The only winning move is not to play that game.
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"Selling print sooner than later was the winning move," Larkin explains.
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Folding up the political ad tent may be the winning move.
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This is the winning move, Mr. President: Surprise the hell out of 'em!
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Freddy: As with all nuclear policy, the only winning move is not to play.
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In some cases, the prearranged signal could simply be: There is a winning move here.
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Hinch scoffed at the suggestion, a winning move for a team now one victory away from a championship.
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The restaurant has indoor seating, but the winning move is to grab a table on the elegant patio.
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But the winning move is to catnap—tapping on the arrow keys gently, only to adroitly spring up when the stop is yours.
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Whether you're looking for a job, or trying to build up your client base, showing your past successes can be a winning move.
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Like Joshua, the artificial intelligence in the 1983 sci-fi classic WarGames, Murphy's system appears to realize that sometimes the only winning move is not to play.
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But Stankey alluded to "the frustration" among consumers with this "fragmentation" and said ultimately a winning move will be to create a new version of a TV bundle.
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Where 12 Monkeys went with this in season two was, ultimately, to suggest that when you're unable to escape time itself, then the only winning move is not to play the game.
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Only a cloistered group of academics and self-important pundits would miss the fact that rhetorically defusing one of the world's most feared dictators by calling him "Rocket Man" is a winning move.
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Colin also thinks it'd be a winning move for Wilson on the field too -- saying the 30-year-old could become a much bigger star than he ever was in the Pacific Northwest.
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But nor is he moved enough by those possibilities to give up what he hopes could be, in a new era of digital fabrication, the winning move in the battle over access to guns.
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"Doing the math, it seems like the winning move is to sit back, let the brave souls sort out the wheat from the chaff, and pay the eBay tax when a winner comes along," Ranker2 wrote.
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All kinds of data—YouTube videos of epic fails, an e-mail to your boss, or that winning move in Overwatch—travel over the internet, but some kinds of data are more tolerant of delays or temporary congestion.
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She enjoyed a good moment early on Tuesday when she turned a general discussion of health care to the topic of women's reproductive rights — a winning move with the crowd in the hall, and presumably with a lot of Democratic voters.
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Related: North Korea's Counterfeit Benjamins Have Vanished Targeted killing became the centerpiece of the contingency plan because the true winning move on the Korean Peninsula is to never have to meet Pyongyang and its enormous numbers of military personnel on a battlefield.
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But after another officer, Edward M. Nero, was acquitted in a bench trial last month, the public began to suspect that the officers' strategy — claiming that their failure to use a seatbelt for Mr. Gray was common practice in the department — was a winning move.
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The only winning move; all other moves lose. For instance, if 1.Kd6 then 1...Kf5 puts White in zugzwang and Black wins.
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Deutch is married and has three children.Anthony Man,"Going Vegan Was Winning Move for South Florida Congressman," Sun Sentinel, 12 September 2014. He is a vegan.
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Merckx made the winning move when he attacked on the descent of the Intelvi Pass. During the off-season, Merckx had his displaced pelvis tended to by a doctor.
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Shimanoumi has shown a preference for tsuki and oshi techniques which involve pushing and thrusting rather than grasping his opponent's mawashi or belt. His most common kimarite or winning move is oshidashi, the push-out.
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Instead of playing the winning move though, she played a move that lost her her queen. As a result, she lost that game. She didn't recover from that, and lost the next 2 games as well.
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Meisei has shown a preference for yotsu techniques which involve grasping his opponent's mawashi or belt and favors the hidari-yotsu, or left-hand inside grip. His most common kimarite or winning move is yorikiri, the force-out.
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For example, it's always right to make a winning move in a board game. ## The Advisors which identify a sub-problem go into Tier 2. For example, going around a wall in a maze. ## Every other Advisor is Tier 3.
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The race started with 55 riders. Giovanni Gerbi made his winning move at a railroad crossing. He jumped up the crossing and back onto the course and rode ahead, while a few riders behind crashed. Gerbi stretched his advantage to forty minutes.
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Kakizoe was an oshi-sumo specialist, preferring pushing and thrusting techniques. His most common winning move was oshi-dashi (push-out), which accounted for around 43 percent of his career victories. He was vulnerable to defeat if his opponents grab hold of his mawashi.
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Kxb6, with a drawn game by insufficient mating material. Promotion to bishop is the only winning move, threatening mate with Bb7 that the enemy bishop, being confined to dark squares, is helpless to prevent 1. c8=B! B\any 2. Nd7 B\any 3.
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Now we replace each crossing with this construction: The intersection is eliminated by adding 6 vertices and redrawing the edges as shown. The result is a planar graph, and the same player can force a win as in the original graph: if a player chooses to move "up" from V in the transformed game, then both players must continuing moving "up" to W or lose immediately. So moving "up" from V in the transformed game simulates the move V→W in the original game. If V→W is a winning move, then moving "up" from V in the transformed game is also a winning move, and vice versa.
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Daijuyama's favoured kimarite or techniques were migi-yotsu (a left arm outside, right hand inside grip on his opponent's mawashi), uwatenage (overarm throw) and utchari (ring edge throw). His most common winning move by far was yori-kiri (force out), which accounted for nearly half his victories.
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He was an oshi-sumo specialist, preferring pushing and thrusting techniques. He was however also capable of fighting on the mawashi or belt, where he preferred a migi-yotsu (left hand outside, right hand inside) grip. His most common winning move was oshi-dashi (push out), followed by yori-kiri (force out).
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Having discovered the concept of mutual assured destruction ("WINNER: NONE"), the computer tells Falken that it has concluded that nuclear war is "a strange game" in which "the only winning move is not to play." WOPR relinquishes control of NORAD and the missiles and offers to play "a nice game of chess".
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The balance is achieved because the first player will intentionally make a move that is sufficiently "bad" that it is not clear to the second player whether it is a winning move or a losing move. It is up to the judgement of the second player to make this difficult determination and invoke the pie rule accordingly.
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Yuta faced Li in the final, winning by resignation in 208 moves. An Younggil, 8p from South Korea, commented on the game, saying "[Yuta] played this game wonderfully. White 112 was the winning move. [Yuta]’s endgame was perfect, and [Li] didn’t get any chances afterwards. This game should be one of [Yuta]’s best games, I’m sure".
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Kasuganishiki's favourite techniques are listed on his profile at the Sumo Association as pushing and thrusting, or tsuki/oshi, but his most common winning move in his career was actually yori-kiri, or force out, using the opponent's mawashi or belt. He also regularly used oshi-dashi, the push out, and hataki-komi, the slap down.
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Asōfuji had a weight disadvantage against most of his competitors in the sekitori ranks, and had to rely on his technical skill. Among his favourite techniques were nage, or throws. His most common winning move over the six tournaments from July 2007 to May 2008 was uwatedashinage, or "pulling outer-arm throw", but he was also adept at shitatenage, or inner-arm throws.
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The name Checkmate is taken from the winning move in chess, and its hierarchy is modeled after the various pieces of a chess game; one King, one Queen and several Bishops, Rooks, Knights and Pawns. The Bishops oversaw the Rooks behind the scenes while the Rooks planned missions and supervised the field agents, or Knights, and the Knights' support, the Pawns.
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After the game started with a French Defence, Levitsky made some suboptimal moves, and then a big mistake allowing Marshall to win a . Levitsky tried to counterattack, but Marshall's unexpected winning move put his queen—his most valuable piece—on a square where it could be captured by three of Levitsky's pieces. Legend says that this move immediately triggered a shower of gold.
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Except for the case of "pathological" game trees (which seem to be quite rare in practice), increasing the search depth (i.e., the number of plies searched) generally improves the chance of picking the best move. Two-person games can also be represented as and-or trees. For the first player to win a game, there must exist a winning move for all moves of the second player.
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Eventually Marcus Burghardt, Francisco Ventoso, and Óscar Freire joined the leaders with roughly 25 km to go. The six managed to hold off the remaining peloton and, with less than 1 km to go, Burghardt caught Freire by surprise and made the winning move. Burghardt's teammate, Hammond, managed to catch hold of Freire's wheel and overtook the Spaniard in the sprint for a one-two finish.
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When an ender exists, the next player can win by following a strategy-stealing argument. If one of the non-ender moves can win, the next player takes that winning move. And if none of the non-ender moves wins, then the next player can win by playing the ender and forcing the other player to make one of the other non-winning moves.
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Asanoyama has shown a preference for yotsu techniques which involve grasping his opponent's mawashi or belt. His most common kimarite or winning move is yorikiri, the force-out. His preferred grip is migi-yotsu, a right arm inside and left hand outside position, although in the run-up to the March 2020 tournament he worked on obtaining a left hand inside grip as well.
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Like many wrestlers, Kasugaō was fond of yotsu-sumo or grappling techniques, his most common winning move being yori-kiri or force out. His favourite grip on the mawashi was migi-yotsu, with his left hand outside and right hand inside his opponent's arms. However, he was also adept at throws, his next two most often used techniques being kote-nage, the armlock throw, and uwate-nage, the outer-arm throw.
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He was also skilled at tsuki or thrusting techniques, and his second most common winning move after yorikiri was oshidashi, or push out. He sometimes used harite, or slaps to the face, a technique that was criticized by a member of the Yokozuna Deliberation Council. Weighing in at 133 kg in November 2012, Harumafuji became the first yokozuna since Chiyonofuji in 1982 to also be the lightest man in the top division.
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The three quickly distinguished themselves as the winning move. Cunego was the first to try to sprint for the stage win, after a hairpin left-hand turn, but Evans timed his sprint better and won, putting Cunego second on the stage. Cunego rode the Giro's first mountain stage the next day with the race's elite behind a winning breakaway. Cunego climbed Monte Terminillo with Evans, Vinokourov, Ivan Basso, and Stefano Garzelli to sixth place.
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Howson perfectly set up Simon Yates for the winning move with a blistering attack ahead of the final climb, thinning out the field before the acceleration of Yates. With a few kilometers to go Yates made the decisive attack on the last climb, holding off Angel Madrazo, Alexander Vdovin, Javier Moreno, and David Belda to take an impressive solo victory and set the race record for the fastest ascent of the final climb.
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Taihō was noted for his skill and power when he grabbed his opponents' mawashi or belt– techniques known as yotsu-sumo. His preferred grip was hidari-yotsu, a right hand outside, left hand inside position. His most common winning move was yori-kiri, a straightforward force out, which accounted for about 30 percent of his wins. His most frequently used throws were sukuinage (the beltless scoop throw) and uwatenage (the overarm throw).
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Fiorenzo Magni, a rare Italian in Belgian classics, won so many intermediate prizes during his long solo flight that they would have bought him a house (see above). He was one of nine to escape the field at Ingelmunster. The others cracked one by one until Magni was alone by Strijpen – the point where he made his winning move the previous year. He rode the last 75 km alone to win the Ronde for the third successive year.
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Gary William Lane (born 4 November 1964) is a professional chess player and author. He became an International Master in 1987 and won the Commonwealth Chess Championship in 1988. He has written over thirty books on chess, including Find the Winning Move, Improve Your Chess in 7 Days and Prepare to Attack. There have been translations in French, Italian, Portuguese and Spanish. In the 1980s the ITV documentary "To Kill a King" was screened nationwide in Great Britain.
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If Blue then moves their bottom piece to the left, they win. If they are foolish enough to move their center piece instead, then Red wins by moving their top- right piece to the center. Thus with "2-ply lookahead", player Red can see the result of their (bad) move of the bottom piece (the first ply), realize that Blue then has a winning move (the second ply), and hence Red will choose to not make that move.
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She later arrives to hear about Tenri and the girls argue over kissing Keima, but also sees that Tenri beat Keima in a match. Keima offers to help Nanaka train; they engage in some practice games where Keima initially beat her, but eventually they end up about even. Keima arranges for a final match between Nanaka and Tenri. Nanaka is about to lose, but when Tenri makes a mistake on her drop piece, Nanaka counters with a winning move.
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Over the course of the race, many riders sought to break away from the peloton. While some breakaways lasted for some time, all were eventually retrieved. The final attempt, by Roman Kreuziger, ultimately contributed to the winning move: > Andy Schleck led the peloton at a steady pace over the Kruisberg while > Gasparotto did the same over the famous Eyserbosweg. In the descent > Kreuziger sneaked away on his own and he rode up the following climb of the > Fromberg on the big ring.
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Basso won the Gran Premio di Lugano in late February. After Caruso launched an attack that effectively softened the field, Basso's winning move came as his teammate was caught. He drew 's Fabio Duarte with him, and defeated him in the sprint 16 seconds ahead of the front of the remaining field. The team came to the first monument race of the season, Milan–San Remo, without a real field sprinter, despite that race's tendency to end in a sprint.
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The Trucks then made their return to Iowa Speedway. Ross Chastain would dominate most of the race, leading 116 laps. Due to NASCAR allowing the teams only two sets of tires, James Buescher made the call to pit late to take a final set of sticker tires while others had used up their sets. This would prove to be the winning move as Buescher made his way past Chastain and held him off on two green white checkered attempts to take his second win of the season.
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GW was able to benefit from its savviness in the miniatures business, and integrating "Titanicus" in the popular WH40K universe proved a winning move. Space Marine, another miniatures and rules set (for two opposing Space Marine armies), followed after (in 1989). The two could be played as individual games or as a combined game. Where Adeptus Titanicus included six plastic Titan models with swappable weapons and styrofoam buildings, Space Marine included folded card buildings with styrene roofs alongside its sprues of infantry and vehicles.
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Unknown to Fringe division, Jones reports to William Bell aboard the container ship (seen in "Nothing As It Seems") that Olivia and team have created a cure for the nanites. Bell references a chess game that he has been playing for 40 years that a winning move doesn't mean winning the game. He explains that the art of chess is to be willing to sacrifice one's most valuable piece to open up opportunity. He remarks that he needs to sacrifice the bishop to win the game.
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The third big one happened with 7 laps to go caused by Kyle Busch collecting Brad Keselowski, Kevin Harvick and several others. Brendan Gaughan took the worst hit as his car ended up flipping midair once before landing back on its wheels. Blaney led the field back to green with three laps to go on the last lap Ryan Newman was leading when Blaney made the winning move bumping into Newman, causing a photo finish. On the replay it showed Blaney beating Newman by .
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For example, suppose that there are initially 10 coins. The Zeckondorf representation is 10 = 8 + 2, so a winning move by the first player would be to remove the smallest Fibonacci number in this representation, 2, leaving 8 coins. The second player can remove at most 4 coins, but removing 3 or more would allow the first player to win immediately, so suppose that the second player takes 2 coins. This leaves 6 = 5 + 1 coins, and the first player again takes the smallest Fibonacci number in this representation, 1, leaving 5 coins.
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In this 1959 game between Whitaker and Ferriz, White sacrificed a rook for a knight in order to exchange a pair of pawns and reach this position, and announced that it was a draw because (1) the queen cannot mate alone, and (2) the black king and pawn cannot approach to help . However, endgame tablebase analysis shows Black to have a forced win in 19 moves starting with 50... Qc7+ (the only winning move), taking advantage of the fact that the rook is currently unprotected – again illustrating how tablebases are refining traditional endgame theory.
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Later he would put his race winning move down to inexperience. Guesdon also took victories at the Classic Haribo and a stage in the Tour du Limousin. Guesdon had to wait until 2000 for his next major victory, a stage in the Critérium du Dauphiné Libéré, a feat he repeated in 2002. Despite a complete lack of victories between this win and his next win, over three-and-a-half years later in the 2006 Tropicale Amissa Bongo, Guesdon remained loyal to Française des Jeux and Française des Jeux to him.
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In the film WarGames, the supercomputer WOPR simulates all possible games of tic-tac-toe as a metaphor for all possible scenarios of a nuclear war, each of them ending in a nuclear holocaust (mutual assured destruction). The computer then exclaims, "A strange game; the only winning move is not to play." In the Star Trek canon, the Kobayashi Maru simulation is a no-win scenario designed as a character test for command track cadets at Starfleet Academy. It first appears in the film Star Trek II: The Wrath of Khan.
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In the Preakness Stakes, Affirmed set the pace. Alydar made his big move on the far turn, at the same point in the race where Affirmed made his winning move in the Derby. Affirmed held a short lead entering the stretch and held it to defeat Alydar by a neck. Alydar's partisans assumed that the mile distance of the Belmont, two furlongs longer than the Derby and 5/16 of a mile longer than the Preakness Stakes, would favor Alydar with his finishing style and staying pedigree, and he would deny Affirmed the Triple Crown.
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Behind him, though, Pagenaud began to put heavy pressure on Power and in turn 12 was able to get by. This would prove to be the winning move of the race, as no caution period came, forcing Daly to pit on lap 84. One more incident did occur, though, on lap 87, when Sébastien Bourdais braked too late into turn 4, causing him to collide with Takuma Sato and send both of course. Sato was able to continue, while Bourdais' race ended with his car stuck in a gravel trap.
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Go-Stop (), also called Godori (, after the winning move in the game) is a Korean fishing card game played with a hanafuda deck (in Korean, hwatu ()). The game can be called Matgo () when only two players are playing. The game is derived from similar Japanese fishing games such as Hana-awase and Hachihachi, though the Japanese hanafuda game Koi-koi is in turn partially derived from Go-Stop. Modern Korean-produced hwatu decks usually includes bonus cards specifically intended for play with Go-Stop, unlike Japanese hanafuda decks.
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Jockey Garrett Gomez said, "She really showed a great turn of foot and to be able to overcome that slow pace like she did is amazing. You can see her stride gets longer as she gets closer to the wire." On March 14, she faced her biggest test yet in the Grade 1 Santa Margarita Invitational, where she was the even money favorite. The race was nearly a carbon copy of her two previous wins, with Life Is Sweet starting her winning move around the far turn to eventually win by lengths.
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He followed eventual race winner Gilbert when the Belgian made his winning move on the course's penultimate climb, eventually coming in fourth at the finish, 14 seconds down. Denifl was the team's top rider two days later in Montréal. Part of a late breakaway, he occupied third position on the road until the final moments, when Gilbert and his teammate Jurgen Roelandts surpassed him, leaving him fifth on the day. Back in Europe later in September, the team achieved podium finishes at the Grand Prix de la Somme and the Grand Prix d'Isbergues.
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In combinatorial game theory, there is a minimax algorithm for game solutions. A simple version of the minimax algorithm, stated below, deals with games such as tic-tac-toe, where each player can win, lose, or draw. If player A can win in one move, their best move is that winning move. If player B knows that one move will lead to the situation where player A can win in one move, while another move will lead to the situation where player A can, at best, draw, then player B's best move is the one leading to a draw.
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Soap Opera Digest gave King's casting a "Thumbs Up!" and said that the decision was a "winning move". The magazine also applauded Bushman for her "adequate" portrayal of Summer, but said that King "blends the right amount of brooding teen angst and vulnerability to creat a compelling character" that can make viewers angry because of her decisions, but also makes viewers "sympathize with her". The magazine also thought King's skill as an actress made the transition "seamless". Max Ehrich, who portrays Fenmore, said Bushman's ousting was "bitter sweet" but noted that he also enjoyed working with King.
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Nim is typically played as a misère game, in which the player to take the last object loses. Nim can also be played as a normal play game, where the player taking the last object wins. This is called normal play because the last move is a winning move in most games, even though it is not the normal way that Nim is played. In either normal play or a misère game, when the number of heaps with at least two objects is exactly equal to one, the next player who takes next can easily win.
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American George Hincapie tried to spark a winning move on the Leberg. Frustrated, he found nobody to help him, particularly as Van Petegem's Lotto team had two men further up the road. Bruylandts was the next to give it a go, taking Serguei Ivanov with him as Michael Boogerd leapt across to catch the tail end of the move. They were soon caught by the group of favourites, but the attack signaled the coming of the crucial point in the race, with the often decisive climbs of the Tenbosse, the Muur and Bosberg still to come.
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Beim, Paul Morphy: A Modern Perspective, Russell Enterprises, 2006 In the introduction to the Traité and in the notes to the games, however, there are some important considerations that can be defined as modern. The authors, in fact, stress the concept that at the beginning of the game the forces stand in equilibrium. Correct play on both sides maintains this equilibrium, and leads to a drawn game; therefore, a player can win only as a consequence of an error made by the opponent. From this perspective there is no such thing as a winning move, and even the most skilled master can do nothing against these "natural laws" of the game.
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In 1997, at the age of seventeen, he became junior national road race champion; he made his winning move on the climb to in the northern region of Friuli-Venezia Giulia. He was then given a place in the national team at the 1997 UCI Road World Championships in San Sebastián, Spain; he took part in the junior road race, finishing in 104th position. In April 2001, riding for the Site–Frezza amateur team, Scarponi came second to Yaroslav Popovych in the Giro del Belvedere one- day race. In April–May 2001, he won the fifth stage and came second overall in the Giro delle Regioni, again to Popovych.
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On the final climb, the San Fermo della Battaglia, Bennett put in several attacks that managed to shed Vlasov, but Fuglsang would put in the winning move moments later and dropped Bennett in return. Fuglsang soloed to victory and, in doing so, became the first Danish winner of the race. After Fuglsang had won, as German rider Maximilian Schachmann of was kilometers away from finishing, he was side-swiped by an errant non-race car that drove across the road and his path, causing him to fall and become visibly upset and angry at race officials. As a result of the crash, Schachmann fractured his collarbone.
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Experts have not absolutely resolved what the outcome of a game will be where both sides use perfect play. However, analysis of thousands of high-quality games (most of them computer-generated) appears to lead to a reliable conclusion (pending actual proof if true) that, on the standard 8×8 board, perfect play on both sides results in a draw. When generalizing the game to play on an n×n board, the problem of determining if the first player has a winning move in a given position is PSPACE-complete. On 4×4 and 6×6 boards under perfect play, the second player wins.
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Nibali celebrating victory in the 2018 Milan–San Remo In March 2018, Nibali won Milan-San Remo, his third cycling monument, becoming the first Italian winner of La Classicissima since Filippo Pozzato in 2006. Nibali had attacked on the Poggio di San Remo, and managed to hold off the sprinters in the closing kilometers to seal victory. Two weeks later, he finished 24th in his maiden Tour of Flanders, which included an attack on the Kruisberg that sparked the winning move of Niki Terpstra. Nibali withdrew from the 2018 Tour de France after stage 12, having suffered a crash on the ascent of the Alpe d'Huez after spectator interference.
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Rather than running in the Champion Chase at the Festival, connections made the decision to run Fortria in the Cheltenham Gold Cup. In the race, he came up against the other top chaser of the era, Mandarin, who had won two Hennessy Gold Cups and two King George VI Chases. Fortria hit the front in what looked like a winning move, until Mandarin came driving up the inside under Fred Winter to triumph by a length. The two horses were ten lengths clear of their rivals. Fortria then ran in the Punchestown Handicap Chase over two miles, where he was third to Owen’s Sedge, conceding 23 lbs.
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The winner is the player who removes the last coin. As Golomb observes, the "cold" positions of this game (the ones in which the player who is about to move is losing) are exactly the positions of the form 2y where y belongs to the Moser–de Bruijn sequence. A winning strategy for playing this game is to decompose the current number of coins, n, into x+2y where x and y both belong to the Moser–de Bruijn sequence, and then (if x is nonzero) to remove x coins, leaving a cold position to the other player. If x is zero, this strategy is not possible, and there is no winning move..
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At Talladega in the fall, he ended up in the closest finish in truck series history by ending up second to Kyle Busch in 0.002 of a second, who passed underneath Almirola below the yellow line. The 1-2 finish was the same as the previous race in 2009 but the finish was controversial because of the yellow line rules (as NASCAR rules state that a driver must not advance his position by going below the yellow line even if he is forced down there). But officials determined that Busch had the lead before going below the yellow line thus making Busch's winning move legal. In 2011, Almirola drove the No. 88 Nationwide Series car for JR Motorsports.
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The present day race starts and finishes in Zürich, in previous years the finish was on the Oerlikon velodrome in Zürich but that was abandoned a number of years ago. The race is held over a distance of 241 km with over 3000 metres of climbing, consisting of one 72.5 km lap and four 42.1 km circuits, this shorter lap includes four ascents of both the Pfannenstiel and Forch climbs, the final climb of the Pfannenstiel is just 15 km from the finish in Zürich and is often the launching point for the winning move in the race. Between 1993 and 1999 the race started in Basel and finished in Zürich and was known as the Grand Prix Suisse.
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"I loved and believed in Uriah Heep but it kicked the shit out of me in the end," were his parting words. Then John Sinclair quit deciding to join Ozzy Osbourne and keyboardist Phil Lanzon (Grand Prix, Sad Café) came in to fit in immediately into the Box-envisaged scheme of things. American singer Steff Fontaine, formerly of Christian metal band Joshua, joined in July 1986 but he was criticised for being totally "unprofessional" (he missed, for some reason, a San Francisco gig) and was sacked in September 1986 after just one American tour. Fontaine's position was offered then to ex-Grand Prix, Praying Mantis and Stratus vocalist Bernie Shaw, and that in retrospect was a winning move.
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The break of seven in Savona The 2014 Milan San Remo was won by a powerful sprint from Alexander Kristoff of who started his sprint with about 150m to go and surged clear of a fading Mark Cavendish. Fabian Cancellara of finished 2nd for a 3rd time in this race and on the podium for a 5th time in seven years. Ben Swift of took a surprise 3rd place, ahead of Juan José Lobato () and Mark Cavendish (). Two of the pre-race favourites missed out towards the finish, with John Degenkolb puncturing as they hit the Poggio and André Greipel suffering from cramps after chasing to get back in the winning move on the descent of the Poggio.
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The first player wins in Nim if and only if the nimber is not zero, so from this analysis we can conclude that the first player wins if and only if the starting number of stones in a one-pile game of Nim is not zero; the winning move is to take all the stones. If we change the game so that the player to move can take up to 3 stones only, then with stones, the successor states have nimbers , giving a mex of 0. Since the nimber for 4 stones is 0, the first player loses. The second player's strategy is to respond to whatever move the first player makes by taking the rest of the stones.
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While a chess puzzle is any puzzle involving aspects of chess, a chess problem is an orthodox puzzle in which one must play and win or draw a game, starting with a certain composition of pieces on the chess board, and playing within the standard rules of chess. Orthodox chess problems involve positions that can arise from actual game play (although the process of getting to that position may be unrealistic). The most common orthodox chess puzzle takes the form of checkmate in n moves. The puzzle positions are seldom similar to positions from actual play, and the challenge is not to find a winning move, but rather to find the (usually unique) move which forces checkmate as rapidly as possible.
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As more drivers reached the blocked turn, the Safety Car was deployed so that marshals could remove Albers' car. Both Renault drivers pitted immediately, but Räikkönen - acting on instructions from McLaren chief strategist Neil Martin - continued on in what was to prove a winning move. Though this seemingly put Räikkönen in a bad spot, as all of his close competitors had pitted, he fought back with a series of brilliant laps that would give him a 34.7-second lead by the time he pitted on lap 42. Alonso, whose car was substantially slower as it was full of fuel, and whose rear tyres were wearing rapidly, was unable to catch up, and Räikkönen, after pitting, returned to the track still 13 seconds ahead.
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Much of the pre-race attention for the month focused heavily on rookie Nigel Mansell, the reigning Formula One World Champion, who switched to the CART Indy car series during the offseason. A large international media contingent arrived at the track creating a huge frenzy surrounding the Englishman. Mansell was competitive all afternoon, and was leading the race on lap 184 as the field was coming to a restart. His inexperience on oval circuits, however, led to him misjudging the restart speed and he was quickly passed down the main stretch by Fittipaldi, which proved to be the winning move. Fittipaldi, Arie Luyendyk and Mansell finished 1st–2nd–3rd, the first time foreign-born drivers swept the top three finishing positions since 1915.
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Alessandro Ballan in 2012 As a consequence, the element of "luck" is arguably one of the reasons why there has never been a rider able to win the Tour of Flanders more than three times, as even the best and greatest specialists of their time suffer bad luck or are foiled by unpredictable race circumstances occasionally. Since the race's restyling in 2012, the climbs of Oude Kwaremont, Paterberg and Koppenberg, just south of Oudenaarde, are the heart of the action. The Kwaremont is a long section of cobbles that starts sharply before gradually levelling out. It is the site where powerful riders often make the race-winning move, as Fabian Cancellara demonstrated in 2013, when he attacked with Peter Sagan on the lower slopes of Kwaremont before distancing the Slovak on the Paterberg.
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Chris Froome (right) and Rigoberto Urán (left) (pictured on stage seventeen) finished the Tour in first and second, respectively, in the general classification. The final high mountain stage of the Tour, the eighteenth, saw Barguil claim his second stage victory of the race on the summit finish at Col d'Izoard; he was initially caught by the group of overall favourites on the final climb after being the one of last survivors from the breakaway, with only Darwin Atapuma () ahead. Barguil's winning move came with remaining, passing Atapuma to win by twenty seconds. A three-way sprint for fourth place saw Bardet finish just ahead of Froome with Urán placing fifth; Bardet moved up to second overall, six seconds ahead of Urán, with Froome holding a 23-second advantage.
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No two cold positions can differ by a square, because if they did then a player faced with the larger of the two positions could move to the smaller position and win. Thus, the cold positions form a set with no square difference: :0, 2, 5, 7, 10, 12, 15, 17, 20, 22, 34, 39, 44, … These positions can be generated by a greedy algorithm in which the cold positions are generated in numerical order, at each step selecting the smallest number that does not have a square difference with any previously selected number. As Golomb observed, the cold positions are infinite, and more strongly the number of cold positions up to n is at least proportional to \sqrt n. For, if there were fewer cold positions, there wouldn't be enough of them to supply a winning move to each hot position.
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Seirawan later called Kramnik's move "a tragedy". ChessBase described the events as follows: "Kramnik played the move 34...Qe3 calmly, stood up, picked up his cup and was about to leave the stage to go to his rest room. At least one audio commentator also noticed nothing, while Fritz operator Mathias Feist kept glancing from the board to the screen and back, hardly able to believe that he had input the correct move. Fritz was displaying mate in one, and when Mathias executed it on the board Kramnik briefly grasped his forehead, took a seat to sign the score sheet and left for the press conference, which he dutifully attended." During it he stated that he had planned the supposedly winning move 34...Qe3 already when playing 29...Qa7, and had rechecked the line after each subsequent move.
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The second player has no winning strategy so the first player has one. It is nevertheless possible for the first player to lose by making a sufficiently bad move, since although that stone has value, it may have significantly less value than the second move—an important consideration for understanding the nature of the pie rule. If the "pie rule" is in force, however, the second player wins, because the second player can in principle evaluate whether or not the first move is a winning move and choose to invoke the pie rule if it is (thereby effectively becoming the first player). In practice, assuming the pie rule is in force and the official Schensted/Titus board is being used, Y is a very well balanced game giving essentially equal chances for any two players of equal strength.
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On the final summit finish on Stage 19, Wiggins and Froome dropped all of their rivals and attempted to catch Valverde, who was out in front. Ultimately, they came up short due to Froome having to wait three times for Wiggins as the race leader was several metres behind his domestique on certain parts of the climb, although they took second and third to extend their advantage over Nibali. Sky made a late call to chase down the day's breakaway on Stage 18, in the hope of giving Cavendish a stage victory to repay his work as a domestique. However, a late attack by Luis Leon Sanchez and Nicholas Roche looked set to be the winning move, only for Cavendish to sprint past the pair in the final 200 metres to take his second stage win of the race.
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Watanabe was promoted to the rank of professional 4-dan on April 1, 2000 at the age of 15 after winning the 26th 3-dan league (October 1999 to March 2000) with a record of 13 wins and 5 losses, thus becoming the fourth junior high school student after Hifumi Katō, Kōji Tanigawa and Yoshiharu Habu to become a shogi professional. Watanabe made his first appearance in a major title match in October 2003 when he challenged Habu for the Ōza title. Watanabe led the match 2 games to 1 before Habu won the last two games to defend his title. Even though he lost the match, Watanabe was called "The man who made Habu shake" (羽生を震えさせた男 habu wo furuesaseta otoko) because Habu's hand visibly shook when making the winning move during the deciding fifth game.
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No matter how many cards are able to be played, a turn ends with a player placing a card from their hand into one of their discard piles (unless they play the winning move of putting their last goal card into play, in which case they win and no discard is required). If everyone has a high goal card at the start of play, there may be many turns where the players draw just one card and then decide which card to add to the discard piles until someone gets a sufficient number of cards saved up in the discard piles of cards to reach their high number. Or one person may end up with a low goal card and, in reaching that one and then ending their turn, they will have unavoidably helped someone else to reach their higher number goal card. As play continues, many cards can accumulate in the discard piles.
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The optimal strategy in Fibonacci nim can be described in terms of the "quota" (the maximum number of coins that can currently be removed: all but one on the first move, and up to twice the previous move after that) and the Zeckendorf representation of the current number of coins as a sum of non- consecutive Fibonacci numbers. A given position is a losing position (for the player who is about to move) when is less than the smallest Fibonacci number in this representation, and a winning position otherwise. In a winning position, it is always a winning move to remove all the coins (if this is allowed) or otherwise to remove a number of coins equal to the smallest Fibonacci number in the Zeckendorf representation. When this is possible, the opposing player will necessarily be faced with a losing position, because the new quota will be smaller than the smallest Fibonacci number in the Zeckendorf representation of the remaining number of coins.
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To find out which move to make, let X be the nim-sum of all the heap sizes. Find a heap where the nim-sum of X and heap-size is less than the heap-size - the winning strategy is to play in such a heap, reducing that heap to the nim-sum of its original size with X. In the example above, taking the nim-sum of the sizes is . The nim-sums of the heap sizes A=3, B=4, and C=5 with X=2 are : A ⊕ X = 3 ⊕ 2 = 1 [Since (011) ⊕ (010) = 001 ] : B ⊕ X = 4 ⊕ 2 = 6 : C ⊕ X = 5 ⊕ 2 = 7 The only heap that is reduced is heap A, so the winning move is to reduce the size of heap A to 1 (by removing two objects). As a particular simple case, if there are only two heaps left, the strategy is to reduce the number of objects in the bigger heap to make the heaps equal.
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