head record. In a three-team round-robin, where A defeats B, B defeats C, and C defeats A, all three competitors will have a record of one win and one loss, and a tiebreaker will need to be used to separate

12840-451: The victor is gradually arrived at through multiple rounds of play, teams who perform poorly, who might have been quickly eliminated from title contention, are forced to play out their remaining games. Thus games are played late in the competition between competitors with no remaining chance of success. Moreover, some later matches will pair one competitor who has something left to play for against another who does not. It may also be possible for

12960-457: The winner of Aeroflot Open 2006. [REDACTED] GM Evgeny Alekseev qualified as the winner of Aeroflot Open 2007. [REDACTED] GM Ian Nepomniachtchi qualified as the winner of Aeroflot Open 2008. [REDACTED] GM Étienne Bacrot qualified as the winner of Aeroflot Open 2009. [REDACTED] GM Lê Quang Liêm qualified as the winner of Aeroflot Open 2010. [REDACTED] GM Lê Quang Liêm qualified as

13080-550: The winner of Aeroflot Open 2011. [REDACTED] GM Mateusz Bartel qualified as the winner of Aeroflot Open 2012. The 42nd Dortmund Sparkassen Chess Meeting took place between July 12 and July 20, 2014, in the "Orchesterzentrum NRW" in Dortmund, Germany. The eight-player round-robin tournament consisted of 7 games of Classical Chess. The field was led by Vladimir Kramnik, Fabiano Caruana, and Michael Adams. Players received 100 minutes for 40 moves, then an additional 50 minutes for 20 additional moves, and finally 15 minutes for

13200-515: Was Ruthenia . In Russian, the current name of the country, Россия ( Rossiya ), comes from the Byzantine Greek name for Rus', Ρωσία ( Rosía ). A new form of the name Rus ' , Росия ( Rosiya ), was borrowed from the Greek term and first attested in 1387. The name Rossiia appeared in Russian sources in the late 15th century, but until the end of the 17th century

13320-449: Was elected President of the Russian SFSR. In August 1991, a coup d'état attempt by members of Gorbachev's government, directed against Gorbachev and aimed at preserving the Soviet Union, instead led to the end of the Communist Party of the Soviet Union. On 25 December 1991, following the dissolution of the Soviet Union , along with contemporary Russia, fourteen other post-Soviet states emerged. The economic and political collapse of

13440-631: Was a Hellenistic polity that succeeded the Greek colonies, was also overwhelmed by nomadic invasions led by warlike tribes such as the Huns and Eurasian Avars . The Khazars , who were of Turkic origin , ruled the steppes between the Caucasus in the south, to the east past the Volga river basin, and west as far as Kyiv on the Dnieper river until the 10th century. After them came the Pechenegs who created

13560-670: Was dissolved by the All-Russian Central Executive Committee . An alternative socialist establishment co-existed, the Petrograd Soviet , wielding power through the democratically elected councils of workers and peasants, called soviets . The rule of the new authorities only aggravated the crisis in the country instead of resolving it, and eventually, the October Revolution , led by Bolshevik leader Vladimir Lenin , overthrew

13680-515: Was found at Kostyonki–Borshchyovo , and at Sungir , dating back to 34,600 years ago—both in western Russia . Humans reached Arctic Russia at least 40,000 years ago, in Mamontovaya Kurya . Ancient North Eurasian populations from Siberia genetically similar to Mal'ta–Buret' culture and Afontova Gora were an important genetic contributor to Ancient Native Americans and Eastern Hunter-Gatherers . The Kurgan hypothesis places

13800-581: Was half Neanderthal and half Denisovan, and lived some 90,000 years ago, was also found within the latter cave. Russia was home to some of the last surviving Neanderthals, from about 45,000 years ago, found in Mezmaiskaya cave . The first trace of an early modern human in Russia dates back to 45,000 years, in Western Siberia . The discovery of high concentration cultural remains of anatomically modern humans , from at least 40,000 years ago,

13920-441: Was his first Dortmund tournament victory. [REDACTED] GM Vladimir Fedoseev qualified as the winner of Aeroflot Open 2017. [REDACTED] GM Vladislav Kovalev qualified as the winner of Aeroflot Open 2018. [REDACTED] GM Kaido Külaots qualified as the winner of Aeroflot Open 2019. [REDACTED] FM Thomas Michalczak ( 2239 ) won Sparkassen Chess Meeting Open A swiss-system tournament with

14040-419: Was led by Vladimir Kramnik, Fabiano Caruana, and Maxime Vachier-Lagrave. Players received 100 minutes for 40 moves, then 50 minutes for 20 additional moves, then 15 minutes for the rest of the game plus 30 seconds per move starting from move one. [REDACTED] GM Evgeniy Najer qualified as the winner of Aeroflot Open 2016. Maxime Vachier-Lagrave won the tournament on July 16 with 1 game to spare. This

14160-584: Was populated by Finno-Ugrian peoples. From the 7th century onwards, the incoming East Slavs slowly assimilated the native Finno-Ugrians. The establishment of the first East Slavic states in the 9th century coincided with the arrival of Varangians , the Vikings who ventured along the waterways extending from the eastern Baltic to the Black and Caspian Seas. According to the Primary Chronicle ,

14280-539: Was the foundation of the United Nations Security Council . During the war, Soviet civilian and military death were about 26–27 million , accounting for about half of all World War II casualties . The Soviet economy and infrastructure suffered massive devastation, which caused the Soviet famine of 1946–1947 . However, at the expense of a large sacrifice, the Soviet Union emerged as

14400-695: Was triggered by the humiliating failure of the Russo-Japanese War . The uprising was put down, but the government was forced to concede major reforms ( Russian Constitution of 1906 ), including granting freedoms of speech and assembly , the legalisation of political parties, and the creation of an elected legislative body, the State Duma . In 1914, Russia entered World War I in response to Austria-Hungary 's declaration of war on Russia's ally Serbia , and fought across multiple fronts while isolated from its Triple Entente allies. In 1916,

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