Application of Greedy Algorithm in Exodia Deck in Yu-Gi-Oh! Trading Card Game

Transcription

1 Applicatin f Greedy Algrithm in Exdia Deck in Yu-Gi-Oh! Trading Card Game Luqman Faizlani Kusnadi Prgram Studi Teknik Infrmatika Seklah Teknik Elektr dan Infrmatika Institut Teknlgi Bandung, Jl. Ganesha 10 Bandung 40132, Indnesia luqmankusnadi@students.itb.ac.id Abstract Yu-Gi-Oh! Trading Card Game is a battlebased trading card game in which players draw cards frm their respective decks and take turns playing cards nt the field. The game usually played by tw players. The bjective f each player is t defeat his/her ppnent by reducing their life pints t zer r by using particular card s effect. Exdia deck is a ppular deck in this game. The bjective f this deck is t win a game by drawing cards as much as pssible until five parts f Exdia cards are in the player hand. This paper will cver an analysis f greedy algrithm t chse the right card in each sub-turn, until the bjective f this deck is achieved. Even thugh there are s many variatin f Exdia deck, we will nly use nly ne particular deck. - Index Terms Yu-Gi-Oh! Trading Card Game, Exdia, Greedy Algrithm. they are discarded, such as used spell cards r mnsters that are destryed in battle. [1] 4. Mnster Card Zne: A field f five spaces where Mnster cards are placed when successfully summned. [1] 5. Spell/Trap Card Zne: A field f five spaces where Spell and/r Trap cards are placed. [1] 6. Field Spell Zne: A designated zne where Field Spell cards are placed. [1] 7. Banished Zne: An unmarked zne utside f the play field in which cards that are designated as Banished by card effects are placed. [1] 8. Pendulum Znes: Tw znes in which Pendulum Mnsters can be placed fr the purpse f Pendulum Summning. [1] I. INTRODUCTION A. Yu-Gi-Oh! Trading Card Game Yu-Gi-Oh! Trading Card Game is a ppular card game develped and published by Knami. This game is based n fictinal game created by Kazuki Takahashi in his japanese cmic with the same title, Yu-Gi-Oh!. The game usually played by 2 players in single duel r 4 players in tag duel. The game is a battle-based trading card game in which players draw cards frm their respective deck and take turns playing cards nt the field. The bjective f each player is t defeat his/her ppnent(s) by reducing their life pints t zer using variety f Mnsters, Spells and Trap cards, r by using particular card effect. Each player starts with 8000 life pints. Sme games using 2000 r 4000 life pints instead f 8000 accrding t players agreement r turnament rules. The game field is divided int several znes, each zne has special functin. 1. Deck: The player s deck cnsisting f cards. [1] 2. Extra Deck: A side-deck cntaing up t 15 cards cnsisting f Fusin, Synchr, and/r Xyz Mnster cards, as well as destryed Pendulum Mnster cards. [1] 3. Graveyard: A zne in which cards are placed when Picture Yu-Gi-Oh! game field Each player turn, cnsist f 6 phases. Each phase has sme rule abut what the player shuld d r shudn t d in that phase. The phases has the fllwing rder. 1. Draw Phase: The turn player draws ne card frm his/her deck. 2. Standby Phase: This phase exists mstly fr card effects that activate r reslve during this specific phase. 3. Main Phase 1: The turn player may summn a mnster, activate cards and effects that they cntrl, change the battle psitin f a mnster, and set cards face-dwn. 4. Battle Phase: The turn player may attack the ppnent's mnsters, r Life Pints if the ppnent cntrls n mnsters, nce with each mnster they cntrl that is in Attack Psitin, while the ppnent may attempt t defend with their wn

2 mnsters, Spells, r Traps. If the turn player cntrls n mnsters, r chses t nt attack during the turn, they may skip this phase. 5. Main Phase 2: A player may d all the same actins that are available during Main Phase 1, except "nrmal summn" a mnster during this phase if they already did s during Main Phase 1. [1] 6. End Phase: much like the standby phase, is mstly used fr card effects that activate/reslve during this specific phase. [1] The game has 3 main card types. Each card type has it s wn rle in a duel. The card types are: 1. Mnster card: Can be used t attack the ppnent t reduce their life pints, defense against ppnent s mnster attack and destry ppnent mnster. Sme mnster als has it s wn effect like a Spell card. [1] 2. Spell card: Can be played either frm the hand, r set n the field fr later use. They can either pwer up mnster cards attack/defense, destry ther cards, increase life pints, draw cards, increase a mnster's level etc. [1] 3. Trap card: Cards that are activated in respnse t certain situatins, mst ften when an ppnent activates an effect r attacks. They are set face dwn n the field and cannt be activated n the turn they were placed dwn. [1] B. Exdia Deck Exdia deck is ne f the mst ppular deck in Yu-Gi- Oh! Trading Card Game. The main cards f this deck is 5 part f Exdia card, there are: 1. Exdia the Frbidden One. 2. Right Arm f the Frbidden One. 3. Left Arm f the Frbidden One. 4. Right Leg f the Frbidden One. 5. Left Leg f the Frbidden One. Picture 1.2 Five Exdia cards The text in Exdia the Frbidden One card said that, When yu have "Right Leg f the Frbidden One", "Left Leg f the Frbidden One", "Right Arm f the Frbidden One" and "Left Arm f the Frbidden One" in additin t this card in yur hand, yu win the Duel. The card s effect implies that we win the duel when we have all f the card abve in the hand. Basically, the bjective f this deck, is t draw cards as much as pssible until these five cards are in ur hand. There are s many variatin f Exdia deck ut there. One f the ppular deck variatin is using Ryal Magical Library card as the main engine. The text in this card said that, Each time a Spell Card is activated, place 1 Spell Cunter n this card (max 3). Yu can remve 3 Spell Cunters frm this card t draw 1 card. Basically, every 3 spell cards is activated, we can draw 1 card. This variatin usually als using Magical Citadel f Endymin card as the sub-engine. This card can supprt Ryal Magical Library by prviding additinal Spell Cunter fr the card t use the effect. Picture 1.3 Ryal Magical Library card (left) and Magical Citadel f Endymin card (right) We will use Exdia deck with this engine in ur analysis. A. Greedy Algrithm II. THEORIES Greedy Algrithm is a simple and straightfrward algrithm that is used t slve ptimizatin prblem. Optimizatin prblem here, can be a maximalizatin r minimizatin prblem. The principle f this algrithm is take what yu can get nw, that means, it will chse the best ptin that is available nw withut cnsidering future cnsequence. Greedy Algrithm creating slutin step by step. There are many chices that needs t be explred in every step f slutin. Therefre, the best chice must be made in every step. Every decicin that have been taken can t be altered in the next step. This algrithm apprach is make a decicin that seems will give the best chice, by chsing the lcal ptimum in every steps and hping it will reach the best slutin r glbal ptimum. Frmally, Greedy algrithm can be stated by the fllwing elments: 1. Candidate set, C The candidate set (C) is the set f all the elements that are pssibly will be the slutins. An element f this set may be a set as well. At each step in the algrithm, an element is taken frm this set and inserted int slutin set (S). 2. Slutin set, S The slutin set (S) is the set f elements that are selected thrughut the prcess f algrithm. This set, at the end f the prcess, will represents the

3 slutin f the prblem. As its elements are taken frm the candidate set (C), slutin set is a subset f candidate set. 3. Selectin functin Selectin functin are the functin that assigns values t slutin candidates in the candidate set and selects a candidate that has the best value (in terms f the prblem instance, maximum, fr example) and remves it frm candidate set. The selectin functin f greedy algrithm can be mre than ne, depending the prblem instance. 4. Feasibility functin Feasibility functin is the functin that tests whether the candidate selected by the selectin functin is feasible t put t the slutin set. Being feasible means that when it s cmbined with ther candidates in the slutin set, the new candidate des nt vilate any cnstraints that exists. A new candidate will be taken frm the candidate set by the selectin functin if the existing candidate is nt feasible t put t the slutin set. The prcess are t keep ging until n elements are left in the candidate set r until a certain gal r limit is reached by the slutin set. 5. Objective functin. The bjective functin is the functin that becme the gal f the slutin f the prblem. Typically, bjective functin can t be expressed in the cde, but rather becme the glbal gal f the cde itself. It makes the best glbal slutin (maximum r minimum). [2] Every greedy algrithm has the same general scheme. Generally, the scheme f greedy algrithm is: 1. Create an empty set as a slutin set (S). [2] 2. Chse a candidate (by using selectin functin) frm candidate set C [2] 3. Substract C with the chsen candidate frm the secnd step. [2] 4. Check using feasibility functin whenever the slutin set is feasible. If feasible add the candidate int slutin set. [2] 5. Check using bjective functin whenever the slutin set is cmplete If nt cmplete, repeat frm the secnd step. [2] Frm the descriptin abve, the pseud cde fr greedy algrithm generally: functin greedy (input C:candidate_set) himpunan_kandidat { Return the slutin f greedy ptimizatin prblem input: candidate set C utput: slutin set S with th same type as the candidate set} Declaratin: x : candidate S : slutin_set Algrithm: S {} { initialize S with empty set } while (nt SOLUTION(S)) and (C {} ) d x SELEKSI(C) {chse a candidate frm C} C C - {x} { remve that candidate frm candidate set} if FEASIBLE(S {x}) then S S {x} endwhile { SOLUTION(S) r C = {} } if SOLUTION (S) then return S write( n slutin ) III. PROBLEM ANALYSIS Yu-Gi-Oh! Trading Card Game is a cmplex game with many variatin in the term f gameplay r the card itself. T simplify this, we chse an Exdia deck as the main fcus f ur analysis. The Exdia deck itself has s many variatin. As we said befre we will even mre fcused ur analysis in Exdia deck with Ryal Magical Library card as the main engine. The deck is cnsist f the fllwing cards. Mnster cards: - 5 cards f Exdia parts - 3 Ryal Magical Library Spell cards: - 3 Magical Citadel f Endymin (Field spell card) - 1 One Day f Peace - 3 Upstart Gblin - 3 Terrafrming - 3 Brken Bamb Swrd - 3 Glden Bamb Swrd - 3 Dark Wrld Dealings - 3 Magical Mallet - 3 Relad - 3 Tn Table f Cntens - 1 Tn Wrld - 1 Pt f Duality - 2 Spell Pwer Grasp

4 Picture 3.1 The cmplete deck list T simplify ur analysis we nly cnsider all card s effect that has an effect n increasing r reducing the number f cards in the hand r the deck. S, any card effect like increase yur life pints by 1000, destry ppnent card and smething similar will nt be cnsidered. The card effect f all cards in the deck are: - Ryal Magical Library +1 cunter fr each activated spell card Remve 3 cunter, draw 1 card - Magical Citadel f Endymin +1 cunter fr each activated spell card Once per turn if Ryal Magical Library n the Mnster Zne, remve 3 cunter, draw 1 card - One Day f Peace; Upstart Gblin Draw 1 card - Terrafrming Add Magical Citadel f Endymin frm deck t the hand - Glden Bamb Swrd If Brken Bamb Swrd n the spell card zne Draw 2 cards - Dark Wrld Dealings Draw 1 card, remve 1 card frm hand - Magical Mallet; Relad Shuffle all card frm hand, and draw the same amunt - Tn Table f Cntent Add Tn Table f Cntent r Tn Wrld frm deck t the hand - Pt f duality Draw 3 cards, return 2 t the deck. - Spell Pwer Grasp +1 cunter t 1 card n the field Sme imprtant aspect t remember: - All spell cards except Magical Citadel f Endymin can nly be activated nce each card, after that that it sent t graveyard. - The effect f Ryal Magical library can be activated many times as lng as it has 3 cunters. - Ryal Magical Library can nly be summned nce per turn, due the rule f Yu-Gi-Oh! Trading Card Game. T even mre simplify ur prblem, we use an assumptin that ppnent act will nt affect ur cards, s, we can say that we play a game withut ppnent. We will use the fllwing term in ur analysis: - Turn: Turn is a player turn, in Yu-Gi-Oh! Trading Card Game, 1 turn is frm the draw phase until the end phase. - Sub-turn: Sub turn is every state after the activatin f card effect. The greedy strategy we use here, is t chse the card with the highest pririty in each sub-turn s we hpe that we can get all Exdia cards with as few turns as pssible. The pririty f each card is determined by the card functinality. Frmally, ur prblem can be stated as: 1. Candidate set The candidate set in ur prblem is a set f all card effect that can be activated during this sub-turn. 2. Slutin set The set f all activated cards effects until all Exdia cards in the hand. 3. Selectin functin Chse the card effect with the highest pririty, the pririty itself is determined by the card functinality and the state f cards n the field. 4. Feasibility functin Check whenever the card effect can be activated. 5. Objective functin The number f turn spent is minimum IV. APPLICATION Firstly, we implements the selectin functin, the selectin functin must determine each card pririty by cnsidering it s card effect. We use the fllwing rules in determining cards pririty: 1. The lwest pririty is cards with n effect f drawing r adding card frm the deck. In ur case, is Brken Bamb Swrd card and Tn Wrld card. 2. The secnd lwest pririty is card with the effect f adding the ther card frm the deck t the hand 3. The next pririty is cards effect with the effect f replacing card(s) in the with card(s) frm the deck. The cards is, Relad, Magical Mallet and Dark Wrld dealings. 4. The secnd highest pririty is a card with the effect f drawing card. In ur case, is Upstart Gblin card, One Day f Peace card, Glden Bamb Swrd and Ryal Magical Library drawing effect. 5. The highest pririty is the main engine f the deck. First ne is nrmal summning Ryal Magical Library and placing Magical Citadel f Endymin n the field card zne. The pseud cde fr the selectin functin is:

5 functin select (input C:candidate_set) himpunan_kandidat { Return the candidate with highest pririty frm candidate set C input: candidate set C utput: a candidate } Declaratin: Algrithm: fr each (candidate c in C) if(c.effect = NO_EFFECT) c.pririty = 1; if(c.effect = ADD) c.pririty = 2; if(c.effect = REPLACE) c.pririty = 3; if(c.effect = DRAW) c.pririty = 4; {c.effect = MAIN} c.pririty = 5; end fr return (candidate with highest pririty) After that, we implements the feasibility functin, the functin is quite simple as it fllw the rule f the game and card effect limitatin The rules are: 1. Nrmal summn can nly be invked nce per turn. 2. Ryal Magical Library drawing effect can nly be activated after it summned n the mnster card zne and when it has 3 cunters 3. Magical Citadel f Endymin draw effect can nly be activated when there is Ryal Magical Library n the mnster card zne. 4. Glden Bamb Swrd card s effect can nly be activated when there is Brken Bamb Swrd n the spell card zne. 5. Cards with the effect f adding ther card frm the deck can nly be activated when the card t be added still exist in the deck. The pseud cde fr feasibility functin is: functin feasible (input c:candidate, f: field) himpunan_kandidat { Return whenever the candidate is feasible r nt input :a candidate utput } Declaratin: :true, if the candidate set is feasible false, if the candidate set nt feasible Algrithm: if(c.effect = NORMAL_SUMMON) if(fied.isalreadynrmalsummn()) if(c.effect = DRAW) if(c.card = RyalMagicalLibrary) if(c.has3cunter and c.isonmnsterzne) if(c.card = MagicalCitadelfEndymin) if(c.has3cunter and f.mnsterzne. isexist(ryalmagicallibrary)) if(c.card = GldenBambSwrd) if(f.spellzne.isexist(brkenbambsw rd)) {c.effect = ADD} if(f.deck.isexist(c.effect.card)) The main greedy functin will be much alike the general greedy functin we described befre. With the difference, when n candidate is feasible, that s nt means there are n slutin, but, we g t the next turn, draw 1 card, and repeat all the step with additin f 1 card. This prcess stpped when all Exdia cards in the player hand. V. CONCLUSION Exdia deck is ne f the ppular deck in Yu-Gi-Oh! Trading Card Games. This deck bjective is t win a duel using Exdia cards effect. Greedy algrithm can be used in this kind f deck t minimize the number f turn spent in a game using this deck. By chsing lcal maximum we can draw as much as pssible card frm the deck until all five cards f Exdia part cllected. The slutin f this prblem using greedy algrithm is nt the best slutin if we can see the card sequence in the deck. But, because in the real game we can t see card sequence in the deck, the slutin can

6 be the best slutin depends n the selectin functin we describe. VI. ACKNOWLEDGMENT Luqman Faizlani Kusnadi as the authr wants t express his grateful thanks t Gd fr His blessing during the prcess f making this paper, deepest gratitude t Mr. Rinaldi Munir and Masayu Leylia Khdra, ST., as the lecturers f IF 2211 Strategi Algritma. REFERENCES [1] Yu-Gi-Oh! Trading Card Game Official Rulebk Versin 8.0. Knami Digital Entertainment. [2] Munir, Rinaldi, Diktat Kuliah IF2211 Strategi Algritma, Bandung [3] Retreived 16 Mei 2014 PERNYATAAN Dengan ini saya menyatakan bahwa makalah yang saya tulis ini adalah tulisan saya sendiri, bukan saduran, atau terjemahan dari makalah rang lain, dan bukan plagiasi. Bandung, 19 Mei 2014 Luqman Faizlani Kusnadi,