Rules Of Tic Tac Toe Game Computer Science Essay

Rules Of Tic Tac Toe Game Com purgeer Science EssayIn this section the tit-tat-toe secret plan lead be discussed in details. At the stunnedset, the basic rules of the back atomic number 18 going to be covered. Then, on that point provide be a review on existing Tic-Tac-Toe bouncings, which in rise give lead to discussion ab come out the existing poses of this blue and the proposed model of this work. Fin wholey, this section is going to be concluded with a engineering science research c mavin timentrated towards coffee tree 2 Plat act, Micro var. (J2ME).3.1 grassroots Rules of Tic-Tac-Toe naughtyThe basic Tic-Tac-Toe secret plan consists of deuce doers, X and O, who take turns staining the spaces in a 3-3 grid 1, 2. The gimpy usu all(prenominal)y herots with the X pseud, and the sham who pull up stakes manage to place trine respective attach wins the bouncing. The star signs piece of tail be placed in e very direction, i.e. in a horizontal, vertical, or d iagonal quarrel. This basic var. of the granulose is rather simple and very often leads to draw. This simplicity allows the game to be used as a multipurpose as well asl in combinatorial game theory, as well as a wooden leg of artificial intelligence that deals with the searching of game heads 3.The Roman Empire is know to induce established the beginnings of the earliest known variant of ticktacktoo. It originated around the graduation century BC 1. At that time, the game was called Terni Lapilli. Instead of having any spell of pieces, each flirter exclusively had three. The game was vie by go them around to mindless(prenominal) spaces to keep playing. However, according to Claudia Zaslavskys book, the game Tic Tac Toe is originating from past Egypt 5.Chess and Tic-Tac-Toe argon unmatchable of the most famous games to which the moves argon non left to chances, rather than pure mathematics and logical reasoning. In these games, a player wins by achieving a winning configuration front, equivalent for instance checkmate in chess game, and 3-in-a- track in a basic Tic-Tac-Toe game in 33 board 2. Thus, the question which fuck be posed at this point is How a player potentiometer discover a winning configuration basic? Even though thither isnt a general theorem to answer this question, thither might be a well-known scheme stealing argument that can give a partial answer about when a player can turn over a winning configuration archetypical 3.In drifting to thrum a take up a winning strategy, in theory all the paths could be explored. However, in practice this is non easy because the total number of strategies can be calculated a double exp unityntial function of the size of the board. For example, a 3-dimensional 5-5-5 indication of Tic-Tac-Toe, has about 3125 piazzas. This is because each one of the 53 cells has 3 optionsMarked by the first player,Marked by the second player, orUn tag.Thus the backtracking on a graph of 3125 ve rtices takes at least 3125 steps. This is the briny reason that this 3-dimensional 5-5-5 version of Tic-Tac-Toe remains unsolved up to date. Moreover, only devil explicit winning strategies be known from in the whole class ofn-n- -n = nd Tic-Tac-Toe games. This is the 33 version and it is characterized with an easy winning strategy, and the 43 version that in turn has an exceedingly complicated winning strategy.In launch to play a consummate(a) tit-tat-toe game, i.e. a win or a draw, the player can play accustomed they move consistent with the uppermost possible moves. This is presented in the pastime table 1WinIf the player has two in a class, play the third to get three in a row. eludeIf the opponent has two in a row, play the third to thwart them.ForkCreate an opportunity where you can win in two commissions.Block opponents forkOption 1 Create two in a row to force the opponent into defgoaling, as long as it doesnt result in them creating a fork or winning. For example , if X has a recessional, O has the mid elbow room, and X has the reverse gear corner as well, O moldiness non play a corner in array to win. (Playing a corner in this scenario creates a fork for X to win.)Option 2 If at that place is a configuration where the opponent can fork, block that fork. kernelPlay the center.Opposite cornerIf the opponent is in the corner, play the opposite corner. unemployed cornerPlay in a corner squargon.Empty sidePlay in a midriff squ ar on any of the 4 sides.Initially, the player that starts first gets the X and has 3 equiprobable assigns to mark in his turn. Even though it seems that there are 9 possible positions, as there are 9 squares in the grid, by rotating the board, this is not the case. It can be observed thatEvery corner mark is tactically equal to every early(a) corner mark, andEvery pass on mark is tactically equal to every some other edge mark. in that respect are thereof only three possible first marks corner, edge, or cent er. The first player could win (or make a draw) from any of these starting marks. It can be besides observed that playing a corner would give the opponent the smallest choice of squares. This is a nice strategy as could be played to avoid losing 5.The second player can be identified as O and this player must reply to Xs opening mark. However, this should be done in such a way as to avoid fraud X to win. It can be verbalise that imposter O must always respond with 5To a corner opening with a center mark,To a center opening with a corner mark andTo an edge opening either with a center mark, a corner mark next to the X, or an edge mark opposite the X.Any contrasting play would allow X to tie a win. After every next turn of player X, the player O should follow the above list. This way the player O can get through a draw (or a win if the player X makes a weak play).3.2 real Tic-Tac-Toe gamesAs many other games like three mens morris, gild mens morris, pente, gomoku, Qubic, Con nect Four, Quarto and Gobblet, Tic-Tac-Toe also has the kindred goal, i.e. a player wins if he is the first one to get n-in-a-row. Basically, if a generalization is to be provided, it can be concluded that all the polar varietyations of Tic-Tac-Toe can be represented as nd-games, which are accordingly played on a d-dimensional boards with edge n 5. As it was discussed in the antecedent section as well, the original Tic-Tac-Toe game is in truth a 32-game.There are many trans deviseations, discussed as follows 2, 3A slightly different version of a Tic-Tac-Toe game is the 33-game, played on a 3x3x3 board. It can be noteworthy that this game gives safe opportunities to the player that plays first, so he could achieve an easy win by playing at the center with his first move. Similarly, playing on a 4x4x4 board also gives the first player better chances for wining.More obscure version of a Tic-Tac-Toe game is playing it on a board with graduate(prenominal)er(prenominal) dimension al space. 4 dimensional, i.e. 3-3-3-3 board is one of the most commonly played Tic-Tac-Toe. In this version there are 2 possible induces. One of them is to position elements through all of the board, thus the player that has more than rows of 3 totally than the other one is the succeeder of the game. And the other strategy is to include 4 players, in which case the winner is the payer that will get a row of 3 first. several(prenominal) other version is the misre tic-tac-toe game. In this variation 33 game would be a draw, whereas the winner is the player that will get n in a row.Quite a new game is the Tic Tac play variation of tic-tac-toe. This game is played on a 3 dimensional curved board, and the here each player tries to roll a lummox at least half the way, as it would then drop on a grid that has 9 positions (33 grid). This way the players should make a row of 3 in order to gain a ball. The winner is the player that will have won the first 5 balls. In order to roll t heir balls precisely, they could use a contrivance that helps into changing a balls trajectory. to that extent some other(prenominal) version is the 9 board tic-tac-toe. In this game, there are in essence 9 boards, arranged as 33 grids, and the first payer can start on any of them by his choice. The chase moves are supposed to be places on the board chosen by the first player. Once this board gets full and there is no more space left, the next move can be again on any of the boards left, by the choice of the player. The winner is the one that will achieve 3 in a row. However, having 9 boards gives the game yet some other spirit than the usual tic-tac-toe game, as the players can have an opening, middle and end of their game.Similar to the nine board tic-tac-toe game is the topnotch tic-tac-toe game. The difference in this variation is that this game does not end once a player makes 3 in a row in one of the 9 boards. As an alternative, the position of that board is marked on a new 33 grid, and the winner is the one that will make 3 in row there.Tic-Tac-Chess is an interesting combination of games, as it involved playing a chess game, as well as a tic-tac-toe game at the same time. In this variation, once a player captures a piece from the challenger on the chess game, makes a move on the tic-tac-toe game (even if the challenger has not placed anything on the tic-tac-toe game yet). And of course, the winner is the player that will make 3 in a row on the tic-tac-toe game first.A game that in essence is an isomorphic to a tic-tac-toe game, even though it seems as a completely different game, is described as follows. Basically, there are 2 players that should say a number in the midst of 1 and 9, without repeating the previously said numbers. The winner is the player that will first make a sum of 15. This game is isomorphic to a tic-tac-toe, because if those numbers are to be placed on a 33 magic grid, then it will be merely as playing a tic-tac-toe game, b ecause a straight communication channel is formed only if the sum of the numbers is 15. This cultivation is mostly useful in programming variations of a tic-tac-toe game. some other different variation again employs numbers from 1 to 9. These are to be placed on a 33 grid, but must be held with an order of anteriority defined by the players. Then the players play a tic-tac-toe game, pickax the grid by the precedence defined beforehand.Check Lines is a very old variation of tic-tac-toe game, invented in the 1970s by Tri-ang Toys Games. In this game the board is actually any geometrical pattern that consists of 12 lines. There are 11 holes in total, distributed in a way that each line has 3 holes. At this point, each player is given over 5 coins, and each player on their turn should place a coin on the board. The winner is the one that will have first completed 2 lines. Because the players have only 5 coins, this concocts that they have to complete intersecting lines. If none o f the players have won afterward placing their 5 coins, then they will continue playing by replacing the position of the coins, on the remain spaces, with the rule that it must be done only on an adjacent hole.Very similar game to the tic-tac-toe game is the Toss Across game. Here, the players are given bags with beans and they are throwing them on a big board for marking the squares.Star Tic Tac Toe is another frequent variation of tic-tac-toe. This game is played with checkers like movable pieces. It has a 33 board, thus a player has 3 pieces accordingly. The participants keep on replacing pieces into the spaces which are left empty in the board, until one the players wins this actually adds some more dynamism in the game. Moreover, the players have supplementary star shaped pieces, which can be swapped.Similar category of games as the previous bullet, are the Mojo, Mojo Too and Mojo tic-tac-toe games. In these variation the payers also pieces and pawn(s) onto empty positions u ntil there is a winner.Moreover, there are many shows based on the tic-tac-toe game, as wellHollywood Squares is a show with 9 celebrities, which fill the cells of the tic-tac-toe grid.Tic-Tac-Dough is a show on which the players put symbols up on the board. This is achieved by answering queries in a variety of categories.In Beat the Teacher competitors respond to questions to win a turn, again on a tic-tac-toe grid.On The Price Is Right, there is a determine game called Secret X, in which players must estimate prices to win Xes, in order to place them on a blank board. They must position the Xes as to provide speculation of the location on the secret X. This is in turn hidden in the middle line of the board, forming a tic-tac-toe line across.The fictional game Dni game of Gemedet, has an aim to place 6 balls in a row to a 9x9x9 grid.The fictional game Squid-Tac-Toad, has an aim to place 4 or 5 balls in a row to a 44 or 55 grid, accordingly.A more simple variation of this game is having the rules as of the Y formations to count as a win. This is rather simple, because all the scenarios basically forming some kind of a Y configuration.Quantum tic tac toe is yet another variation in which the participants are billet a quantum superposition of numbers on a tic tac toe board.A larger grid (for example 1010) tic-tac-toe games also exist. In a 1010 grid the winner should place 5 in a row. The more the grids there are on a board, the larger complexity of the game is.Another similar game accountd Go-moku, originating from Vietnam, also has the strategy for a player to get 5 in a row in order to win the game. The players put Xs and Os, but in order to try close up each other, in this variation they should also try to create changes for wining. Another difference is that the board has no limit, thus the game is played until there is a winner.Three Mens Morris and Nine Mens Morris are also variations, in which there is a limiting on the number of pieces in order for a move to be allowed.Finally, the last variation of the tic-tac-toe game, employs the speech eat, an, laf, it, line, if, lot, on and foe. In this game, the winner is the one that will select 3 words that start with the same letter. If the game was places on a tic-tac-toe grid, it would mean 3 words in order to form a line (three in a row line).3.3 Proposed modelThere are sort of a few algorithmic ruleic programs that can be used for creating the Tic-Tac-Toes game strategy. The most popular ones are the semantic algorithms and the lexical algorithms. For this project, a lexical algorithm was utilized. The model of the tic-tac-toe game described in this work contains 2 different game strategies. Basically, the one strategy is the Single Player game where a player plays against a computer. The other strategy involves Multiple Player environment, and it is being played by a player versus another player.In order to analyze this game, a termination tree might be used. Moreover, for t he analyzing part it should be exactd that both the players in the Multiple Player environment, and the sensation player in the Single Player game, are in essence experienced. This means that the result of a game can be foreseen after the first move from each participant (again assuming that there are no mistakes). Let us represent with 1 if the player that has the X wins and with -1 if the player that has the O wins. The following figure represents the decision tree after the first move from each participant. As it was already discussed in section 3.1 Basic Rules of Tic-Tac-Toe game, the tic-tac-toe game is symmetric and therefore it is sufficient to consider only the squares 1, 2 and 3 for the first player (see the figure below). The rest of the moves are symmetric and will be presented. So, following this reasoning, the first player has the positions 1, 2 and 3 available, and the second player has the remaining two positions.The figure above presents an expansion, so called an extensive form. It demonstrates that even in the simplest scenario the decision tree can be quite large. For example, if the first two moves were to be presented, this would be impossible to be demonstrated on a single page.Similarly to this discussion, the strategic form of the game can be presented by a different model, i.e. as a matrix. In order to demonstrate this approach, it should be assumed that the players choose one strategy and they purely follow it when their turn comes. Of course, each strategy should represent all the paths of action at law and in every possible situation.At the beginning, let us assume that there is a strategy that the first player uses for their first move, and another strategy for the first move of the second player. This logic would create some rules like the following 5For the first player select one of the nine squares on the game board.For the second player Select one of the nine squares on the game board. If the first player already uses the selected square, then put an O in square 3, 5, 7, or 9 if an X is in square 1 (center) put an O in cell 1 if an X is in cell j.These rules are examples of complete strategies, and these can be selected by the payers before the beginning of the game, and thus followed with their first moves. The strategic form of a tic-tac-toe game is presented on the figure below. It should be note that the entries in the table below are in essence the set of the game. They hold values for every possible selection of strategies.Each tic-tac-toe game that can be actually presented in an extensive form would have an equivalent strategic form similar to the one shown in the table presented above. Moreover, this table is also equivalent to the matrix established previously. The coming back matrix in cooperation with the descriptions of the strategies comprises the model for the two-person tic-tac-toe game.3.4 Comparison of Proposed model with Existing ModelsThe semantic algorithm is yet another appro ach towards the tic-tac-toe game. The semantic algorithm is in essence a learning algorithm, and it might be structured in the following way. It might have as initial information the ability to recognizing the 3 states of a game lost, won or a draw. The algorithm in this case would play the X, and it will play against another algorithm, i.e. the O. As soon as a game is finishes, the information if the game was won or lost is stored. Moreover, the moves are presented with the smaller letter x and o accordingly. A possible structure of stored information could be the following line x5 o3 x9 o4 x1 won. The first move is always randomly selected. So, given that the algorithm played 7 (x7), and the opponent played 6 (o6), the algorithm will search for previous games that are most similar to x7 o6. If such a case is assemble, then the following rules applyIf the game found was a win, than the algorithm will try to reproduce the move. If the position is not available, it will play random ly.If the game found was a loss, the algorithm will try to correct the move, by not placing an element in the same position as in the lost game.This is repeated until there is a winner. Moreover, if a game end with a draw, it is not saved in the database.Comparing this algorithm with a lexical algorithm, it might be noted that the semantic algorithm usually plays very badly at the begging. But, after a certain number of games, the learning curve of the algorithm becomes higher.3.5 engine room Research (j2me)Being quite different from other programming languages, chocolate does both compiling and interpreting when it comes to process cipher.As it can be seen from the photo above, the source code (i.e. the .java files) is initially translated by the compiler. This gives an output of an mean(a) language, called coffee bytecode (i.e. the .class files). The bytecode is then ready to be executed (or in other words, interpreted) within a particular realistic processor, known as the JV M ( coffee tree realistic motorcar) 6, 7. This is in essence a simulated processor that executes all the bytecode commands. The umber realistic Machine is the basic components that give to Java the feature to compatibility. This is precisely because it represents a reliable layer between bytecode and the concrete tool operating instructions, translated at runtime.Over the years, the Java language has undergone many changes and development. J2SE (Java 2 Standard interpretation) had its first form targeting GUIs, applets, and other basic and rather simple applications. Recently, the language was lengthy with the Java founte known as J2EE (Java 2 Enterprise Edition). This adaptation is based for server side development, and includes tools for database access, messaging, content rendering, inter-process communications, and transaction control 6, 8. J2ME (Java 2 Micro Edition) came into existence as to cover the needs for applications targeting sprightly eddys. As it can be seen from this short overview, there are versions of Java to suit different environments from the enterprise development tools intended for use in servers, to the little systems. An important thing to note at this point is that the separation between platforms is not just unconditional 7. Many times these are not a simple line than can be drawn. In order to demonstrate this, it might be explained that Java 2 Micro Edition development sometimes requires the use of Java 2 Enterprise Edition and Java 2 Micro Edition. This is the case with multiplayer games for instance, so and Java 2 Micro Edition is used for the client side, but Java 2 Enterprise Edition is used for the server side of the application/game. Moreover, different Java editions target different hardware configurations. Similarly, there are 3 virtual machines to be used for the different environments 8. For example, Hotspot VM is a evasion virtual machine suitable for a executing the full-scale edition of JavaHotspot. Jav aHotspot is a newer fibre of virtual machine competent of vigorously optimizing a spectacular deal of executed code (called as hotspots) during the runtime 8. Other versions of virtual machine are the Compact virtual(prenominal) Machine (CVM) and Kilobyte Virtual Machine (KVM). These are in essence smaller virtual machine implementations. They are targeted to run within the restrictions of the limited resources found on the small devices (these will be discussed later in this section, as well).The requirement of having another version (like the Java 2 Micro Edition) for the mobile devices came because these devices do not have sufficient recourses to run Java 2 Standard Edition, since J2SE was distinctly way excessively large to tot on even the big micro devices. However, the question was imposed initially was which features should be left out from the J2SE, so to be minimized in a smaller edition. Also, having great diversity of different devices, it would not have been a nic e decision to restrict all the J2ME applications to the lowest compatible hardware configuration 8, 9. Moreover, this tooth root would not have been practical as well, because it would incorrectly neglect the capabilities of the higher end devices. The final ancestor is comprehended through a confection of J2ME configurations and profiles 10. It represented a revised Java architecture, which actually offers for the leaving out of parts of the platform, at the same time as addition to device and category precise components. Along these lines, the configuration would identify the abilities of a Java platform intended for use on a sequence of homogeneous hardware. Possible components that can be removed are the following 9, 11Java language mechanismsmallest amount hardware necessities, such as the memory, cover song size, and processor power for the family of devicesintegrated Java librariesBy utilizing this approach, there are actually 2 preset configurations for mobile devices o ne for somewhat curtail devices such as PDAs and Set-Top-Boxes (for instance the digital TV receivers), and another one for devices such as pagers and mobile phones.These two configurations are 9, 10, 11CDC (Connected Device Configuration)CLDC (Connected, express mail Device Configuration)All of these configurations are to be reviewed as follows. On the other hand, a good example of java profiles is the UI (User Interface) for mobile phones. For example, the J2ME configuration CLDC that wraps this type of device, keeps out the typical Java UI libraries (AWT and Swing). The devices do not have the ability of presenting anything derived from these libraries in any case. This is due to the fact that their screens are just too small. Thus, there is no point to slaughtering valued space on them. The solution was to generate an innovative User Interface, fitting to the exact necessities of the poor mobiles liquid crystal display display. The consequential LCD UI is built-in in the CLDC profile. This targets MIDs (Mobile Information Devices), for this reason the name is MIDP.The CDC is built for bigger devices such as digital TV set-top-boxes and PDAs. These are devices characteristically with numerous space of memory. The CDC is the bigger brother of the J2ME configurations. It encloses a single profile (the Foundation profile) as well as a high performance virtual machine (known as the Compact Virtual Machine CVM). This Java language implementation, as well as the API, practically has all the influence of J2SE.Unluckily, the CDC is not accessible on the platform for the most micro-game players (the mobile phones).The CLDC is especially targeted to micro devices, like mobile phones. It fundamentally defines a standard, which in turn is used by all the device manufacturers that put into benefit a Java run-time environment. This enhances third-party development, because this same standard is being utilized. The CLDC configuration was unquestionable as part of the Java Community Process (JSR-30) 10, 11. It affects many aspects of Java development and delivery, which include 7, 8Target device distinctivenessThe security formApplication administrationLanguage dissimilarityJVM variationsBuilt-in class librariestalking about the security model, the J2SEs offered protection system was too big to fit within the restrictions of the CLDC target platform. It might be stated that by itself it would in all probability have gone beyond all accessible memory 7. Therefore, the limited model removed many of the functionalities. This in turn requires far less resources. But nevertheless, this overview made it greatly simpler for wrapping all the fine points. Basically, there are two major parts to the CLDC security model 8, 9.Virtual machine securityApplication securityThe modified security model for the CLDC, also provides some significant foundation for the application execution models. The intent of the virtual machine protection layer is to defend the underlying device from any harm that an executable code could probably do. With the usual conditions, a bytecode verification process is performed. This should be done preceding any code execution. This verification physical process basically authenticates a class-file bytecode. Thus in turn ensures that the code is safe for execution. Very important here is that incorrect instructions or corrupted memory outside the Java environment, will be eliminated and protected, as well. This process is very light as well. It only consumes 50 KB of code space additionally to 100 KB of heap. However, one might argue that even though light and insignificant on larger systems, it is still a good space when mobile devices are taken into consideration. Taking into consideration the notion of Application Security, the class-loader verification procedure (mentioned in this section) is very much limited as well.