康尼島（英語：），又译科尼島，是位於美國紐約市布魯克林區的半島，原本為一座海島，其面向大西洋的海灘是美國知名的休閒娛樂區域。居民大多集中位於半島的西側，約有六萬人左右，範圍西至希捷社區，東至布萊登海灘和曼哈頓海灘，而北至葛瑞福山德社區。 二十世紀前葉在美國極為知名的太空星際樂園即是以康尼島作為主要的腹地，該樂園在二次大戰後開始衰退，並持續荒廢了許久。在最近幾年，康尼島因為凱斯班公園的開幕而重新繁榮起來，凱斯班公園是職棒小聯盟球隊布魯克林旋風的主要球場。旋風隊在當地十分受到歡迎，每季開賽時都會吸引許多球迷到場觀戰。 ..

Anjos da guarda são os anjos que segundo as crenças cristãs, Deus envia no nosso nascimento para nos proteger durante toda a nossa vida. Argumenta-se que a Bíblia sustenta em algumas ocasiões a crença do anjo da guarda: "Vou enviar um anjo adiante de ti para ..

Altay Cumhuriyeti (Rusça: Респу́блика Алта́й / Respublika Altay; Altay Türkçesi: Алтай Республика / Altay Respublika), Rusya'nın en güneyinde yer alan, federasyona bağlı bir özerk cumhuriyet. Orta Asya'da Asya kıtasının coğrafî merkezinin hemen kuzeyinde ve ..

沙羅週期長度為18年11天，本週期包含70次日食，其中公元3000年以前有49次。 註：下表各項數據均為食分最大地點的情況。寬度指該地點食甚時刻月球的本影（全食時）或偽本影（環食時）落在地表的寬度，持續時間指該地點食既到生光的時間，即全食或環食的持續時間，全環食（亦稱混合食）發生時，食分最大處為全食。最後兩項參數不適用於偏食。 本周期最終結束於3378年6月17日。

希西家王 (希伯來語：，英語：）是猶大末年的君主，也是猶大國歷史中極尊重上帝的君王，在位29年。終年54歲。他在位的年份有兩種說法：其一是前715年-前687年；另一種是前716年-前687年。他的德行在其前後的猶大列王中，没有一個能及他。其希伯來名字的意思是“被神加力量”。 希西家的父親亞哈斯是一個背逆上帝的君王。因此在希西家當政之初的猶大國，無論政治，宗教上都极其黑暗。根據《聖經》記載，因为北國以色列被亞述攻滅，亞述王可以趁勢来攻打猶大國；又猶大的先王亞哈斯曾封鎖了聖殿之路，引導舉國崇拜偶像，大大得罪上帝。若非上帝的憐憫，為了堅定向大衛家所說的應許，猶大國的暫得幸存。希西家在二十五歲就登基作王，且正在國家危急之秋，由於行耶和華上帝眼中看為正的事，因而得上帝的憐憫，得以成功脫離亞述大軍的攻擊和一場致死的大病。他樂於聽從當代先知以賽亞的指導，使他為上帝大發熱心。 ..

The OnePlus 2 (also abbreviated as OP2) is a smartphone designed by OnePlus. It is the successor to the OnePlus One. OnePlus revealed the phone on 28 July 2015 via virtual reality, using Google's Cardboard visor and their own app. OnePlus sold out 30,000 units ..

兴隆街镇，是中华人民共和国四川省内江市资中县下辖的一个乡镇级行政单位。 兴隆街镇下辖以下地区： 兴隆街社区、兴松村、玄天观村、三元村、金星村、三皇庙村、双桥村、红庙子村、华光村、高峰村、芦茅湾村、篮家坝村、五马村和解放村。

Национальная и университетская библиотека (словен. Narodna in univerzitetna knjižnica, NUK), основанная в 1774 году, — один из важнейших образовательных и культурных учреждений Словении. Она располагается в центре столицы Любляна, между улицами Турьяшка (Turjaška ..

Mauser M1924 (или M24) — серия винтовок компании Mauser, использовавшихся в армиях Бельгии и Югославии. Внешне напоминают чехословацкие винтовки vz. 24, в которых использовались стандартный открытый прицел, патроны калибра 7,92×57 мм (или 8×57 мм), укороченные ..

第三条道路（英語：），又称新中间路线（Middle Way），是一种走在自由放任资本主义和传统社会主义中间的一种政治经济理念的概称。它由中间派所倡导，是社会民主主义的一个流派，英国工党称其为「现代化的社会民主主义」。它的中心思想是既不主张纯粹的自由市场，也不主张纯粹的社會主義，主张在两者之间取折衷方案。 第三条道路不只单单是走在中间，或只是一种妥协或混合出来的东西，第三条道路的提倡者看到了社会主义和资本主义互有不足之处，所以偏向某一极端也不是一件好事，第三条道路正正是揉合了双方主义的优点，互补不足而成的政治哲学。 ..

A **solved game** is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly.
This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance;
solving such a game may use combinatorial game theory and/or computer assistance.

A two-player game can be solved on several levels:^{[1]}^{[2]}

- Ultra-weak
- Prove whether the first player will win, lose or draw from the initial position, given perfect play on both sides. This can be a non-constructive proof (possibly involving a strategy-stealing argument) that need not actually determine any moves of the perfect play.
- Weak
- Provide an algorithm that secures a win for one player, or a draw for either, against any possible moves by the opponent, from the beginning of the game. That is, produce at least one complete ideal game (all moves start to end) with proof that each move is optimal for the player making it. It does not necessarily mean a computer program using the solution will play optimally against an imperfect opponent. For example, the checkers program Chinook will never turn a drawn position into a losing position (since the weak solution of checkers proves that it is a draw), but it might possibly turn a winning position into a drawn position because Chinook does not expect the opponent to play a move that will not win but could possibly lose, and so it does not analyze such moves completely.
- Strong
- Provide an algorithm that can produce perfect moves from any position, even if mistakes have already been made on one or both sides.

Despite their name, many game theorists believe that "ultra-weak" proofs are the deepest, most interesting and valuable. "Ultra-weak" proofs require a scholar to reason about the abstract properties of the game, and show how these properties lead to certain outcomes if perfect play is realized.^{[citation needed]}

By contrast, "strong" proofs often proceed by brute force—using a computer to exhaustively search a game tree to figure out what would happen if perfect play were realized. The resulting proof gives an optimal strategy for every possible position on the board. However, these proofs are not as helpful in understanding deeper reasons why some games are solvable as a draw, and other, seemingly very similar games are solvable as a win.

Given the rules of any two-person game with a finite number of positions, one can always trivially construct a minimax algorithm that would exhaustively traverse the game tree. However, since for many non-trivial games such an algorithm would require an infeasible amount of time to generate a move in a given position, a game is not considered to be solved weakly or strongly unless the algorithm can be run by existing hardware in a reasonable time. Many algorithms rely on a huge pre-generated database, and are effectively nothing more.

As an example of a strong solution, the game of tic-tac-toe is solvable as a draw for both players with perfect play (a result even manually determinable by schoolchildren). Games like nim also admit a rigorous analysis using combinatorial game theory.

Whether a game is solved is not necessarily the same as whether it remains interesting for humans to play. Even a strongly solved game can still be interesting if its solution is too complex to be memorized; conversely, a weakly solved game may lose its attraction if the winning strategy is simple enough to remember (e.g. Maharajah and the Sepoys). An ultra-weak solution (e.g. Chomp or Hex on a sufficiently large board) generally does not affect playability.

Moreover, even if the game is not solved, it is possible that an algorithm yields a good approximate solution: for instance, an article in *Science* from January 2015 claims that their heads up limit Texas hold 'em poker bot Cepheus guarantees that a human lifetime of play is not sufficient to establish with statistical significance that its strategy is not an exact solution.^{[3]}^{[4]}^{[5]}

In game theory, **perfect play** is the behavior or strategy of a player that leads to the best possible outcome for that player regardless of the response by the opponent. Perfect play for a game is known when the game is solved.^{[1]} Based on the rules of a game, every possible final position can be evaluated (as a win, loss or draw). By backward reasoning, one can recursively evaluate a non-final position as identical to the position that is one move away and best valued for the player whose move it is. Thus a transition between positions can never result in a better evaluation for the moving player, and a perfect move in a position would be a transition between positions that are equally evaluated. As an example, a perfect player in a drawn position would always get a draw or win, never a loss. If there are multiple options with the same outcome, perfect play is sometimes considered the fastest method leading to a good result, or the slowest method leading to a bad result.

Perfect play can be generalized to non-perfect information games, as the strategy that would guarantee the highest minimal expected outcome regardless of the strategy of the opponent. As an example, the perfect strategy for rock paper scissors would be to randomly choose each of the options with equal (1/3) probability. The disadvantage in this example is that this strategy will never exploit non-optimal strategies of the opponent, so the expected outcome of this strategy versus any strategy will always be equal to the minimal expected outcome.

Although the optimal strategy of a game may not (yet) be known, a game-playing computer might still benefit from solutions of the game from certain endgame positions (in the form of endgame tablebases), which will allow it to play perfectly after some point in the game. Computer chess programs are well known for doing this.

- Awari (a game of the Mancala family)
- The variant of Oware allowing game ending "grand slams" was strongly solved by Henri Bal and John Romein at the Vrije Universiteit in Amsterdam, Netherlands (2002). Either player can force the game into a draw.
- Chopsticks
- The second player can always force a win.
^{[citation needed]} *Connect Four*- Solved first by James D. Allen on October 1, 1988 and independently by Victor Allis on October 16, 1988.
^{[6]}The first player can force a win. Strongly solved by John Tromp's 8-ply database^{[7]}(Feb 4, 1995). Weakly solved for all boardsizes where width+height is at most 15 (as well as 8×8 in late 2015)^{[6]}(Feb 18, 2006). - English draughts (checkers)
- This 8×8 variant of draughts was
**weakly solved**on April 29, 2007 by the team of Jonathan Schaeffer. From the standard starting position, both players can guarantee a draw with perfect play.^{[8]}Checkers is the largest game that has been solved to date, with a search space of 5×10^{20}.^{[9]}The number of calculations involved was 10^{14}, which were done over a period of 18 years. The process involved from 200 desktop computers at its peak down to around 50.^{[10]} - Fanorona
- Weakly solved by Maarten Schadd. The game is a draw.
^{[citation needed]} - Free gomoku
- Solved by Victor Allis (1993). The first player can force a win without opening rules.
- Ghost
- Solved by Alan Frank using the
*Official Scrabble Players Dictionary*in 1987.^{[citation needed]} *Guess Who?*- Strongly solved by Mihai Nica in 2016.
^{[11]}The first player has a 63% chance of winning under optimal play by both sides. *Hex*- A strategy-stealing argument (as used by John Nash) shows that all square board sizes cannot be lost by the first player. Combined with a proof of the impossibility of a draw this shows that the game is ultra-weak solved as a first player win.
- Strongly solved by several computers for board sizes up to 6×6.
- Jing Yang has demonstrated a winning strategy (weak solution) for board sizes 7×7, 8×8 and 9×9.
- A winning strategy for Hex with swapping is known for the 7×7 board.
- Strongly solving Hex on an
*N*×*N*board is unlikely as the problem has been shown to be PSPACE-complete. - If Hex is played on an
*N*×(*N*+1) board then the player who has the shorter distance to connect can always win by a simple pairing strategy, even with the disadvantage of playing second. - A weak solution is known for all opening moves on the 8×8 board.
^{[12]}

- Hexapawn
- 3×3 variant solved as a win for black, several other larger variants also solved.
^{[13]} - Kalah
- Most variants solved by Geoffrey Irving, Jeroen Donkers and Jos Uiterwijk (2000) except Kalah (6/6). The (6/6) variant was solved by Anders Carstensen (2011). Strong first-player advantage was proven in most cases.
^{[14]}^{[15]}Mark Rawlings, of Gaithersburg, MD, has quantified the magnitude of the first player win in the (6/6) variant (2015). After creation of 39 GB of endgame databases, searches totaling 106 days of CPU time and over 55 trillion nodes, it was proven that, with perfect play, the first player wins by 2. Note that all these results refer to the Empty-pit Capture variant and therefore are of very limited interest for the standard game. Analysis of the standard rule game has now been posted for Kalah(6,4), which is a win by 8 for the first player, and Kalah(6,5), which is a win by 10 for the first player. Analysis of Kalah(6,6) with the standard rules is on-going, however, it has been proven that it is a win by at least 4 for the first player. - L game
- Easily solvable. Either player can force the game into a draw.
- Losing chess
- Weakly solved as a win for white beginning with 1. e3.
^{[16]} - Maharajah and the Sepoys
- This asymmetrical game is a win for the sepoys player with correct play.
- Nim
- Strongly solved.
- Nine men's morris
- Solved by Ralph Gasser (1993). Either player can force the game into a draw.
^{[17]} - Order and Chaos
- Order (First player) wins.
^{[18]} - Ohvalhu
- Weakly solved by humans, but proven by computers. (Dakon is, however, not identical to Ohvalhu, the game which actually had been observed by de Voogt)
- Pangki
- Strongly solved by Jason Doucette (2001).
^{[19]}The game is a draw. There are only two unique first moves if you discard mirrored positions. One forces the draw, and the other gives the opponent a forced win in 15. - Pentago
- Strongly solved.
^{[20]}The first player wins. - Pentominoes
- Weakly solved by H. K. Orman.
^{[21]}It is a win for the first player. - Poddavki ("Russian Give-away Checkers")
- Solved by Osipov and Morozev in 2011. A white win.
^{[citation needed]} *Quarto*- Solved by Luc Goossens (1998). Two perfect players will always draw.
- Qubic
- Weakly solved by Oren Patashnik (1980) and Victor Allis. The first player wins.
*Renju*-like game without opening rules involved- Claimed to be solved by János Wagner and István Virág (2001). A first-player win.
- Sim
- Weakly solved: win for the second player.
- Teeko
- Solved by Guy Steele (1998). Depending on the variant either a first-player win or a draw.
^{[22]} - Three men's morris
- Trivially solvable. Either player can force the game into a draw.
- Three Musketeers
- Strongly solved by Johannes Laire in 2009, and weakly solved by Ali Elabridi in 2017.
^{[23]}It is a win for the blue pieces (Cardinal Richelieu's men, or, the enemy).^{[24]} - Tic-tac-toe
- Trivially strongly solvable because of the small game tree.
^{[25]}The game is a draw if no mistakes are made, with no mistake possible on the opening move. - Tigers and Goats
- Weakly solved by Yew Jin Lim (2007). The game is a draw.
^{[26]}

- Chess
- Fully solving chess remains elusive, and it is speculated that the complexity of the game may preclude its ever being solved. Through retrograde computer analysis, endgame tablebases (strong solutions) have been found for all three- to seven-piece endgames, counting the two kings as pieces.
- Some variants of chess on a smaller board with reduced numbers of pieces have been solved. Some other popular variants have also been solved; for example a weak solution to Maharajah and the Sepoys is an easily memorable series of moves that guarantees victory to the "sepoys" player.
- Go
- The 5×5 board was weakly solved for all opening moves in 2002.
^{[27]}The 7×7 board was weakly solved in 2015.^{[28]}Humans usually play on a 19×19 board which is over 145 orders of magnitude more complex than 7×7.^{[29]} - International draughts
- All endgame positions with two through seven pieces were solved, as well as positions with 4×4 and 5×3 pieces where each side had one king or fewer, positions with five men versus four men, positions with five men versus three men and one king, and positions with four men and one king versus four men. The endgame positions were solved in 2007 by Ed Gilbert of the United States. Computer analysis showed that it was highly likely to end in a draw if both players played perfectly.
^{[30]}^{[better source needed]} - m,n,k-game
- It is trivial to show that the second player can never win; see strategy-stealing argument. Almost all cases have been solved weakly for
*k*≤ 4. Some results are known for*k*= 5. The games are drawn for*k*≥ 8. - Reversi (Othello)
- Weakly solved on a 4×4 and 6×6 board as a second player win in July 1993 by Joel Feinstein.
^{[31]}On an 8×8 board (the standard one) it is mathematically unsolved, though computer analysis shows a likely draw. No strongly supposed estimates other than increased chances for the starting player (Black) on 10×10 and greater boards exist.

- 1 2
Victor Allis (1994). "PhD thesis: Searching for Solutions in Games and Artificial Intelligence" (PDF).
*Department of Computer Science*. University of Limburg. Retrieved 2012-07-14. - ↑ H. Jaap van den Herik, Jos W.H.M. Uiterwijk, Jack van Rijswijck,
*Games solved: Now and in the future*,*Artificial Intelligence*134 (2002) 277–311. - ↑ Bowling, M.; Burch, N.; Johanson, M.; Tammelin, O. (Jan 2015). "Heads-up limit hold'em poker is solved" (PDF).
*Science*.**347**(6218): 145–9. CiteSeerX 10.1.1.697.72. doi:10.1126/science.1259433. PMID 25574016. - ↑ Philip Ball (2015-01-08). "Game Theorists Crack Poker".
*Nature*. Nature. doi:10.1038/nature.2015.16683. Retrieved 2015-01-13. - ↑ Robert Lee Hotz (2015-01-08). "Computer Conquers Texas Hold 'Em, Researchers Say".
*Wall Street Journal*. - 1 2 "John's Connect Four Playground".
*tromp.github.io*. - ↑ "UCI Machine Learning Repository: Connect-4 Data Set".
*archive.ics.uci.edu*. - ↑ Schaeffer, Jonathan (2007-07-19). "Checkers Is Solved". Science. Retrieved 2007-07-20.
- ↑ "Project - Chinook - World Man-Machine Checkers Champion". Retrieved 2007-07-19.
- ↑ Mullins, Justin (2007-07-19). "Checkers 'solved' after years of number crunching". NewScientist.com news service. Retrieved 2007-07-20.
- ↑ Optimal Strategy in "Guess Who?": Beyond Binary Search by Mihai Nica.
- ↑ P. Henderson, B. Arneson, and R. Hayward[webdocs.cs.ualberta.ca/~hayward/papers/solve8.pdf, Solving 8×8 Hex ], Proc. IJCAI-09 505-510 (2009) Retrieved 29 June 2010.
- ↑ Price, Robert. "Hexapawn".
*www.chessvariants.com*. - ↑ Solving Kalah by Geoffrey Irving, Jeroen Donkers and Jos Uiterwijk.
- ↑ Solving (6,6)-Kalaha by Anders Carstensen.
- ↑ Watkins, Mark. "Losing Chess: 1. e3 wins for White" (PDF). Retrieved 17 January 2017.
- ↑ Nine Men's Morris is a Draw by Ralph Gasser
- ↑ "solved: Order wins - Order and Chaos".
- ↑ Pangki is strongly solved as a Draw by Jason Doucette
- ↑ Geoffrey Irving: "Pentago is a first player win" http://perfect-pentago.net/details.html
- ↑ Hilarie K. Orman:
*Pentominoes: A First Player Win*in*Games of no chance*, MSRI Publications – Volume 29, 1996, pages 339-344. Online: pdf. - ↑ Teeko, by E. Weisstein
- ↑ Elabridi, Ali. "Weakly Solving the Three Musketeers Game Using Artificial Intelligence and Game Theory" (PDF).
- ↑ Three Musketeers, by J. Lemaire
- ↑ Tic-Tac-Toe, by R. Munroe
- ↑ Yew Jin Lim. On Forward Pruning in Game-Tree Search. Ph.D. Thesis, National University of Singapore, 2007.
- ↑ 5×5 Go is solved by Erik van der Werf
- ↑ "首期喆理围棋沙龙举行 李喆7路盘最优解具有里程碑意义_下棋想赢怕输_新浪博客".
*blog.sina.com.cn*. (which says the 7x7 solution is only weakly solved and it's still under research, 1. the correct komi is 9 (4.5 stone); 2. there are multiple optimal trees - the first 3 moves are unique - but within the first 7 moves there are 5 optimal trees; 3. There are many ways to play that don't affect the result) - ↑ Counting legal positions in Go Archived 2007-09-30 at the Wayback Machine, Tromp and Farnebäck, accessed 2007-08-24.
- ↑ Some of the nine-piece endgame tablebase by Ed Gilbert
- ↑ "6×6 Othello weakly solved". Archived from the original on 2009-11-01.

- Allis,
*Beating the World Champion? The state-of-the-art in computer game playing.*in New Approaches to Board Games Research.

- Computational Complexity of Games and Puzzles by David Eppstein.
- GamesCrafters solving two-person games with perfect information and no chance

© 2019 raptorfind.com. Imprint, All rights reserved.