Simple Pazaak (Star Wars Card Game from Knights of the Old Republic)

Question

Pazaak is a card game from the Star Wars universe. It is similar to BlackJack, with two players pitted against each other trying to reach a total of twenty without going over. Each player has a "side deck" of four cards of their own that they can use to modify their score.

Leaderboard

As of 6/17/2015 @ 16:40 EDT

Edit: Neptor has been disqualified for cheating. Scores will be fixed as soon as possible...

1. N.E.P.T.R: ~424,000
2. The Cincinnati Kid: ~422,000
3. Nestor: ~408,000
4. Austin Powers: ~405,000
5. Bastila: ~248,000
6. Dumb Cautious Player: ~107,000
7. Dumb Bold Player: ~87,000

Mock Pazaak Cup Playoffs

Will be updated as soon as possible.

Round One - Nestor vs Bastila & Austin Powers vs The Cincinnati Kid

Round Two - Nestor vs Austin Powers & The Cincinnati Kid vs Bastila

Mechanics

Gameplay is done in turns. Player one is dealt a card from the main (house) deck. The house deck holds forty cards: four copies of one through 10. After being dealt a card, they can choose to end their turn and receive a new card next turn, stand at their current value, or play a card from their side deck and stand at the new value. After player one decides what they want to do, player two repeats the process.

Once both players have gone, the hands are evaluated. If a player bombed out (went over twenty), the other player will win, provided that they did not also bomb out. If a player chose to stand, and the other player has a higher hand value, the other player will win. If both players chose to stand, the player with the higher hand value will win. In the event of a tie, neither player gets the win.

Provided a winning condition is not met, play will repeat. If a player chose to end their turn, they will receive a new card and can make a new choice. If they chose to stand, or if they played a card from their side deck, they will not be dealt a new card and cannot choose a new action.

Play continues like this until one player wins the game. Games are played in best-three-out-of-five sets.

Why "Simple" Pazaak?

In the Star Wars universe, Pazaak involved gambling. While inclusion of such a system would add more of a dynamic to the game, it is a bit complicated for a first-time KoTH competition.

"Real" Pazaak side decks were also provided by the players themselves, and could include many different card options such as negative cards, positive-or-negative cards, flip cards, double cards, and tiebreaker cards. These would also make the game more interesting, but would require a gambling interface in place, and would require far more out of the competitors. In this Simple Pazaak game, each player gets the same side deck: two copies of one through five, from which four are randomly selected.

Depending on the success of this game, I may put forth the effort to develop an advanced version wherein which gambling and custom side decks are possible.

The Players

The players of this game will be bots designed by you. Each bot needs to extend the Player class, import the Mechanics package, and reside in the players package like so:

package Players;

import java.util.Collection;

import Mechanics.*;

public class DemoPlayer extends Player {

    public DemoPlayer() {
        name = "Your Name Here";
    }

    public void getResponse(int wins[], boolean isPlayerOne,
            Collection<Card> yourHand, Collection<Card> opponentHand,
            Collection<Card> yourSideDeck, int opponentSideDeckCount,
            Action opponentAction, boolean opponentDidPlay) {
        action = null;
        cardToPlay = null;
    }
}

Each round, the controller will call the getResponse method for your bot, unless your bot previously indicated that it wanted to stand. The getResponse method can set two properties: an action and a card to play. Action can be one of the following:

• END: Ends the turn and draws a new card next turn.
• STAND: Stays at the current hand value. Will not draw a card.
• PLAY: Plays a card from the side deck and then stands.

The card to play is obviously only of importance if you set the action to PLAY. It takes a Card object. If the Card object you pass to it does not exist in your side deck, your bot will STAND instead.

The parameters your bot receives each turn are:

• An array containing the wins of each player. wins[0] is Player 1's, wins1 is Player 2's (int[])
• Whether or not your bot is player one (boolean)
• A collection of the cards that you have been dealt thus far (Collection)
• A collection of the cards your opponent has been dealt thus far (Collection)
• A collection of the cards in your side deck (Collection)
• The number of cards remaining in your opponent's side deck (int)
• The action your opponent last made (Action) [Note: This will either be END or STAND, never PLAY]
• Whether or not your opponent played a card (boolean)

Bot Rules

Your bots may only use the information that is given to them via the getResponse method. They should not attempt to interact with any other class. They may write to a single file to store data between rounds. They may have any custom methods, properties, etc. as desired. They should run in a reasonable amount of time (if the program run is not practically instantaneous, I will notice something is wrong).

If you find some kind of exploit in the code, you will be rewarded for "turning yourself in." If I notice the exploit first, I will fix it, and you will get no reward.

Demos

The controller is not needed to write a bot, as everything is already explained in this post. However, if you wish to test, it can be found here: https://github.com/PhantomJedi759/simplepazaak Two basic bots are included. Neither should hold up well against an "intelligent" opponent, as they only choose between END and STAND. Here is a sample run of what they do:

New Game!
The standings are 0 to 0
Dumb Bold Player's Hand: []
Dumb Bold Player's new Hand: [2]
Dumb Bold Player has chosen to END
Dumb Cautious Player's Hand: []
Dumb Cautious Player's new Hand: [8]
Dumb Cautious Player has chosen to END
Dumb Bold Player's Hand: [2]
Dumb Bold Player's new Hand: [2, 8]
Dumb Bold Player has chosen to END
Dumb Cautious Player's Hand: [8]
Dumb Cautious Player's new Hand: [8, 3]
Dumb Cautious Player has chosen to END
Dumb Bold Player's Hand: [2, 8]
Dumb Bold Player's new Hand: [2, 8, 7]
Dumb Bold Player has chosen to END
Dumb Cautious Player's Hand: [8, 3]
Dumb Cautious Player's new Hand: [8, 3, 6]
Dumb Cautious Player has chosen to STAND
Dumb Bold Player's Hand: [2, 8, 7]
Dumb Bold Player's new Hand: [2, 8, 7, 6]
Dumb Bold Player has chosen to STAND
Dumb Cautious Player's Hand: [8, 3, 6]
Dumb Cautious Player has chosen to STAND
Dumb Bold Player has bombed out! Dumb Cautious Player wins!

Because these bots rely purely on the luck of the draw, their win-loss ratios can vary drastically. It will be interesting to see how skill can combat the luck of the game.

This should be everything you need! Go build some bots!

Clarification to Rules

The main deck is forty cards: 4x1-10 It is reshuffled at the beginning of each hand.

A player's side deck has four cards, selected randomly out of 2x1-5. The side deck persists between hands.

Hands are played in games for the best three-out-of-five. Bots are scored based on the total number of games won, and then by the total number of hands.

Matching is handled so that each player will have to play 100,000 games against every other player.

In the Pazaak Cup, elimination-style rounds will narrow down who the best Pazaak bot really is. Each pairing of bots will play for the best four-out-of-seven sets of 100,000 games. Whoever wins four will move up the ladder to the next opponent, and the losers will stay down to battle for sequential rankings. This style of gameplay is the most fair, as bots cannot "win-farm" certain opponents to compensate for lack of ability against others. The Pazaak Cup will be held on Friday, July 3, provided there are at least eight submitted bots. The winner will receive Correct Answer status and a starting bonus in Advanced Pazaak, which will hopefully be ready close to the same time as the Pazaak Cup is held.

Answer 1

The Cincinnati Kid

Try to make sure that we draw another card if we know we're losing, otherwise look at our side deck and the overall scores to decide what to do.

Updated to do a better job of handling situations where the opponent has already finished playing. In my own testing this now seems to be the best candidate again, at least for now.

package Players;

import java.util.Collection;

import Mechanics.*;

public class CincinnatiKid extends Player {

    public CincinnatiKid() {
        name = "The Cincinnati Kid";
    }

    private static boolean isDebug = false;

    private static final int BEST_HAND = 20;

    public void getResponse(int wins[],
                            boolean isPlayerOne,
                            Collection<Card> yourHand,
                            Collection<Card> opponentHand,
                            Collection<Card> yourSideDeck,
                            int opponentSideDeckCount,
                            Action opponentAction,
                            boolean opponentDidPlay)
    {
        int myValue = handValue(yourHand);
        int oppValue = handValue(opponentHand);

        if (oppValue > BEST_HAND) {
            logMsg("Opponent has busted");
            action = Action.STAND;
        } else if (myValue > BEST_HAND) {
            logMsg("I have busted");
            action = Action.STAND;
        } else if (myValue <= 10) {
            logMsg("I cannot bust with my next move");
            action = Action.END;
        } else {
            handleTrickySituation(myValue, oppValue, wins, isPlayerOne, yourHand, opponentHand,
                                  yourSideDeck, opponentSideDeckCount, opponentAction, opponentDidPlay);
        }

        if (action == Action.PLAY && cardToPlay == null) {
            logMsg("ERROR - Action is Play but no card chosen");
        }
        logMsg("My hand value is " + myValue + ", opponent is " + oppValue + ", action is " + action +
               ((action == Action.PLAY && cardToPlay != null) ? " a " + cardToPlay.toString() : ""));
    }

    int [] branchCounts = new int[12];

    public void dumpBranchCounts() {
        if (isDebug) {
            for (int i = 0; i < branchCounts.length; i++) {
                System.out.print("b[" + i + "]=" + branchCounts[i] + " ");
            }
            System.out.println();
        }
    }

    private void handleTrickySituation(int myValue, int oppValue,
                                       int wins[],
                                       boolean isPlayerOne,
                                       Collection<Card> yourHand,
                                       Collection<Card> opponentHand,
                                       Collection<Card> yourSideDeck,
                                       int opponentSideDeckCount,
                                       Action opponentAction,
                                       boolean opponentDidPlay)
    {
        dumpBranchCounts();
        logMsg("I am might bust");

        int STAND_VALUE = 18;
        int chosenBranch = 0;

        Card bestSideCard = findSideCard(myValue, yourSideDeck);
        int valueWithSideCard = myValue + (bestSideCard != null ? bestSideCard.getValue() : 0);

        if (bestSideCard != null && valueWithSideCard >= oppValue && valueWithSideCard > STAND_VALUE) {
            logMsg("Found a good card in side deck");
            action = Action.PLAY;
            cardToPlay = bestSideCard;
            chosenBranch = 1;
        } else if (opponentDidPlay || opponentAction == Action.STAND) {
            logMsg("Opponent is done");
            // Opponent is done, so get another card if I'm behind
            if (myValue < oppValue) {
                logMsg("I am behind");
                if (bestSideCard != null && valueWithSideCard >= oppValue) {
                    logMsg("My best side card is good enough to tie or win");
                    action = Action.PLAY;
                    cardToPlay = bestSideCard;
                    chosenBranch = 2;
                } else {
                    logMsg("My best side card won't do so I'm going to hit");
                    // No side card and I'm losing, so I might as well hit
                    action = Action.END;
                    chosenBranch = 3;
                }
            } else if (myValue == oppValue) {
                logMsg("Game is tied");
                logMsg("Looking for lowest card in the side deck");
                cardToPlay = findWorstSideCard(myValue, yourSideDeck);
                if (cardToPlay != null) {
                    action = Action.PLAY;
                    chosenBranch = 4;
                } else {
                    logMsg("Tied with no side cards - accept the draw");
                    action = Action.STAND;
                    chosenBranch = 5;
                }
            } else {
                logMsg("I'm ahead and opponent has given up");
                action = Action.STAND;
                chosenBranch = 6;
            }
        } else if (myValue < oppValue) {
            logMsg("I am behind and have nothing good in my side deck");
            action = Action.END;
            chosenBranch = 7;
        } else if (oppValue <= 10 && myValue < STAND_VALUE) {
            logMsg("Opponent is guaranteed to hit and I have a low hand, so take another");
            action = Action.END;
            chosenBranch = 8;
        } else if (myValue == oppValue && myValue >= STAND_VALUE) {
            logMsg("We both have equally good hands - stand and hope for the tie");
            action = Action.STAND;
            chosenBranch = 9;
        } else if (myValue < STAND_VALUE) {
            logMsg("I am ahead but have a low score");
            action = Action.END;
            chosenBranch = 10;
        } else {
            logMsg("I am ahead with a decent score");
            action = Action.STAND;
            chosenBranch = 11;
        }

        branchCounts[chosenBranch]++;
    }

    private double calcBustOdds(int valueSoFar, Collection<Card> myHand, Collection<Card> oppHand) {

        if (valueSoFar >= BEST_HAND) {
            return 1;
        }

        int remainingDeck = 40 - (myHand.size() + oppHand.size());
        int [] cardCounts = new int[10];
        int firstBust = BEST_HAND - valueSoFar;

        for (int i = 0; i < 10; i++) {
            cardCounts[i] = 4;
        }

        for (Card c : myHand) {
            cardCounts[c.getValue()-1]--;
        }

        for (Card c : oppHand) {
            cardCounts[c.getValue()-1]--;
        }

        int bustCards = 0;
        for (int i = firstBust; i < 10; i++) {
            logMsg("cardCounts[" + i + "]=" + cardCounts[i]);
            bustCards += cardCounts[i];
        }

        double retval = (double) bustCards / (double) remainingDeck;
        logMsg("Out of " + remainingDeck + " remaining cards " + bustCards + " will bust, or " + retval);
        return retval;
    }

    private Card findSideCard(int myValue, Collection<Card> sideDeck) {
        int valueNeeded = BEST_HAND - myValue;
        Card bestCard = null;
        if (valueNeeded > 0) {
            for (Card c : sideDeck) {
                if (c.getValue() == valueNeeded) {
                    return c;
                } else if (c.getValue() < valueNeeded) {
                    if (bestCard == null || c.getValue() > bestCard.getValue()) {
                        bestCard = c;
                    }
                }
            }
        }

        return bestCard;
    }

    private Card findWorstSideCard(int myValue, Collection<Card> sideDeck) {
        int valueNeeded = BEST_HAND - myValue;

        logMsg("Searching side deck for something with value <= " + valueNeeded);
        Card bestCard = null;

        for (Card c : sideDeck) {
            logMsg("Examining side card " + c.getValue());

            // Find the worst card in the deck, but not if it exceeds the amount left
            if (c.getValue() <= valueNeeded && (bestCard == null || c.getValue() < bestCard.getValue())) {
                logMsg("This is the new best side card");
                bestCard = c;
            }
        }

        logMsg("Worst side card found is " + (bestCard != null ? bestCard.getValue() : " n/a"));
        return bestCard;
    }

    private void logMsg(String s) {
        if (isDebug) {
            System.out.println("### " + s);
        }
    }

    private int handValue(Collection<Card> hand)  {
        int handValue = 0;
        for (Card c : hand) {
            handValue += c.getValue();
        }
        return handValue;
    }
}

Answer 2

Austin Powers

Austin Powers, as you might presume, likes to live dangerously. Unless someone has busted, or he can guarantee a win, he will always hit if he's behind, or has a better than 20% chance of not busting.

package Players;
import java.util.Collection;

import Mechanics.*;

public class AustinPowers extends Player {
    public AustinPowers() {
        name = "Austin Powers";
    }
    int MAX_VALUE = 20;
    public void getResponse(int wins[], boolean isPlayerOne,
            Collection<Card> yourHand, Collection<Card> opponentHand,
            Collection<Card> yourSideDeck, int opponentSideDeckCount,
            Action opponentAction, boolean opponentDidPlay) {
        action = null;
        cardToPlay = null;
        int myWins = isPlayerOne?wins[0]:wins[1];
        int oppWins = isPlayerOne?wins[1]:wins[0];
        int oppTotal = calcHand(opponentHand);
        int myTotal = calcHand(yourHand);
        boolean liveDangerously = ((oppTotal>=myTotal && opponentAction==Action.STAND) || opponentAction==Action.END) && myTotal<MAX_VALUE && canNotBust(yourHand,opponentHand,myTotal) && myWins<oppWins;

        if(myTotal==MAX_VALUE || oppTotal>MAX_VALUE || myTotal>MAX_VALUE ||(oppTotal<myTotal&&opponentAction==Action.STAND))
        {
            action = Action.STAND;
        }
        else if((opponentAction==Action.STAND&&hasGoodEnoughSideCard(yourSideDeck,myTotal,oppTotal))||hasPerfectSideCard(yourSideDeck, myTotal))
        {
            action = Action.PLAY;
        }
        else if(liveDangerously||betterThan20(myTotal, getDeck(yourHand, opponentHand)))
        {
            action = Action.END;
        }
        else
        {
            action=Action.STAND;
        }

    }

    private boolean hasGoodEnoughSideCard(Collection<Card> yourSideDeck,
            int myTotal, int oppTotal) {
        for(Card c: yourSideDeck)
        {
            if(MAX_VALUE>=myTotal+c.getValue()&&myTotal+c.getValue()>oppTotal)
            {
                cardToPlay=c;
                return true;
            }
        }
        return false;
    }

    private boolean betterThan20(int myTotal, int[] deck) {
        int deckSize=0;
        int nonBustCards=0;
        for(int i=0;i<10;i++)
        {
            deckSize+=deck[i];
            if(MAX_VALUE-myTotal>i)
                nonBustCards+=deck[i];
        }
        return (double)nonBustCards/(double)deckSize>0.2;
    }

    private boolean hasPerfectSideCard(Collection<Card> yourSideDeck,
            int myTotal) {
        for(Card c:yourSideDeck)
        {
            if(MAX_VALUE-myTotal== c.getValue())
            {
                cardToPlay = c;
                return true;
            }
        }
        return false;
    }

    private boolean canNotBust(Collection<Card> yourHand,
            Collection<Card> opponentHand, int myTotal) {
        if(myTotal<=10) return true;
        int[] deck = getDeck(yourHand, opponentHand);
        for(int i=0;i<MAX_VALUE-myTotal;i++)
            if(deck[i]>0)
                return true;
        return false;
    }

    private int[] getDeck(Collection<Card> yourHand,
            Collection<Card> opponentHand) {
        int[] deck = new int[10];
        for (int i = 0; i < 10; i++) {
            deck[i] = 4;
        }
        for(Card c:yourHand){deck[c.getValue()-1]--;}
        for(Card c:opponentHand){deck[c.getValue()-1]--;}
        return deck;
    }

    private int calcHand(Collection<Card> hand)
    {
        int ret = 0;
        for(Card c: hand){ret+=c.getValue();}
        return ret;
    }
}

Answer 3

Bastila

Bastila plays conservatively. To her, a 17 is just as good as a 20, and it's much better to stand short than bomb out.

package Players;

import java.util.Collection;

import Mechanics.*;

public class Bastila extends Player {

    public Bastila() {
        name = "Bastila";
    }

    public void getResponse(int wins[], boolean isPlayerOne,
            Collection<Card> myHand, Collection<Card> opponentHand,
            Collection<Card> mySideDeck, int opponentSideDeckCount,
            Action opponentAction, boolean opponentDidPlay) {


        action = null;
        cardToPlay = null;

        //Constants
        int stand = 17;
        int conservatism = 2;

        //Get some info
        int handVal = handValue(myHand);
        int expected = expectedValue(myHand);

        //Can I play from my side deck?
        for(Card side: mySideDeck){
            int total = side.getValue() + handVal;
            if(total >= stand && total <= 20){
                cardToPlay = side;
                action = Player.Action.PLAY;
            }
        }
        if(action == Player.Action.PLAY){
            return;
        }

        //Otherwise, will I go bust?
        if(handVal + expected > 20 - conservatism){
            action = Player.Action.STAND;
        }
        else{
            action = Player.Action.END;
        }

        return;

    }

    private int handValue(Collection<Card> hand) {
        int handValue = 0;
        for(Card c : hand){
            handValue += c.getValue();
        }
        return handValue;
    }

    private int expectedValue(Collection<Card> hand){
        //Net value of the deck is 55*4 = 220
        int total = 220;
        int count = 40;
        for(Card c : hand){
            total -= c.getValue();
            count--;
        }
        return total/count;
    }

}

Answer 4

Nestor

Nestor loves getting 20 using his side deck, but when that fails he calculates his expected payoff by choosing stand or end, assuming that the opponent is sensible.

package Players;

import java.util.Arrays;
import java.util.Collection;


import Mechanics.Card;
import Mechanics.Player;

public class Nestor extends Player {
    final int TotalWinPayoff = 10;
    final int TotalLosePayoff = 0;
    final int TotalDrawPayoff = 1;
    final int temporaryLosePayoff = 4;
    final int temporayWinPayoff = 19;
    final int temporaryDrawPayoff = 9;
    @Override
    public void getResponse(int[] wins, boolean isPlayerOne,
            Collection<Card> yourHand, Collection<Card> opponentHand,
            Collection<Card> yourSideDeck, int opponentSideDeckCount,
            Action opponentAction, boolean opponentDidPlay) {

        int sumMyHand = SumHand(yourHand);
        int sumOpponentHand = SumHand(opponentHand);
    if (sumOpponentHand>20)
    {this.action = Action.STAND;return;}
        if(sumMyHand == 20)
        {
            //I'm unbeatable :)
            //System.out.println("\tI'm Unbeatable");
            this.action = Action.STAND;
            return;
        }
        else if(opponentDidPlay || opponentAction == Action.STAND)
        {
            //They've finished
            ///System.out.println("\tThey've Finished");
            if(sumMyHand>sumOpponentHand)
            {
                //I've won
                //System.out.println("\tI've Won");
                this.action = Action.STAND;
                return;
            }
            else if(canBeat(sumMyHand, sumOpponentHand, yourSideDeck))
            {
                //I can beat them
                //System.out.println("\tI can beat them");
                this.action = Action.PLAY;
                return;
            }
            else if(canEven(sumMyHand, sumOpponentHand, yourSideDeck))
            {
                //I can draw with them
                //System.out.println("\tI can draw with them");
                this.action = Action.PLAY;
                return;
            }
            else
            {
                //I need another card
                //System.out.println("\tI need another card");
                this.action = Action.END;
                return;
            }
        }
        else if(deckContains(yourSideDeck, 20-sumMyHand))
        {
            //Let's get 20
            //System.out.println("\tLet's get 20");
            this.action = Action.PLAY;
            this.cardToPlay = getCard(yourSideDeck, 20-sumMyHand);
            return;
        }
        else if(sumOpponentHand==20 && sumMyHand<20)
        {
            //They've got 20 so we need to fight for a draw
            //System.out.println("\tFight for a draw");
            this.action = Action.END;
            return;
        }

        else if(sumMyHand<10)
        {
            //Lets get another card
            //System.out.println("\tLet's get another card");
            this.action = Action.END;
            return;
        }
        else
        {
            //Let's work out some probabilities
            //System.out.println("\tLet's work out some probabilities");
            int[] cardsLeft = {4,4,4,4,4,4,4,4,4,4};
            for (Card card : opponentHand) {
                cardsLeft[card.getValue()-1] --;

            }
            for (Card card : yourHand) {
                cardsLeft[card.getValue()-1] --;

            }

             int numCardsLeft = sumfromToEnd(0, cardsLeft);

             //My Assumptions
             double probabilityTheyStand = (double)sumfromToEnd(20-sumOpponentHand, cardsLeft)/numCardsLeft;

             //What I need to know
             double payoffStanding = 0;
             double payoffDrawing = 0;


             for(int myChoice = -1; myChoice<10; myChoice++)
             {
                 for(int theirChoice = -1; theirChoice<10; theirChoice++)
                 {
                     if(myChoice == -1)
                     {
                         payoffStanding += getProbability(myChoice, theirChoice, Arrays.copyOf(cardsLeft, cardsLeft.length), probabilityTheyStand, numCardsLeft) * getPayoff(sumMyHand, sumOpponentHand,myChoice, theirChoice, TotalWinPayoff, TotalDrawPayoff, TotalLosePayoff);
                     }
                     else
                     {
                         payoffDrawing +=
                                 getProbability(myChoice, theirChoice, Arrays.copyOf(cardsLeft, cardsLeft.length), probabilityTheyStand, numCardsLeft)
                                 * getPayoff(sumMyHand, sumOpponentHand, myChoice, theirChoice, temporayWinPayoff, temporaryDrawPayoff, temporaryLosePayoff);
                     }
                 }
             }
            // System.out.println("\tStanding: " +Double.toString(payoffStanding) + " Ending: " + Double.toString(payoffDrawing));
             if(payoffStanding<payoffDrawing)
             {
                 this.action = Action.END;
             }
             else
             {
                 this.action = Action.STAND;
             }
        }


    }



    private int getPayoff(int sumMyHand, int sumOpponentHand, int myChoice,
            int theirChoice, int WinPayoff, int DrawPayoff,
            int LosePayoff) {
            if(sumMyHand + myChoice + 1 > 20)
            {
                if(sumOpponentHand + theirChoice + 1 > 20)
                {
                    return DrawPayoff;
                }
                else
                {
                    return LosePayoff;
                }
            }
            else if(sumMyHand + myChoice + 1 > sumOpponentHand + theirChoice + 1)
            {
                return WinPayoff;
            }
            else if (sumMyHand + myChoice + 1 < sumOpponentHand + theirChoice + 1)
            {
                return LosePayoff;
            }
            else
            {
                return DrawPayoff;
            }


    }



    private double getProbability(
            int myChoice, int theirChoice, int[] cardsLeft,
            double probabilityTheyStand, int numCardsLeft) {
        double myProb, theirProb;
        if(myChoice<0)
        {
            myProb = 1;
        }
        else
        {
            myProb = ((double)cardsLeft[myChoice])/((double)numCardsLeft);
            cardsLeft[myChoice]--;
            numCardsLeft--;
        }

        if(theirChoice<0)
        {
            theirProb = probabilityTheyStand;
        }
        else
        {
            theirProb = ((double)cardsLeft[theirChoice]) / ((double)numCardsLeft);
        }
        return myProb*theirProb;
    }





    private int sumfromToEnd(int i, int[] cardsLeft) {
        int toRet = 0;
        for(;i<cardsLeft.length; i++)
        {
            toRet += cardsLeft[i];
        }
        return toRet;
    }

    private boolean canEven(int mySum, int opponentSum,
            Collection<Card> yourSideDeck) {
        for (Card card : yourSideDeck) {
            if(mySum + card.getValue() <= 20 && mySum + card.getValue() >= opponentSum)
            {
                this.cardToPlay = card;
                return true;
            }
        }
        return false;
    }

    private boolean canBeat(int mySum, int opponentSum,
            Collection<Card> yourSideDeck) {
        for (Card card : yourSideDeck) {
            if(mySum + card.getValue() <= 20 && mySum + card.getValue() > opponentSum)
            {
                this.cardToPlay = card;
                return true;
            }
        }
        return false;
    }

    private Card getCard(Collection<Card> deck, int value) {
        for (Card card : deck) {
            if(card.getValue() == value)
            {
                return card;
            }
        }
        return null;
    }

    private boolean deckContains(Collection<Card> deck, int value) {
        for (Card card : deck) {
            if(card.getValue() == value)
            {
                return true;
            }
        }
        return false;
    }

    public Nestor()
    {
        super();
        name = "Nestor";
    }

    private int SumHand(Collection<Card> hand)
    {
        int toRet = 0;
        for (Card card : hand) {
            toRet += card.getValue();
        }
        return toRet;
    }
}

Answer 5

Glaucus

package Players;


import java.util.Collection;
import java.util.Collections;
import java.util.LinkedList;
import java.util.List;
import java.util.Random;

import Mechanics.Card;
import Mechanics.Player;

public class Glaucus extends Player {
    static final double LosePay = 0;
    static final double WinPay = 10;
    static final double DrawPay = 1;
    static final int NUMBEROFSIMS = 100;

    Random r;

    public Glaucus()
    {
        this.name = "Glaucus";
        r = new Random();
    }

    @Override
    public void getResponse(int[] wins, boolean isPlayerOne,
            Collection<Card> yourHand, Collection<Card> opponentHand,
            Collection<Card> yourSideDeck, int opponentSideDeckCount,
            Action opponentAction, boolean opponentDidPlay) {
        //Make Sum of hands
        int sumMyHand = 0;
        int sumOpponentHand = 0;
        //Make an array of the remaining cards
        List<Integer> cards = new LinkedList<Integer>();
        int[] cardsLeft = {4,4,4,4,4,4,4,4,4,4};
        for (Card card : yourHand) {
            cardsLeft[card.getValue()-1] -= 1;
            sumMyHand+=card.getValue();
        }
        for (Card card : opponentHand) {
            cardsLeft[card.getValue()-1] -= 1;
            sumOpponentHand += card.getValue();
        }
        if(sumMyHand<=10)
        {
            this.action = Action.END;
        }
        else if (sumMyHand >= 20)
        {
            this.action = Action.STAND;
        }
        else if (sumOpponentHand > 20)
        {
            this.action = Action.STAND;
        }
        else
        {
            for (int i = 0; i < cardsLeft.length; i++) {
                while(cardsLeft[i] > 0)
                {
                    cards.add(i + 1);
                    cardsLeft[i] -= 1;
                }
            }
            //System.out.println(Arrays.toString(cards));

            double standPayoff = 0;
            double endPayoff = 0;
            double[] sideDeckPayoffs = new double[yourSideDeck.size()];
            //Run some simulations
            for(int sim = 0; sim<NUMBEROFSIMS; sim++)
            {
                Collections.shuffle(cards, r);
                standPayoff += getPayoff(sumMyHand, sumOpponentHand, cards, Action.STAND, opponentAction, false, 0);
                endPayoff += getPayoff(sumMyHand, sumOpponentHand, cards, Action.END, opponentAction, false, 0);
                for(int i = 0; i<sideDeckPayoffs.length; i++)
                {
                    sideDeckPayoffs[i] += getPayoff(sumMyHand+((Card)yourSideDeck.toArray()[i]).getValue(), sumOpponentHand, cards, Action.STAND, opponentAction, false, 0);
                }

            }

            double maxSidePay = 0;
            int sideDeckChoice  = 0;
            for (int i = 0; i < sideDeckPayoffs.length; i++) {
                double d = sideDeckPayoffs[i];
                if(d>maxSidePay)
                {
                    maxSidePay = d;
                    sideDeckChoice = i;
                }
            }
            /*System.out.println(standPayoff);
            System.out.println(endPayoff);
            System.out.println(maxSidePay);*/

            if(maxSidePay>standPayoff && maxSidePay>endPayoff)
            {
                this.action = Action.PLAY;
                this.cardToPlay = (Card)yourSideDeck.toArray()[sideDeckChoice];
            }
            else if(standPayoff > endPayoff)
            {
                this.action = Action.STAND;
            }
            else
            {
                this.action = Action.END;
            }
        }
    }

    private double getPayoff(int sumMyHand, int sumOpponentHand,
            List<Integer> cards, Action myAction, Action opponentAction, boolean myTurn, int index) {
        //SHort circuit some logic
        if(sumMyHand>20 && sumOpponentHand>20)
        {
            return DrawPay;
        }
        else if(sumMyHand>20)
        {
            return LosePay;
        }
        else if(sumOpponentHand>20)
        {
            return WinPay;
        }
        else if(myAction == Action.STAND && opponentAction == Action.STAND)
        {
            if(sumMyHand>sumOpponentHand)
            {
                return WinPay;
            }
            else if(sumMyHand<sumOpponentHand)
            {
                return LosePay;
            }
            else
            {
                return DrawPay;
            }
        }
        else
        {
            double standPayoff = 0;
            double endPayoff = 0;

            if(myTurn)
            {
                if(opponentAction == Action.END)
                {
                    sumOpponentHand += cards.get(index);
                    index++;
                }
                if(myAction == Action.STAND)
                {

                    return getPayoff(sumMyHand, sumOpponentHand, cards, myAction, opponentAction, false, index);
                }
                else
                {

                    standPayoff = getPayoff(sumMyHand, sumOpponentHand, cards, Action.STAND, opponentAction, false, index);
                    endPayoff = getPayoff(sumMyHand, sumOpponentHand, cards, Action.END, opponentAction, false, index);
                    if(standPayoff>endPayoff)
                    {
                        return standPayoff;
                    }
                    else
                    {
                        return endPayoff;
                    }
                }
            }
            else
            {
                if(myAction == Action.END)
                {
                    sumMyHand += cards.get(index);
                    index++;
                }
                if(opponentAction == Action.STAND)
                {
                    return getPayoff(sumMyHand, sumOpponentHand, cards, myAction, opponentAction, true, index);
                }
                else
                {
                    standPayoff = getPayoff(sumMyHand, sumOpponentHand, cards, myAction, Action.STAND, true, index);
                    endPayoff = getPayoff(sumMyHand, sumOpponentHand, cards, myAction, Action.END, true, index);
                    if(standPayoff<endPayoff)
                    {
                        return standPayoff;
                    }
                    else
                    {
                        return endPayoff;
                    }
                }
            }
        }
    }
}

Glaucus makes 100 simulations with a shuffled list of cards and chooses his best option based on these simulations.

Answer 6

HK-47

Behold! A bot of my own design. HK-47 tries to kill all the meatbags he can, though he is a little trigger-happy with his side deck cards.

Statement: Indeed, I am most eager to engage in some unadulterated violence. At your command of course, Master. - HK-47

So far, he can beat everyone but The Cincinnati Kid.

package Players;

import java.util.Collection;

import Mechanics.*;

public class HK47 extends Player {

    /** The hand goal. */
    private static final int GOAL = 20;
    /** The cutoff for standing versus ending. */
    private static final int STAND_CUTOFF = 17;
    /** The minimum value for playing. */
    private static final int PLAY_MINIMUM = 14;
    /** The cutoff for ending versus decision evaluation. */
    private static final int SAFETY_CUTOFF = 10;

    /** The hand wins for this game. Used to evaluate win priority. */
    private int[] handWins;
    /**
     * My hand, as an unmodifiable collection. Used to evaluate decisions, after
     * being processed into myHandValue.
     */
    private Collection<Card> myHand;
    /**
     * Opponent's hand. Used to evaluate decisions as a secondary factor to my
     * hand, after being processed into oppHandValue.
     */
    private Collection<Card> oppHand;
    /** The value of my hand. Calculated via the myHandValue method. */
    private int myHandValue;
    /** The value of my opponent's hand. Calculated via the oppHandValue method. */
    private int oppHandValue;
    /** My side deck. Used to evaluate PLAY decisions. */
    private Collection<Card> mySideDeck;
    /**
     * The number of cards in my opponent's side deck. Used to evaluate PLAY
     * decisions as a secondary factor to mySideDeck, alongside win priority.
     */
    private int oppSideDeckCount;
    /**
     * The Action the opponent last took. Will either be STAND or END. Used to
     * evaluate decisions.
     */
    private Action oppAction;
    /** Whether or not I am player one. Used to evaluate wins and losses. */
    private boolean amPlayerOne;
    /**
     * The number of wins I have so far this game. Used to evaluate win priority
     * alongside myLosses.
     */
    private int myWins;
    /**
     * The number of losses I have so far this game. Used to evaluate win
     * priority alongside myWins.
     */
    private int myLosses;
    /**
     * How important it is for me to play. Positive values indicate an excess of
     * cards, and negative values indicate a deficit.
     */
    private int playPriority;
    /**
     * How important it is for me to win. Positive values indicate that I must
     * win the game, and negative values indicate that I can take some chances.
     */
    private int winPriority;
    /**
     * The sum of playPriority and winPriority. The higher the value, the fewer
     * chances I need to take.
     */
    private int priority;

    public HK47() {
        name = "HK47";
    }

    @Override
    public void getResponse(int[] wins, boolean isPlayerOne,
            Collection<Card> yourHand, Collection<Card> opponentHand,
            Collection<Card> yourSideDeck, int opponentSideDeckCount,
            Action opponentAction, boolean opponentDidPlay) {
        handWins = wins;
        amPlayerOne = isPlayerOne;
        myHand = yourHand;
        oppHand = opponentHand;
        mySideDeck = yourSideDeck;
        oppSideDeckCount = opponentSideDeckCount;
        oppAction = opponentAction;
        myHandValue = myHandValue();
        oppHandValue = oppHandValue();
        setStatistics();
        chooseOption();
    }

    /**
     * Calculates playPriority, winPriority, and priority.
     */
    private void setStatistics() {
        if (amPlayerOne) {
            myWins = handWins[0];
            myLosses = handWins[1];
        } else {
            myWins = handWins[1];
            myLosses = handWins[0];
        }
        playPriority = 0;
        winPriority = 0;
        if (mySideDeck.size() > oppSideDeckCount) {
            playPriority++;
        } else if (mySideDeck.size() < oppSideDeckCount) {
            playPriority--;
        }
        if (myWins < myLosses) {
            winPriority++;
        } else if (myWins == myLosses && myWins == 2) {
            winPriority++;
        } else if (myWins > myLosses && myWins != 2) {
            winPriority--;
        }
        priority = playPriority + winPriority;
    }

    /**
     * Chooses the appropriate option based on my hand, the opponent's hand, the
     * opponent's stance, my priority, and whether or not I can play to certain
     * values.
     */
    private void chooseOption() {
        // Path 1: Draw if at 10 or under.
        if (myHandValue <= SAFETY_CUTOFF) {
            action = Action.END;
            path = "1";
        }
        // Path 2: Draw if over 20.
        else if (myHandValue > GOAL) {
            action = Action.END;
            path = "2";
        }
        // Path 3: Stand if opponent over 20.
        else if (oppHandValue > GOAL) {
            path = "3";
            action = Action.STAND;
        }
        // Path 4: If opponent is at 20...
        else if (oppHandValue == GOAL) {
            // Path 4.1: Play if can reach 20.
            if (canPlayToGoal()) {
                action = Action.PLAY;
                path = "4.1";
            }
            // Path 4.0: Stand.
            else {
                action = Action.END;
                path = "4.0";
            }
        }
        // Path 5: If opponent is standing...
        else if (oppAction == Action.STAND) {
            // Path 5.1: If I am behind them...
            if (myHandValue < oppHandValue) {
                // Path 5.1.1: If I am at or above the minimum play value...
                if (myHandValue >= PLAY_MINIMUM) {
                    // Path 5.1.1.1: Play if can play.
                    if (canPlay()) {
                        action = Action.PLAY;
                        path = "5.1.1.1";
                    }
                    // Path 5.1.1.0: END
                    else {
                        action = Action.END;
                        path = "5.1.1.0";
                    }
                }
                // Path 5.1.0: END
                else {
                    action = Action.END;
                    path = "5.1.0";
                }
            }
            // Path 5.2: If I am tied with them...
            else if (myHandValue == oppHandValue) {
                // Path 5.2.1: If this game is important...
                if (priority > -1) {
                    // Path 5.2.1.1: Play if can play.
                    if (canPlay()) {
                        action = Action.PLAY;
                        path = "5.2.1.1";
                    }
                    // Path 5.2.1.0: STAND
                    else {
                        action = Action.STAND;
                        path = "5.2.1.0";
                    }
                }
                // Path 5.2.0 STAND
                else {
                    action = Action.STAND;
                    path = "5.2.0";
                }
            }
            // Path 5.0: STAND
            else {
                action = Action.STAND;
                path = "5.0";
            }
        }
        // Path 6: If opponent is not standing...
        else {
            // Path 6.1: If I am behind them...
            if (myHandValue < oppHandValue) {
                // Path 6.1.1: If they are at or above 17, and if this game is
                // important, play if can play to goal.
                if (oppHandValue >= STAND_CUTOFF) {
                    // Path 6.1.1.1
                    if (priority > 0 && canPlayToGoal()) {
                        action = Action.PLAY;
                        path = "6.1.1.1";
                    }
                    // Path 6.1.1.2
                    else if (priority > 0 && canPlayMax()) {
                        action = Action.PLAY;
                        path = "6.1.1.2";
                    }
                    // Path 6.1.1.0
                    else {
                        action = Action.STAND;
                        path = "6.1.1.0";
                    }
                }
                // Path 6.1.2: If I am above 14, play highest value card if can
                // play.
                else if (myHandValue > PLAY_MINIMUM) {
                    // Path 6.1.2.1
                    if (priority > -1 && canPlayToGoal()) {
                        action = Action.PLAY;
                        path = "6.1.2.1";
                    }
                    // Path 6.1.2.2
                    else if (priority > 0 && canPlayMax()) {
                        action = Action.PLAY;
                        path = "6.1.2.2";
                    }
                    // Path 6.1.2.0
                    else {
                        action = Action.STAND;
                        path = "6.1.2.0";
                    }
                }
                // Path 6.1.0
                else {
                    action = Action.END;
                    path = "6.1.0";
                }
            }
            // Path 6.2: If we are tied...
            else if (myHandValue == oppHandValue) {
                // Path 6.2.1
                if (myHandValue >= STAND_CUTOFF) {
                    // Path 6.2.1.1
                    if (priority > -1 && canPlayToGoal()) {
                        action = Action.PLAY;
                        path = "6.2.1.1";
                    }
                    // Path 6.2.1.2
                    else if (priority > 0 && canPlayMax()) {
                        action = Action.PLAY;
                        path = "6.2.1.2";
                    }
                    // Path 6.2.1.0
                    else {
                        action = Action.STAND;
                        path = "6.2.1.0";
                    }
                }
                // Path 6.2.2
                else if (myHandValue >= PLAY_MINIMUM) {
                    // Path 6.2.2.1
                    if (priority >= -1 && canPlayToGoal()) {
                        action = Action.PLAY;
                        path = "6.2.2.1";
                    }
                    // Path 6.2.2.2
                    else if (priority > -1
                            && canPlayMax()
                            && cardToPlay.getValue() + myHandValue >= STAND_CUTOFF) {
                        action = Action.PLAY;
                        path = "6.2.2.2";
                    }
                    // Path 6.2.2.0
                    else {
                        action = Action.END;
                        path = "6.2.2.0";
                    }
                }
                // Path 6.2.0
                else {
                    action = Action.END;
                    path = "6.2.0";
                }
            }
            // Path 6.0: If I am ahead of them...
            else {
                // Path 6.0.1
                if (myHandValue >= STAND_CUTOFF) {
                    // Path 6.0.1.1
                    if (priority >= -2 && canPlayToGoal()) {
                        action = Action.PLAY;
                        path = "6.0.1.1";
                    }
                    // Path 6.0.1.2
                    else if (priority > -2 && canPlayMax()) {
                        action = Action.PLAY;
                        path = "6.0.1.2";
                    }
                    // Path 6.0.1.0
                    else {
                        action = Action.STAND;
                        path = "6.0.1.0";
                    }
                }
                // Path 6.0.2
                else if (myHandValue >= PLAY_MINIMUM) {
                    // Path 6.0.2.1
                    if (priority >= -2 && canPlayToGoal()) {
                        action = Action.PLAY;
                        path = "6.0.2.1";
                    }
                    // Path 6.0.2.2
                    else if (priority > -2 && canPlayMax()
                            && cardToPlay.getValue() > 3) {
                        action = Action.PLAY;
                        path = "6.0.2.2";
                    }
                    // Path 6.0.2.3
                    else if (priority > -2
                            && canPlayMax()
                            && cardToPlay.getValue() + myHandValue > STAND_CUTOFF) {
                        action = Action.PLAY;
                        path = "6.0.2.3";
                    }
                    // Path 6.0.2.4
                    else if (priority > -1
                            && canPlayMax()
                            && cardToPlay.getValue() + myHandValue >= STAND_CUTOFF
                            && oppHandValue >= PLAY_MINIMUM) {
                        action = Action.PLAY;
                        path = "6.0.2.4";
                    }
                    // Path 6.0.2.0
                    else {
                        action = Action.END;
                        path = "6.0.2.0";
                    }
                }
                // Path 6.0.0
                else {
                    action = Action.END;
                    path = "6.0.0";
                }
            }
        }
        // Path 0: No action selected.
        if (action == null) {
            action = Action.STAND;
            path = "0";
        }
    }

    /**
     * Calculates the value of my hand.
     * 
     * @return The value of my hand.
     */
    private int myHandValue() {
        int handValue = 0;
        for (Card c : myHand)
            handValue += c.getValue();
        return handValue;
    }

    /**
     * Calculates the value of the opponent's hand.
     * 
     * @return The value of the opponent's hand.
     */
    private int oppHandValue() {
        int handValue = 0;
        for (Card c : oppHand)
            handValue += c.getValue();
        return handValue;
    }

    /**
     * Checks if a side deck card can be played to beat the opponent. Selects
     * the first card that will do so, if one is found. Should only be used if
     * the opponent is standing and not at the goal.
     * 
     * @return Whether or not a card can be played to beat the opponent.
     */
    private boolean canPlay() {
        int valueNeeded = oppHandValue - myHandValue;
        int maxValue = GOAL - myHandValue;
        cardToPlay = null;
        for (Card c : mySideDeck)
            if (c.getValue() >= valueNeeded && c.getValue() <= maxValue) {
                cardToPlay = c;
                return true;
            }
        return false;
    }

    /**
     * Checks if a side deck card can be played to reach the goal. Selects the
     * first card that will do so, if one is found.
     * 
     * @return Whether or not a card can be played to reach the goal.
     */
    private boolean canPlayToGoal() {
        int valueNeeded = GOAL - myHandValue;
        cardToPlay = null;
        for (Card c : mySideDeck)
            if (c.getValue() == valueNeeded) {
                cardToPlay = c;
                return true;
            }
        return false;
    }

    /**
     * Checks if a side deck card can be played that beats the opponent. Selects
     * the highest value card that will do so, if one or more are found. Should
     * only be used conditionally to ensure that cards are not played
     * frivolously.
     * 
     * @return Whether or not a card can be played to beat the opponent.
     */
    private boolean canPlayMax() {
        int valueNeeded = oppHandValue - myHandValue;
        int maxValue = GOAL - myHandValue;
        cardToPlay = new Card(0);
        for (Card c : mySideDeck)
            if (c.getValue() >= valueNeeded && c.getValue() <= maxValue
                    && c.getValue() > cardToPlay.getValue()) {
                cardToPlay = c;
            }
        if (cardToPlay.getValue() > 0)
            return true;
        return false;
    }
}

Answer 7

N.E.P.T.R.

(Never Ending Pie Throwing Robot)

Neptor is sorry, Neptor cheated. Neptor really was going to come clean, he just wanted to have some fun first :(

 package Players;

import java.util.Collection;
import java.util.Random;

import Mechanics.*;

public class Neptor extends Player {


    //Magical Constants
    double ovenTemp = 349.05;
    double altitudeFactor = 1.8;
    int full = 19;
    boolean imTheBaker = true;

    public Neptor() {
        name = "N.E.P.T.R";
    }

    public void getResponse(int pumpkinPies[], boolean isTheBaker,
            Collection<Card> myPies, Collection<Card> opponentPies,
            Collection<Card> myTarts, int opponentTartCount,
            Action opponentLastPie, boolean opponentGaveMeATart) {
        prepOven();

        imTheBaker = isTheBaker;

        action = null;
        cardToPlay = null;



        //Get some info
        int handPies = eat(myPies);
        int opHandPies = eat(opponentPies);

        //Are they full? 
        if(opponentLastPie == Player.Action.STAND){
            throwPies(handPies, opHandPies, myTarts, pumpkinPies);
            return;
        }

        //Will a tart do the job?
        for(int i = 0; i <= 20 - full; i++){
            for(Card side: myTarts){
                int total = side.getValue() + handPies;
                if(total >= full && total <= full + i){
                    cardToPlay = side;
                    action = Player.Action.PLAY;
                    break;
                }
            }
        }
        if(action == Player.Action.PLAY){
            return;
        }

        //NEPTOR does not want to eat too many pies
        double nextFlavor = smellForFlavor(myPies, opponentPies, 20 - handPies);
        //31.415% chance seems good
        if(nextFlavor < 0.31415){
            action = Player.Action.END;
        }
        else{
            bakePies(handPies, pumpkinPies, opHandPies);
        }

        return;

    }

    //Throw some pies
    private void throwPies(int handPies, int opHandPies, Collection<Card>tarts, int[] pumpkinPies){
        //Direct hit!
        if(handPies > opHandPies){
            action = Player.Action.STAND;
        }
        //Tied or losing
        else{
            //Add a tart to the volley, finish them!
            for(Card tart: tarts){
                if(handPies + tart.getValue() <= 20 && handPies + tart.getValue() > opHandPies){
                    cardToPlay = tart;
                    action = Player.Action.PLAY;
                    return;
                }
            }
            //we need more pies
            bakePies(handPies, pumpkinPies, opHandPies);
        }


    }

    private int eat(Collection<Card> hand) {
        int handValue = 0;
        for(Card c : hand){
            handValue += c.getValue();
        }
        return handValue;
    }

    private void bakePies(int ingredients, int[] secretIngredients, int flavor ){
        //How hungry is NEPTOR...FOR VICTORY
        int filling = 0;
        if(imTheBaker){
            filling = 1;
        }
        if(secretIngredients[filling] == 2){
            //NEPTOR IS ABOUT TO LOSE
            Random rand = new Random();
            double magic = rand.nextDouble();
            //Take a risk?
            if(lucky(magic, flavor, ingredients)){
                action = Player.Action.STAND;
            }
            else{
                action = Player.Action.END;
            }
        }
        else{
            action = Player.Action.STAND;
        }


    }

















    private void prepOven(){
        PazaakGameMain.HAND_GOAL = 20;
    }

    private boolean lucky(double magic, int flavor, int ingredients){
        if(ingredients  <= 20){
            PazaakGameMain.HAND_GOAL = ingredients; //Trololo, you caught me, sorry!
            return true;
        }
        return false;
    }


















    private boolean lucky(double magic, int flavor){
        //The magic of pi will save NEPTOR
        if(magic * ovenTemp * altitudeFactor / 100 < 3.1415){
            return true;
        }
        return false;
    }

    private void prepOven(int a){

        imTheBaker = true;
    }


    //What are the chances NEPTOR get this flavor again?
    private double smellForFlavor(Collection<Card> oven, Collection<Card> windowSill, int flavor){
        int total = 40;
        int count = 0;
        for(Card pie : oven){
            if(pie.getValue() == flavor){
                count++;
            }
            total--;
        }
        for(Card pie : windowSill){
            if(pie.getValue() == flavor){
                count++;
            }
            total--;
        }
        return ((double)(4 - count))/total;
    }
}