罗大佑有歌云:“无聊的日子总是会写点无聊的歌曲……”,我不是歌手,我是程序员,于是无聊的日子总是会写点无聊的程序。程序不能太大,不然没有时间完成;程序应该有趣,不然就达不到消磨时间的目的;程序应该有那么一点挑战性,不然即使写完了也没有进步。

金钩钓鱼游戏是我儿时经常玩的一种扑克牌游戏,规则非常简单,两个玩家,一旦牌发到手里之后,接下来每个人出什么牌基本上已经就定了,玩家没有自己做决策的机会,所以这个游戏很容易用程序自动模拟出来。

 

(一)关于金钩钓鱼游戏

基本规则(简化版):两个玩家(Player),一副扑克(Deck),大小王(Joker)可要可不要,我们的游戏假定包含大小王,洗牌(Shuffle)之后,每个玩家得到同样数目的牌(27张),玩家任何时候不能看自己手里的牌,玩家依次出牌,每次出一张,轮到自己出牌时,抽出自己手中最底下的一张牌放到牌桌(Board)上,牌桌上的牌按照玩家出牌的顺序摆成一条长链。J(钩)是最特殊的一张牌,当某个玩家出到J时,便将牌桌上的所有牌都归为己有,并放到自己牌池的最上面(与出牌时恰恰相反),此即所谓“金钩钓鱼”,此时牌桌清空,再由此玩家重新出牌。另外,当自己出的牌与牌桌上的某张牌点数相同时,便将牌桌中那张牌及其之后的牌都归为己有(包含自己刚出的那张),再由此玩家重新出牌,比如牌桌上的牌为3,7,8,4,9,当某个玩家出了8,便将牌桌上的8,4,9连同自己刚出的8一并收回,派桌上剩下3,7。最后,谁手中的牌最先出完,谁就输了。

 

(二)对于一副牌的建模

由于花色(Suit)对于此游戏并不重要,所以对扑克牌建模时省略了对花色的建模,同样,由于不需要比较大小,牌的点数(Rank)可以用String来表示(其中王用”W”表示)。

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package com.thoughtworks.davenkin.simplefishinggame;

public class Card {
    private String rank;

    public Card(String rank) {
        this.rank = rank;
    }

    public String getRank() {
        return rank;
    }
}
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一副扑克(Deck)由54张牌组成:

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package com.thoughtworks.davenkin.simplefishinggame;

import java.util.ArrayList;
import java.util.Collections;

public class Deck {
    ArrayList<Card> cards = new ArrayList<Card>();

    public Deck() {
        buildDeck();
    }

    private void buildDeck() {
        buildNumberCards();
        buildCard("J");
        buildCard("Q");
        buildCard("K");
        buildCard("A");
        buildJokerCard();
    }

    private void buildJokerCard() {
        cards.add(new Card("W"));
        cards.add(new Card("W"));
    }

    private void buildNumberCards() {
        for (int rank = 2; rank <= 10; rank++) {
            buildCard(rank);
        }
    }

    private void buildCard(int rank) {
        for (int index = 1; index <= 4; index++) {
            cards.add(new Card(String.valueOf(rank)));
        }
    }

    private void buildCard(String rank) {
        for (int index = 1; index <= 4; index++) {
            cards.add(new Card(rank));
        }
    }

    public ArrayList<Card> getCards() {
        return cards;
    }

    public void shuffle() {
        Collections.shuffle(cards);
    }
}
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Deck不仅包含54张牌,还定义了洗牌(shuffle)等方法。

 

(三)对玩家的建模

玩家(Player)有自己的名字和自己手中所剩的牌,最重要的是出牌(playCard)成员方法:

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package com.thoughtworks.davenkin.simplefishinggame;

import java.util.ArrayList;
import java.util.List;

public class Player {
    ArrayList<Card> cards = new ArrayList<Card>();
    String name;

    public Player(String name) {
        this.name = name;
    }

    public String getName() {
        return name;
    }

    public ArrayList<Card> getCards() {
        return cards;
    }

    public void obtainCards(List<Card> cardsToAdd) {
        cards.addAll(cardsToAdd);
    }


    public void playCard(Board board) {
        board.addCard(cards.get(0));
        System.out.println(name + " played " + cards.get(0).getRank());
        board.displayCards();
        cards.remove(0);
    }

    public void displayCards() {
        System.out.print("Cards for " + name + ": ");
        for (Card card : cards) {
            System.out.print(card.getRank() + " ");
        }

        System.out.println();

    }

}
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游戏开始需要发牌,专门定义了一个CardDistributor来发牌,每个玩家得到相同数量的牌。当然,发牌动作应该在洗牌之后:

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package com.thoughtworks.davenkin.simplefishinggame;

import java.util.List;

public class CardDistributor {

    public void distributeCards(Deck deck, List<Player> players) {
        int cardsPerPlayer = deck.getCards().size() / players.size();
        int startIndex = 0;
        for (Player player : players) {
            player.obtainCards(deck.getCards().subList(startIndex, cardsPerPlayer + startIndex));
            startIndex += cardsPerPlayer;
        }
    }
}
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玩家在出牌时,需要将自己手中的一张牌转移到牌桌上(Board),而当Player出牌之后,牌桌应该确定是否有将被Player“钓”进的牌,于是在Borad中还定义了getCardsToBeFished方法:

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package com.thoughtworks.davenkin.simplefishinggame;

import java.util.ArrayList;
import java.util.List;

public class Board {
    ArrayList<Card> cards = new ArrayList<Card>();

    public ArrayList<Card> getCards() {
        return cards;
    }

    public void addCard(Card card) {
        cards.add(card);
    }

    public List<Card> getCardsToBeFished() {
        if (cards.size() == 1)
            return null;

        List<Card> cardsToBeFished;
        Card lastCard = cards.get(cards.size() - 1);
        if (lastCard.getRank().equals("J")) {
            cardsToBeFished = cards;
        } else {
            cardsToBeFished = getCardsOfRangeFishing(lastCard);
        }
        return cardsToBeFished;
    }

    public void displayCards() {
        System.out.print("Current cards on board:");
        for (Card card : cards) {
            System.out.print(card.getRank() + " ");
        }
        System.out.println();
    }

    public void removeFishedCards(List<Card> cardsToBeFished) {
        int endIndex = getCards().indexOf(cardsToBeFished.get(0));
        ArrayList<Card> newCards = new ArrayList<Card>();
        newCards.addAll(cards.subList(0, endIndex));
        cards = newCards;
    }

    private List<Card> getCardsOfRangeFishing(Card lastCard) {
        int startIndex = -1;
        for (Card card : cards) {
            if (card == lastCard)
                break;
            if (card.getRank().equals(lastCard.getRank())) {
                startIndex = cards.indexOf(card);
            }
        }

        if (startIndex != -1)
            return cards.subList(startIndex, cards.indexOf(lastCard) + 1);
        return null;
    }
}
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(四) 对整个游戏的建模

整个游戏定义了一个FishingManager来集中管理,FishingManager包括所有玩家,牌桌等成员变量。

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package com.thoughtworks.davenkin.simplefishinggame;

import java.util.ArrayList;
import java.util.ListIterator;

public class FishingManager implements FishingRuleChecker, AfterPlayListener {
    ArrayList<Player> players = new ArrayList<Player>();
    private Player currentPlayer;
    Board board;
    private ListIterator<Player> iterator;

    public FishingManager() {
        board = new Board();
    }

    private void resetPlayerIterator() {
        iterator = players.listIterator();
    }

    public void addPlayers(ArrayList<Player> players) {
        this.players.addAll(players);
        resetPlayerIterator();
    }

    @Override
    public Player nextPlayer() {
        if (iterator.hasNext()) {
            return iterator.next();
        }
        resetPlayerIterator();
        return nextPlayer();
    }

    @Override
    public Player whoFailed() {
        ListIterator<Player> listIterator = players.listIterator();
        while (listIterator.hasNext()) {
            Player currentPlayer = listIterator.next();
            if (currentPlayer.getCards().size() == 0)
                return currentPlayer;
        }

        return null;
    }

    @Override
    public void afterPlay() {
        if (board.getCardsToBeFished() == null)
            return;
        doFish();
        nextPlayer();
    }

    private void doFish() {
        System.out.println(currentPlayer.getName() + " fished cards");
        currentPlayer.obtainCards(board.getCardsToBeFished());
        board.removeFishedCards(board.getCardsToBeFished());
        currentPlayer.displayCards();
        board.displayCards();
    }

    public void start() {
        int count = 0;
        while (true) {
            currentPlayer = nextPlayer();
            currentPlayer.displayCards();
            currentPlayer.playCard(board);
            afterPlay();
            count++;
            if (whoFailed() != null) {
                break;
            }
        }

        System.out.println(whoFailed().getName() + " has failed.");
        System.out.println("Total: " + count + " rounds");
    }

    public static void main(String[] args) {
        FishingManager manager = new FishingManager();
        Player player1 = new Player("Kayla");
        Player player2 = new Player("Samuel");
        ArrayList<Player> players = new ArrayList<Player>();
        players.add(player1);
        players.add(player2);

        Deck deck = new Deck();
        deck.shuffle();
        CardDistributor distributor = new CardDistributor();
        distributor.distributeCards(deck, players);

        manager.addPlayers(players);
        manager.start();
    }
}
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FishingManager还应该包含游戏规则,比如决定输赢和玩家出牌顺序等,于是定义一个游戏规则接口FishingRuleChecker,并使FishingManager实现FishingRuleChecker接口:

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package com.thoughtworks.davenkin.simplefishinggame;

public interface FishingRuleChecker {
    Player nextPlayer();
    Player whoFailed();
}
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同时,当每个玩家出牌之后,FishingManager应该决定是否有鱼上钩,并执行钓鱼操作,于是定义了一个AfterPlayListener接口,FishingManager也实现了
AfterPlayListener接口:

package com.thoughtworks.davenkin.simplefishinggame;

public interface AfterPlayListener {
    public void afterPlay();
}

 

(五)有趣的现象

运行FinshingManager便可以自动模拟整个游戏过程,笔者比较感兴趣的是:所有玩家一共出多少手牌之后游戏结束?于是笔者做了10000次模拟试验,得到的结果为:最大14023手,最小66手,平均1303手,请数学高手帮忙证明一下是否有个统计学意义上的期望值。出牌次数分布图如下:

上图中,横轴为游戏轮次(一共10000次),纵轴为每次游戏所对应的出牌手数。

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