chess evolution visualization

JOURNAL OF LATEX CLASS FILES, VOL. 6, NO. 1, JANUARY 2007 1

Chess Evolution VisualizationWei-Li Lu, Yu-Shuen Wang, and Wen-Chieh Lin

Abstract—We present a chess visualization to convey the changes in a game over successive generations. It contains a scorechart, an evolution graph and a chess board, such that users can understand a game from global to local viewpoints. Unlikecurrent graphical chess tools, which focus only on highlighting pieces that are under attack and require sequential investigation,our visualization shows potential outcomes after a piece is moved and indicates how much tactical advantage the player canhave over the opponent. Users can first glance at the score chart to roughly obtain the growth and decline of advantages fromboth sides, and then examine the position relations and the piece placements, to know how the pieces are controlled and howthe strategy works. To achieve this visualization, we compute the decision tree using artificial intelligence to analyze a game,in which each node represents a chess position and each edge connects two positions that are one-move different. We thenmerge nodes representing the same chess position, and shorten branches where nodes on them contain only two neighbors,in order to achieve readability. During the graph rendering, the nodes containing events such as draws, effective checks andcheckmates, are highlighted because they show how a game is ended. As a result, our visualization helps players understand achess game so that they can efficiently learn strategies and tactics. The presented results, evaluations, and the conducted userstudies demonstrate the feasibility of our visualization design.

Index Terms—Chess visualization, graph

F

1 INTRODUCTIONChess is one of the most popular two-player strategyboard games in the world. Players usually polishtheir chess skills, including strategy and tactics, byreading experts’ comments and play books. Giventhat computers have recently surpassed humans inplaying chess, modern artificial intelligence (AI) hasemerged as a helpful tool for analyzing the interactionof pieces and the evolution of a game. AI’s thoroughand deep searching enables the depiction of chesspositions after more than ten moves. Therefore, it iscapable of analyzing long-term positional advantagesof a game. However, all the current chess tools [1],[2] assist users in analyzing games by visualizingspatial information. For the example shown in Figure1, Arena indicates that the opposing black knight canbe captured (background in green); the white pawnmay be captured while it is protected by a castle(background in yellow); and the white knight will becaptured if nothing is done to prevent it (backgroundin red). The visualization also indicates the best twomoves for White to win in the current position usingarrows. Purple and light blue stand for the best andthe second best moves, respectively. As for the gameevolution, it simply describes a sequence of chessmoves using algebraic chess notation [3]. Hence, usershave to sequentially investigate the game and buildthe global strategies in mind to answer the questions

• W. L. Lu, Y. S. Wang, and W. C. Lin are with the Department ofComputer Science, National Chiao Tung University, Taiwan

E-mail: [email protected]: [email protected]: [email protected]

1 Nh4-f5+, Bd7xf5+, Kh6-h5, Rf3-h3+, Ng6-h4, Rh3xh4+, Kh5-g6, Rh4-h6+

2 Ng3-f5+, Bd7xf5, Nh4xf5+, Kh6-h5, Rf3-h3+, Ng6-h4, Rh3xh4+, Rh4-h6+

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Nh4xg6, h7xg6, c2-c3, Rg8-e8, h2-h3, Kh6-g7, Ng3-e2, c6-c5, d4xc5, Qc7xc5+, Ne2-d4, Qc5-b6, Rf3-f2, Bd6-c5, Rf1-d1, Bc5xd4, c3xd4, Qb6xd4, Bd3-c4, Re8-e1+, Rd1xe1, Qa5xe1, Rf2-f1

4 b2-b3, Ng6xh4, Rf3-f2, Qc7-a5, a2-a4, Qa5-c3, Ng3-e2, Qc3-d2, f4-f5, Qd2-g5, g2-g3, Qg5-e3, Kg1-h1

5 c2-c3, Ng6xh4, Rf3-f2, c6-c5, Bd3-e2, c5xd4, c3xd4, Qc7-b6, Rf1-d1, Qb6xb2, Be2-h5, Qb2-c3, Bh5xf7, Rg8xg3, h2xg3, h2xg3, Qc3xg2, Bf7xd5, Bd6xf4,

Fig. 1. (left) Current chess visualization tool (Arena[1]) focuses only on highlighting pieces that are underattack and step-by-step moves. (right) Long-term movesequences containing strategies can only be repre-sented using algebraic chess notation [3], which is verydifficult to understand.

such as ”Why does the player give up the game?”, ”Isthere a way to escape from king hunt?”, and ”Howdoes the player turn defeat into victory?”

We present an evolution visualization system toconvey subtle trends of a chess game. Thus, insteadof investigating chess positions sequentially, users areallowed to examine a chess game from global tolocal viewpoints. The analysis of a game is obtainedfrom recording and linking successive chess positionsmade by players, followed by utilizing AI to grow adecision tree from this recorded structure. Essentially,a decision tree is a directed graph, where each noderepresents a chess position and edges are the legalplies between two positions. An intuitive way tovisualize the chess evolution is to render the whole


decision tree. Yet numerous nodes and complex edgescan cause serious visual clutter. Furthermore, differentnodes in the tree may represent the same chess posi-tion, thus resulting in perceptual misleading. Thesereadability problems should be well handled in chessevolution visualization.

We conditionally simplify a game decision tree bymerging nodes that represent the same chess positionand then discarding nodes that have little correlationto the game evolution. The node merging revealschess position relations that are invisible in a decisiontree, while the node discarding achieves readability.Our system then renders the simplified graph in 2Dspace, where node locations are determined usingGraphViz [4], and edge thicknesses are computedbased on how good the chess move is. By highlightingthe nodes containing critical events, such as draws,effective checks and checkmates, this evolution graphshows the circumstance of each chess position, in-cluding potential advantages and disadvantages af-ter a number of moves. To convey the global trendthroughout a game, we also align a score chart, whichcontains the current score and the potential scorefluctuation with our evolution graph. This is doneto quantize the two players’ tactical advantages ateach move. By integrating these two global visualclues, our evolution visualization reveals potentialend positions of a game and answers why a playerwould consider giving up a game although there arestill many pieces left on the board.

Our technique leverages AI to analyze a chess gameand is capable of conveying the subtle trends tothe users. This global-to-local visualization enablesexperts to quickly obtain the overview and criticalevents that lead to winning or losing a chess game. Italso allows novice players to preview potential chesspositions in future moves to know how an opponentmay respond and learn how the strategy works. Toevaluate our technique, we compared our chess evo-lution graph to professional comments, existing graphvisualization designs, and current chess tools. We alsoconducted a user study with 21 participants, includingnovice players, experienced players, and an expert.Experimental results show that our visualization fitsthe tactical points raised by experts and is capable ofhelping players understand chess games efficiently.

2 RELATED WORK

Chess AI. AI long has been developed to play chess.Existing techniques focus on board evaluation andgame tree pruning. The former evaluates how gooda position is based on piece locations, tactics, kingsafety, board control, and passed pawns, etc. [5]. Thelatter strives to determine the best move by searchingthe minimal tree because exploring all possible movesis impractical. Therefore, alpha beta algorithm [6],[7], quiescence search [8], null-move pruning [9], [10],

[11], [12], and other selective enhancements [13] havebeen presented to avoid searching sub-trees that haveminimal tactical advantages. We refer the readers to[14] for more details, because our work focuses onevolution visualization.

Chess visualization. All current chess visualiza-tions focus on an instant instead of an overall evolu-tion of a game, even though the AI engines behind thesystems contain long-term tactical knowledge. Arena[1] and Fritz [2] show pieces that are under attack andstep-by-step piece moves to guide players in beatingtheir opponents. The thinking machine [15] sketchesinvisible thoughts of an AI to convey how the pro-gram searches for the best move based on the currentchess position. In contrast, our chess evolution graphshows all position relations throughout a game andhelps players predict future moves that an opponentmay use in respond, in order to enhance their chessskills.

Tree and Graph visualization. Trees and Graphsare often used to represent relations between entities.The visualization of these structures allows users todiscover intrinsic, hidden, non-trivial, and potentialvaluable knowledge [16]. The main difference of thesetwo structures is the existence of cycles. Generally,tree visualizations can be categorized according toedge representation, alignment, and dimensionality[17]. That is, explicit representations clearly showconnectivity using edges [18], [19] while implicit onesfocus on data hierarchy [20]. The layout could beradial [18], [19], [21] or axis-parallel [22], [23]; the for-mer places the root at the center and grows childrennodes outward, whereas the latter maps tree levelsparallel to one axis and span the structure to another.Finally, trees could be rendered in 2D or 3D spaces.In contrast to tree visualizations, where cycles do notexist, algorithms developed to graph visualizationsstrive to minimize crossovers and edge wiggles [24],[25], [26] with the purpose of enhancing readabilityand aesthetics. Moreover, plenty of navigation andclustering techniques are presented to improve spaceefficiency due to visual clutter in high complexitygraphs. On the one hand, navigation approaches [27],[28] magnify regions of interest while shrinking ordiscarding the rest to show graph details. On theother hand, clustering methods [29] show the maintrunk of a graph by hiding nodes and edges that areless important. Both categories of methods reveal onlypartial information due to the limitations of humancognitive ability.

Time-varying data visualization. A large amountof research works have been presented that focus ontime-varying data analysis and visualization. Theseworks attempted to reveal temporal trends of theunderlying data by transforming the data into visualmeans for exploring complex relations. Some studieswere presented to handle scientific imaging [30], [31].Some of them applied dynamic graphs to information


visualization [32], [33], [34]. They showed changesof state over time while preserving the mental mapand achieving good aesthetic quality. Although theseworks can be utilized to visualize relations over suc-cessive generations, they were not designed to conveydecisions and the induced events in a chess game.Therefore, they are not sufficient in visualizing chessevolutions and helping players polish their chessskills.

Storyline visualization. Storyline visualization isa technique that is often used to convey sequentialrelational information. Each entity is represented asa narrow line going from left to right as time goesby and are grouped together if the entities haveinteractions. Kim et al. [35] developed a visualiza-tion system for genealogical data, which facilitatesthe identification of marriages, parent-child relations,siblings, and cousins over time. Ogawa and Ma [36]presented a technique to visualize software projectevolution and to depict the scale and revisions ofdevelopment to viewers who are not familiar with theproject. Cui et al. [37] introduced a TextFlow methodto convey complex relations among topic evolutiontrends, critical events, and keyword correlations sothat people can know well current affairs. Reda et al.[38] presented a social network visualization methodto reveal gradual changes of community structuresover a period of time, thus allowing analysts to un-derstand the formation, evolution, and dissolution ofcommunities.

Our chess evolution visualization can also be con-sidered as a kind of storyline visualization. However,its complexity is much higher than that of a generalstoryline visualization, because many potential chesspositions after successive moves can be identified. Inaddition, our system conveys high level tactics andstrategies computed by AI, which is very helpful infacilitating chess learning.

3 DESIGN METHODOLOGY

The goal of our graph design is to reveal chess gameevolutions. It ought to show potential chess positionsafter successive moves and highlight events such asdraws, effective checks, and checkmates. The checks thatlead to a worse position are neglected. For clarity, weuse position to represent a game instant and location toindicate where a node is placed in the latter part ofthis paper.

Given that a position contains many piece locations,it is challenging to simultaneously show both spatialand sequential information of a game. This prob-lem becomes even worse when offense and defensein a game is complex. Thus, we focus on showingsequential relations of chess positions and pointingout the successive moves achieving either tangiblegain or loss. Apart from the evolution graph, oursystem additionally provides a chess board for the

reference of piece placements. It shows how the piecesare controlled after a graph node is clicked. Ourinteractive interface also allows the examination of thechess board and the evolution graph on the fly so thatusers can realize game strategies easily.

Our system leverages an AI engine called Stockfish1

to analyze a chess game and generate its evolutiongraph. That is, we record the sequence of chess po-sitions made by players throughout a game and feedthem into the chess engine to compute for the decisiontree. This is followed by branch pruning, node merg-ing, and branch shortening. To achieve an insightfulanalysis, the depth of the decision tree in our systemis set to 20, which has the grandmaster chess level andis able to predict the chess positions after 10 moves2.Once the decision tree is determined, we pick up 4to 9 move sequences that take larger advantages fromthe opponent at each position and discard the remainsbecause we assume that the goal of a player is to beatthe opponent. Specifically, suppose the player’s moveappear in the nth best sequence from a position. Wepick the 1st to 4th best sequences if n ≤ 4, the 1st

to nth best sequences if 4 < n ≤ 8, and the 1st to8th best sequences plus the sequence that containsthe player’s move if n ≥ 9. The consideration toonly eight best sequences is based on more than 250game play analyses in the GBR-ch tournament 20073,where the eight best sequences contain 93.4% of thepiece moves made by players; taking the remaining6.6% moves would lead to much worse positionsand eventually lose the game. Note that all the realchess positions made by players are retained in thetree. Mistakes leading to failure are presented in ourevolution graph.

3.1 Evolution graph generationOur system computes a directed graph that revealstactical knowledge from a decision tree and conveysa chess game evolution. We focus on the chess po-sitions made by players and visualize potential po-sitions they may achieve. The tree usually containsduplicated notes because a decision tree only spanspotential moves at each node but neglects the factthat different move sequences may lead to an identicalchess position. In addition, considering general chessgames have 40 moves on average, rendering all theselected move sequences at each chess position wouldresult in serious visual clutter (Figure 2.a). To preventthis problem, we merge the duplicated nodes (Fig-ure 2.a→b) and shorten the branches (Figure 2.b→c)where the nodes on them have no events and containonly a parent and a child. We also compute node loca-tions using GraphVis [4] to minimize edge crossingsand achieve readability in our visualization. Hence,

1. http://stockfishchess.org/2. Each move contains two plies, one for White and one for Black.3. http://www.angelfire.com/games3/smartbridge/


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Fig. 2. (a) The evolution of a chess endgame is com-puted using Stockfish engine and stored in a decisiontree. Chess positions and legal plies are represented innodes and edges, respectively. Chess positions playedby players and containing events are highlighted usingour visual encodings (Section 3.2). (a)→(b) Our sys-tem merges the nodes representing the same chessposition to reveal position relations. (b)→(c) We alsoshorten branches where nodes on them have only twoneighbors to achieve readability. Notice that the nodesthat are highlighted or adjacent to those highlightedpersist during our graph simplification.

this evolution graph allows users to easily trace nodesvia directed edges and foresee potential chess posi-tions in the future. For example, in Figure 2.c, thenodes filled with white are the chess positions atwhich White can check Black, whereas the nodes filledwith white and a red crown are the chess positionsat which White can checkmate Black. Detailed visualencodings of nodes and edges are described in Section3.2 and Figure 3. By tracing the evolution graph, onecan easily identify that White will dominate the gameeventually because many nodes derived from the firstmove show the Black’s king is checked or checkmated.

Graph simplification. An intuitive way to mergeduplicated nodes is to compare all pairs of arbitrarynodes in a tree and merge them together if piece loca-tions on the nodes are identical. The process repeatsuntil nodes in the tree are all different (Figure 2.b).Given that the cost of this brute force strategy is ex-

pensive, we apply the hash table technique presentedby Hyatt and Cozzie [39] to reduce the number ofcomparison and speed up the merging process. Theedges are re-directed whenever nodes are merged toform the evolution graph. The position relations of achess game are then revealed. However, in Figure 2.b,there are some move sequences in the graph, wherenodes have only a parent and a child. These sequencesshow that the subsequent game evolution is simpleand can be shortened if there are no events on them(Figure 2.c). Namely, only nodes that have events orhave more than two children will persist. Given thatour visualization focuses on the chess positions madeby players, their moves are also retained in the graph.

Graph layout. Our system computes the 2D loca-tion of each node to visualize the evolution graph.This graph is expected to extend from left to right asthe move number increases and to spread potentiallocations in the vertical direction. The edges are thenrendered according to the determined node locations.Specifically, we apply GraphVis [4] to compute anevolution graph G = {V,E}, where vi = {xi, yi} ∈ Vis the node location and {i, j} ∈ E is a directed edgefrom node i to node j. This tool first determines theorder of each node in the horizontal direction fh(v)and then the order in the vertical direction fv(v). Forthe connected nodes i and j, if their horizontal ordersare not adjacent, i.e., |fh(vi)− fh(vj)| > 1, it inserts avirtual node from order min{fh(vi), fh(vj)}+1 to ordermax{fh(vi), fh(vj)}−1 and connects the inserted andthe original nodes to form a chain. As a result, thestraight arrow from vi to vj can be replaced by anarrow on a Bezier curve, in which the virtual nodesserve as the control points, thus enhancing flexibilityand reducing edge crossing. After that, the objectivefunction is optimized to determine node locations.That is, ∑

{i,j}∈E

kijωij |vi − vj |, subject to

|va − vb| ≥sa + sb

2+ d, where

kij =

1 if both i and j are virtual nodes2 if one of i and j is a virtual node8 if both i and j are real nodes

, (1)

ωij = 5 × 104 if both node i and node j are chesspositions made by players and ωij = 104 other-wise, a and b are nodes with fh(va) = fh(vb) and|fv(va)−fv(vb)| = 1, sa and sb are the radii of node aand node b, respectively, and d is a constant parameterdenoting the shortest distance between nodes. Clearly,the edge with a larger kijωij would be shorter after theoptimization because the accumulated energy growsrapidly if the corresponding edge length |vi − vj |increases. Considering short and straight edges arepreferable in achieving readability, we set kij to alarger value if either of its connecting node is visible.We also set ωij to a larger value if the move from i to


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The position is in draw.

White gives a check to Black.

Black gives a check to White.

White gives a checkmate to Black.

Black gives a checkmate to White.

The turn for White to control armies.

The turn for Black to control armies.

One move to the next position.

Several moves to the next position.

Fig. 3. Our system renders an evolution graph to convey potential positions throughout a chess game (left). In thisgraph, the actual moves made by users and the virtual moves estimated by AI are represented using circles andsquares, respectively. We show the detailed meaning of each primitive at the right table. Notice that the primitivescould be combined for additional meanings. For example, a white solid circle with a black border means Whitegives a check to Black and it is the turn for Black to react. In addition, directed edges connecting nodes arerendered in either solid or dotted arrows to indicate a single move or multiple moves, respectively. Furthermore,the thicker the arrow is, the better position the move achieves. To better understand a game evolution, we alsolabel a move number in those nodes made by players (the main trunk) to represent the game progression.

j is made by players so that people can trace players’moves sequentially without frequently switching at-tention. Finally, parameter d controls the spaciousnessof nodes, which is set to 0.5 in all our experiments.

We utilize GraphViz to minimize Equation 1, whichconsiders node distances and edge chain straightnessduring optimization. For more details, we refer thereaders to the directed graphs drawing techniquepresented by Gansner et al. [40].

3.2 Evolution graph rendering

We render the evolution graph to convey the subtletrend of a game, where its x coordinate shows themove number, while the y coordinate indicates thespread of potential chess positions. The nodes con-taining events, such as draws, effective checks andcheckmates, are highlighted. We also label a movenumber in the nodes that represent chess positionsmade by players, in order to show the progression of agame. Finally, darkseagreen is selected as backgroundcolor to achieve a harmonic viewing experience andenhance the contrast in the evolution graph.

Visual encoding of a node. Fundamentally, thereare three design principles in our node appearance toachieve readability. 1) Circles and squares are used torepresent positions made by players and computedby the chess engine, respectively. 2) Black and whiterepresents the side that has advantage. Specifically,the boundary color shows the turn to control armies.The solid color shows the side that enjoys the event.In the case of a tie position, the node is filled with

gray. 3) The chess position indicating that the kingwill be captured is additionally filled with a redcrown icon. Therefore, based on the composition ofthe mentioned principles, we come up with a setof nodes representing different kinds of meanings asshown in Figure 3 (right). The two examples shownbelow illustrate how the composition works.

The node filled with white and a red crown iconmeans White gives a checkmate to Black. The blackboundary shows that it is Black’s turn to respond.

The node filled with black and a red crown iconmeans Black gives a checkmate to White. Given thatthis node is computed using AI and does not actuallyhappen in a game, for a clear visualization, our systemdoes not indicate the side that can control armies, asexplained in the next paragraph.

We highlight draws, effective checks, and check-mates because the ultimate goal in chess is to capturethe opposing king and prevent one’s own king frombeing captured. These events reveal potential endingsof a game and should be emphasized. Specifically, adraw or a checkmate shows a game result and aneffective check takes the advantage by enforcing theopponent trades either a piece or a worse positionfor the king. Our system highlights all graph nodescontaining events. However, the side that can con-trol armies is indicated only on the nodes made byplayers. All the predicted chess positions are renderedwith a black hallow square unless these positions havean event. We do so because the nodes computed bythe chess engine do not actually happen in a game.They can be abstracted to enhance the visual saliency


of real positions in a game.Visual encoding of an edge. We render directed

graph edges using solid and dotted arrows to con-nect two chess positions achieved by a move ora sequence of moves, respectively. We also rendersolid arrows with different thicknesses to indicate therelative gained advantage of a move compared withthe other moves starting from the same position. Thatis, good moves are rendered with thick arrows whilebad moves are rendered with thin ones. Let δij be thegained advantage from position i to position j, andmini be the minimal value of δij among edges comingout of node i, we compute the thickness of each edgeusing

wij =

{(log(δij −mini))2 if δij > miniα if δij = mini

, (2)

where α = 1 in all our experiments, followed by nor-malizing wij to a value within 1 and 30. A logarithmis used here because the gained values are typicallyamong [−30000, 30000]. Without this transformation,a serious mistake or a genius attack would resultin other moves that have smaller gained values in-comparable. Note that each normalization considersonly a small set of edges starting from node i, andthe thickness comparison between edges starting fromdifferent nodes are meaningless. We show an examplein Figure 3 for illustration.

3.3 Score chart

Given that the evolution graph represents potentialmoves at each chess position, we show a score chartat the bottom of the graph to reveal the quantizedpositional advantages of two players throughout agame. In this chart, the color of each primitive isused to indicate the side; its x coordinate is alignedwith the move number of the evolution graph; andits y coordinate shows the log value of the scorecomputed by the chess engine. Considering our goalis to convey a game evolution, the score chart containsnot only the actual advantage of players in each movebut also potential advantages they could obtain ifthey chose the other moves predicted by the engine.Here, we plot a circle on the chart to represent theactual score at the nth move made by a player. Torepresent the potential scores at the nth move thatthe player may obtain, we check the computed movesequences from the n − 1th to the nth move andrender a score band to show the fluctuation of theestimated player’s potential advantages. These scorebands are also rendered with translucency to preventocclusion. As a result, knowing how much loss amistake would cause and how likely to turn defeatinto victory becomes intuitive with the use of ourscore chart, as shown in Figures 6, 5, 7, and 8.

Fig. 4. Our system highlights the branches derivedfrom the 4th Black’s move so that users can trace themeasily.

4 RESULTS AND DISCUSSIONS

We implemented and tested our visualization systemon a desktop PC with Core i7 3.0 GHz CPU. The mostexpensive part of this visualization process is analysis,which may take up to 40 minutes to compute the deci-sion tree. Fortunately, this step can be precomputed inadvance. Meanwhile, our graph generation requires 3seconds on average, including node merging, branchshortening and node position determination, whichcan also be precomputed. Finally, the graph renderingis in real time. Our system allows users to interac-tively explore the changes in a game over successivegenerations to help them learn tactics and strategies.

Our system allows users to investigate a chess gameevolution from global to local viewpoints. It conveysinformation from growth and decline of tactical ad-vantages throughout a game globally, to position re-lations and potential events locally, which may occurwhenever a piece is moved. To trace position relations,users can click on the node of interest and our systemwould then enhance visual difference by reducing thecolor saturation of the nodes and edges that are notderived from this interested node (Figure 4). Besides,as some nodes are degenerated to dotted arrows afterthe branch shortening process, our system also allowsthe user to click on a dotted arrow, which wouldsmoothly transit the arrow to a sequence of nodes(see our accompanying video), thus enabling users toobserve detailed piece movements. Given that spatialpiece placements are also provided, users can goback and forth to examine the chess board and theevolution graph to know how the tactics work in agame.

We tested our chess evolution visualization on a va-riety of real-world examples, including chess puzzles,chess played by both humans, by both computers,and by a human and a computer. This interactivevisualization helps players gain a better understand-ing of a game because they can go back and forthto examine the potential chess positions and the suc-cessive moves responded by an opponent after thetactics are applied. Thus, users can understand whythe critical move leads a game to a loss or turnsdefeat into victory. To demonstrate the feasibility ofour visualization, we listed the professional comments


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Fig. 5. Our chess visualization shows the evolution of a game, wherein the top evolution graph conveys positionrelations and highlights critical events, while the bottom score chart reveals the advantages of the Black andWhite players. In this contest, Black once had a better position even though he is at the defense position.However, he eventually lost the game after making a number of mistakes in moves 9, 10, 12, 24, and 26.

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Fig. 6. Our evolution visualization shows that Whitekeeps the offense position until the 38th move. How-ever, he made a mistake and the game eventuallyended in a tie.

downloaded from a famous chess database4, whichverify that our system successfully highlights thetactical points. Please refer to the results shown inFigures 3–9, 7, 8, our supplemental materials andour accompanying video, especially when the piecemovements are difficult to visualize in still images.

4.1 Case StudiesCase 1: Moderate Player vs. Moderate Player. Figure5 shows a game played in World Open U2200. TheWhite and Black players are James Plaskett and SergeiShipov, respectively. Both are moderate players. Inthis game, our visualization reveals that White didnot play very well at the 9th and 10th moves becausethe passed arrows are relatively thinner than others.

4. http://www.chessbase.com/

Hence, the player lost his first hand advantage. Thealigned score chart also shows this fact. However, asBlack kept making faults at the 9th, 10th, 12th, 24th,and the 26th moves, White eventually dominated thegame. Notice that the passed arrows starting fromthe mentioned positions are relatively thinner thanthe computed ones. Our evolution graph also revealsthat the checkmate to Black is unavoidable after the27th move. The estimated positions with highlightedevents after this move explain the reason why Blackgave up the game. We show the original commentsfrom the annotator in our supplemental materials forthe reference.

Case 2: Expert vs. Expert. Figure 6 shows a gameplayed in Buenos Aires WCh. The White and Blackplayers are Jose Raul Capablanca and AlexanderAlekhine, respectively. Both players are experts. Inthis game, both players chose almost the best movesthroughout the game. Given that White is on theoffense, his tactical advantage is slightly over hisopponent’s before the 38th move. However, he madea mistake at the 38th move, and Black also caughtthe opportunity immediately to reach a draw, as wehighlight in the top image of Figure 6. The onlycomment from the annotator in this game is “A hugemissed opportunity and possible turning point of thematch. Blowing Alekhine off the board as White,Capablanca walks into a perpetual check on his finalmove. Simply 38. Ke2 instead of 38. Kf2 would havewon easily.”. This comment supports our highlights.

Case 3: Deep Blue vs. Kasparov. Figure 7 showsa world-famous game played by Deep Blue andGarry Kasparov, wherein the computer played asWhite and the chess grandmaster played as Black.This was the second game in the 1997 rematch. Inthis game, the 37th move played by Deep Blue wasso ingenious and considered counterintuitive. IBM


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Fig. 9. Our visualization points out the solution thatcan solve the chess puzzle even though it has to takesix successive moves to checkmate the Black’s king.Notice the chess positions represented using circles.

Corporation was then accused of cheating becauseKasparov considered that there must be superior in-telligence behind Deep Blue. However, as shown inFigure 7, today’s improved chess engine is capable ofdemonstrating the move to be the best during thatgame. Kasparov’s anxiety also made him commit anunprecedented mistake after the move and forfeit aposition that could have ended the match in a tie. Onecan also observe that the numbers of effective checksand checkmates to Black grew rapidly after the 38th

move, indicating that Deep Blue gradually controlledthe game. Hence, it came as no surprise that the chessgrandmaster eventually resigned.

Case 4: AI vs. AI. Figure 8 shows a blitz chessplayed by Stockfish and AnMon5 engines, where bothof them had only 5 seconds to respond and theywere not able to perform deep and thorough searchesduring a game. In this game, Stockfish played asWhite and AnMon played as Black. Our post anal-ysis revealed that computers did not make seriousmistakes even in such a time-constrained scenario be-cause they iteratively increased the spread and depthof the searching space while humans might miss someimportant pieces. As Stockfish was at the offenseposition and its chess level was higher than that ofAnMon, it was not surprising that White dominatedthe game from the first move and Black eventuallysurrendered. Besides, by zooming to the graph, onecan observe that Black did not play well when its kingwas under attack at the 28th and 33rd moves, whichaccelerated the game’s conclusion.

Case 5: Chess Puzzle. Figure 9 demonstrates theevolution graph of the chess puzzle shown in Figure1. The goal of this puzzle is to play as White andgive a checkmate to Black within six moves. One canobserve that in Figure 1, there are so many piecesleft on the chess board and White does not dominatethe game at that position. Considering there are somany potential chess positions, finding six successivemoves to checkmate Black is very difficult. However,by observing our evolution graph, it is now easier toknow that there is a way to checkmate Black’s kingby successive checks. Suppose White makes a correct

5. http://wbec-ridderkerk.nl/html/details1/AnMon.html

decision at each position (white circular nodes), Blackhas only one legal move in return and eventually theking is checkmated. Although it is difficult to find thecheckmate sequence, our visualization points out thesolution clearly.

4.2 LimitationsOur chess visualization focuses on the evolution ofa game. It shows the potential positions and tacticaladvantages after successive moves. Users, however,must still examine the piece placements to understandhow an event occurs and how a strategy works.Thus, we claim that our system is not presentedto replace existing chess GUIs but to complementthem. We believe that fusing our evolution graph andpiece placements seamlessly would greatly help usersunderstand chess tactics and strategies. In addition,this framework visualizes present chess games, wherethe potential chess positions are precomputed. Thus,we plan to extend our chess evolution visualizationsystem, which can dynamically update the graphstructure based on user’s query while minimizingunpleasant visual artifacts.

5 EVALUATIONS

5.1 Comparison to visualization designsAn important key to learn chess tactics is to forecastpotential positions and to predict how an opponentmay respond in successive generations. Therefore, agood chess evolution visualization should be ableto help players understand what would happen insuccessive moves and how a certain position couldbe reached. Given that current chess tools such asArena [1] and Fritz [2] focus on spatial piece place-ments, using this kind of visualization, it is difficultto interpret chess position relations after successivegenerations because users have to memorize all pieceplacements in each step. In contrast, using graph visu-alization, in which nodes with events are highlightedand sequential node relations are indicated, users areallowed to trace connecting arrows and then obtainthe results when making decisions. Generally, theremay be some graph designs that can be used toshow chess evolutions. For example, the graph couldhave: 1) a simplified or full structure, 2) an implicitor explicit representation, 3) a radial or axis parallelalignment, and 4) a 2D or 3D appearance. In thepresented system, we adopt a simplified graph thatenhances visual clearance, an explicit representationwith edges that depicts position relations, an axisparallel alignment that allows obtaining game stageseasily, and a 2D appearance that is free from occlusion.Furthermore, our visualization is carefully designed tofit the demands of chess evolution visualization. Thetheoretical analysis below shows the advantages.

Radial vs. Axis-Parallel. We choose the axis-paralleldesign to visualize the chess evolution because the


evolution is nearly sequential and it seldom reverses.For example, only few players move back the piecesand the captured pieces cannot be taken back. Thischaracteristic is verified in our results, which indicatethat almost all edges follow a left to right direction.The only exception in our experimental results is the39th move in Figure 6 because the game falls intothe state of threefold repetition. Given that the axis-parallel layout matches the concept of most chessevolutions, we confirm that our design is intuitive andis sufficient in revealing the changes in a game oversuccessive generations. Although a radial graph lay-out may also achieve the aim, this design inevitablyintroduces many edge intersections because chesspositions that have similar move numbers are po-tentially connected. While branches extend outwardbut in different directions, those connected nodesare placed far away from each other. Therefore, itbecomes more difficult to traverse sequential movesand foresee the potential chess positions after a certainposition using this layout. In addition, due to lengthydistances between the connected nodes, users haveto switch their attention frequently when investigat-ing the graph structure. Our supplemental material(ModerateRadial.pdf ), which shows the radial layout ofthe graph in Figure 5, verifies that the design is notcapable of conveying game evolutions.

Full vs. Simplified. Rendering the full tree wouldresult in serious visual clutter because of the complexstructure. Specifically, a chess game has 40 actualmoves on average, and a chess position in a decisiontree usually has eight potential move sequences topredict future tactical advantages (Section 3.1). Toverify the difficulty of discovering a game evolutionfrom an unsimplified structure, we show the fulldecision tree of Figure 7 in our supplemental material(DeepBlueFull.pdf ) for comparison.

Implicit vs. Explicit. Given that our goal is topresent relations among chess positions, it is impor-tant to have an explicit representation with edgesthat clearly shows how a chess position is achieved.Implicit ones, such as a treemap that focuses onhighlighting hierarchy, is not appropriate.

2D vs. 3D Although 3D visualization provides anadditional dimension for data exhibition, most infor-mation visualizations are achieved in 2D due to flatdisplays. While the graph structure might be complex,this strategy also prevents node and edge occlusions,thereby allowing users to trace chess positions easily.

5.2 Comparison to current chess visualization

Some chess visualization tools have been presentedto help players better understand a chess game andpolish their chess skills. The most popular tools areArena [1] and Fritz [2], both of which focus on spatialpiece locations, while their main difference is the useof different AI engines. Our system has the same

rationale but cuts into the point from sequential rela-tions of chess positions. Considering that both Arenaand Fritz visualize a chess game in a similar way,and Arena is an open source project but Fritz is acommercial one, we mainly compared Arena to oursystem.

To understand a chess game using Arena, userscould click forward, backward, and input a movenumber to inspect the position with correspondingpiece locations, move indications, and highlights tothose pieces that are under attack. Clearly, the visual-ization in this tool focuses on the spatial relations ofpieces. The long-term evolutions are conveyed usingalgebraic chess notation [3], which are difficult tounderstand. Under this circumstance, users have toinvestigate chess positions sequentially and memorizewhat has happened previously in each step, in orderto understand the changes in a game over successivegenerations. Users also have to pay attention to multi-ple paths from a junction that lead to different resultsupon examination. Therefore, getting wise to a chessstrategy using Arena is difficult and time consuming.

In contrast, our visualization is designed to conveythe sequential relations of chess positions. Users canpan and zoom into the evolution graph so as toobserve its topology while examining events, advan-tages, and piece placements of the interesting nodes.To understand a chess game, users can also trace con-necting arrows of our graph to obtain the following: 1)the success or failure, 2) the involved chess positions,and 3) the potential weak points of a strategy basedon the graph connectivity. They can then investigatepiece locations by clicking a small number of nodesto obtain piece placements and fully interpret thestrategy. Given that not all potential chess positionsafter the start of a strategy is involved, which is notnecessarily investigated, and the sequential relationsof chess positions are shown, the global-to-local view-points allows users to become more familiar with achess strategy easily.

5.3 User study

We conducted a user study to verify the feasibilityof our chess evolution visualization. We designed amultiple-choice questionnaire according to the sug-gestions of a chess expert. A total of 21 participantswere asked to answer the evolutional questions byinvestigating our visualization system and Arena [1].These participants came from diverse backgroundsand their ages ranged from 23 to 32 years. About67% were novice players. They were aware of chessrules but had only little game experience. Given thatno participants had used our system and only few ofthem were familiar with Arena, they were trained touse both systems before the study. Each training tookabout 10 minutes, i.e., 5 minutes for instruction and 5minutes for practice.


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Questionnaire. The participants were asked to an-swer two sets of questions, where each set contained 8questions; each set of questions were answered basedon the help from our system and Arena, respectively.The questionnaire included the move number to com-plete a chess puzzle, the judgment of tactical advan-tages among players, the critical moves leading to awin or a loss, and the chance to turn defeat into vic-tory. Some of the questions related to local events andcan be answered by observing highlights on a singlechess position; some were about long-term tactics andrequired participants to investigate successive chesspositions before providing their answer. We refer thereaders to the user study questionnaire attached inour supplemental materials for more details.

Environment. To achieve a fair study, both theinterfaces were displayed on a 27-inch screen with theresolution of 1920×1080; the chess engines behind thetwo GUIs were identical; two sets of the questionswere the same but with different orders and phras-ings. Furthermore, answering the sets of questionsassisted by different graphical interfaces was done in arandom order. We also asked the participants to takea 10-minute break before answering the second setof questions to avoid bias. All the user studies wereperformed in a quiet room, and each questionnairetook a participant about 50 minutes on average. Wealso found that most participants did not know thetwo sets of questions were the same until we toldthem the truth.

Results. We collected the answering time, error, andpreference of each user during the study. Figure 10shows the box and whisker plot to depict the an-swering time, and the bar chart to represent the meancorrect rate. As can be seen, by using our visualizationsystem, users took less time to answer questions butachieved higher correct rates. This phenomenon wasmore obvious in the 2nd to 5th questions because

the questions related to global evolution. While usingArena requires sequential investigation, answeringthese questions was difficult and time consuming.In contrast, our visualization shows the entire trendof a game in a 2D space, thus making it easier tofind out the key moves that result in winning orlosing a game. Regarding the 6th to 8th questions, theparticipants were asked to examine a number of chessgames, but the questions were about local events, theadvantage of our system was slightly weakened inthis scenario because the answers could be figuredout in less than five moves. Finally, as for the 1st

question, the goal was to find sequences that can endthe game in two moves, our evolution visualizationonly slightly outperforms Arena because the questionwas very simple. However, the mean correct rate andthe answering time still showed that our visualizationwas much better than Arena even in terms of findinglocal events and strategies.

The hypothesis in the user study is that our chessevolution graph outperforms Arena in terms of bothcorrect rate and answering time. We apply the Re-peated Measures Analysis of Variance (RM-ANOVA)to analyze these two factors and verify the hypothesisafter the study. As shown in Table 1, the reported post-hoc comparisons are significant at the p < 0.08 level.

Preference. Participants were asked to fill out sat-isfaction surveys after completing the questionnaire.The survey contained multiple areas, including in-tuitive interface, enjoyment, easy of use, efficiency,and helpfulness in teaching chess. The ratings rangedfrom 1 to 5, where 1 indicated totally disagree and5 indicated totally agree. Figure 11 shows the ratingsfor both techniques. As can be seen, our visualizationsystem is preferable compared with the traditionalchess interface due to its global-to-local investigationmanner.

We also asked for comments from the participants.


question 1 2 3 4 5 6 7 8p-value (time) 1.3 ×10−3 1.7 ×10−3 4.7×10−7 1.0 ×10−3 4.1 ×10−3 7.1 ×10−2 2.9 ×10−5 6.0×10−6

p-value (correct rate) 7.7 ×10−2 4.6 ×10−5 3.8 ×10−3 3.5×10−6 1.2 ×10−2 6.4 ×10−3 1.5 ×10−2 1.8 ×10−2

TABLE 1The significance values with respect to time and correct rate in our user study

They confirmed the quality and the feasibility of thisnew visualization system. Some participants did notget used to our design in the beginning because theyhad used traditional graphical interface for years.Nevertheless, in the end, they were very happy to seethis new tool as they found that the global perspectiveof conveyance provided to be very useful. They thenpreferred our visualization because investigating theentire chess game step by step was no longer neces-sary, and the graph structure provided a much moreintuitive way to point out successive moves comparedwith the algebraic notation sequences. For example,they could browse the bottom score chart to obtainthe overall growth and decline of players’ advantageswith respect to the move number, and then check thethickness of each arrow to determine whether or notthere was another better move from the position ofinterest. Finally they were able to trace the branches topredict the outcome of successive moves. The seniorplayers especially liked the highlights provided for ef-fective check events because many checks often resultin a worse position, which might be traps setup bythe opponent. Generally, after using our system for awhile, most players agreed that our new visualizationdesign is useful. Some chess teachers also lookedforward to the system suitable for young childrenbecause our current evolution graph was still abstractto them. Thus, we consider involving these juniorplayers in the development and the evaluation of aproduction-level system in the near future.

Summary. Our conducted user study and the col-lected user preferences highly support the fact that thepresented chess evolution visualization is sufficient inrevealing long-term strategies in a game. Specifically,participants took less time but got higher correctrate when utilizing our visualization to answer thequestions related to global evolution. These resultsare not surprising because the trend of a chess gameis disclosed in our evolution graph and a sequentialinvestigation is not needed. Moreover, users can fore-see potential events in the future and examine spatialpiece movements to help them easily understand theinterested tactic.

6 CONCLUSIONS

We have presented a chess evolution visualizationsystem, which enables the user to understand a gamefrom a global-to-local viewpoint. This visualizationconveys the change over successive moves using agraph, in which the x and y coordinates represent the

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move number and the spread of potential positions,respectively. Given that sequential examination of achess game is not necessary, experts can check ourvisualization to quickly understand the overview andcritical events of a chess game. Furthermore, noviceplayers can preview potential chess positions in futuremoves to predict how an opponent may respond andto learn chess tactics. The evaluation of our graphdesigns, the verification of professional commentsto our visualization results, and the conducted userstudy demonstrate the feasibility of our system.

We emphasize that our system focuses on sequen-tial relations among chess positions. To help thembe aware of a strategy, users still have to investigatespatial piece movements so as to fully understandhow the strategy works. Considering that users haveto switch their attention in between the evolutiongraph and the piece placements, which may interrupttheir thoughts, we plan to integrate the two kinds ofinformation seamlessly in our future work.

ACKNOWLEDGEMENTS

We thank the anonymous reviewers for their con-structive comments. We are also grateful to BenjaminHildreth for narrating the demo video, to Ke-JungChen for helping us edit the demo video, and toall the users who participated in the user study.This work was supported in part by the National


Science Council (101-2628-E-009-020-MY3, 102-2221-E-009-083-MY3, 101-2628-E-009-021-MY3, and 102-2221-E-009-082-MY3) and the UST-UCSD InternationalCenter of Excellence in Advanced Bioengineeringsponsored by the Taiwan National Science CouncilIRiCE Program (NSC-101-2911-I-009-101).

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Wei-Li Lu received the BS and MS degreesfrom the Department of Computer Scienceand Information Engineering, National Cen-tral University, Taiwan, in 2011, and from theDepartment of Computer Science, NationalChiao Tung University, Taiwan, in 2013, re-spectively. Now, he is working in FoxconnElectronics Inc. His research interests in-clude computer graphics and visualization.


Yu-Shuen Wang received the BS and PhDdegrees from the Department of ComputerScience and Information Engineering, Na-tional Cheng-Kung University, in 2004 and2010, respectively. He is currently an assis-tant professor of the Department of Com-puter Science at National Chiao Tung Univer-sity (http://people.cs.nctu.edu.tw/ yushuen/).He leads the Computer Graphics and Visu-alization Lab at the Institute of MultimediaEngineering. His research interests include

computer graphics, computational photography, and visualization.

Wen-Chieh Lin is an associate professor atthe Department of Computer Science, Na-tional Chiao Tung University, Taiwan. He re-ceived the BS and MS degrees in control en-gineering from National Chiao Tung Univer-sity, Hsinchu, Taiwan, in 1994 and 1996, re-spectively, and the Ph.D. degree in Roboticsfrom the School of Computer Science atCarnegie Mellon University, Pittsburgh, in2005. His research interests span severalareas of computer graphics and computer

vision. In particular, he is interested in physics-based animation, real-time rendering, and texture modeling and manipulation.

chess evolution visualization

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