Finding the probability of going infinite with Nexus of Fate

package nexusoffate;

import java.util.Arrays.*;

public class NexusOfFate {

    public static void main(String[] args) {

        //Declare variables
        int ExtraCardDrawPerTurn=2;
        double[][][][] TransitionMatrix = new double[21][41][21][41];
        int ExtraTurns; int CardsInDeck; int FROMExtraTurns; int FROMCardsInDeck; int TOExtraTurns; int TOCardsInDeck; int BETWEENExtraTurns; int BETWEENCardsInDeck;
        boolean WeGoInfinite;
        //Note that since we draw cards after casting Nexuses, we'll always have at least 4 cards in library at that point
        //State with 0 extra turns, 0 cards in library => Absorbing, opponent took a turn
        //State with 20 extra turns, 0 cards in library => Absorbing, we go infinite

        TransitionMatrix[0][0][0][0]=1;
        TransitionMatrix[20][0][20][0]=1;

        for ( FROMExtraTurns=0; FROMExtraTurns<=10; FROMExtraTurns++){
            for ( FROMCardsInDeck=4; FROMCardsInDeck<=40; FROMCardsInDeck++){

                WeGoInfinite=false;
                if (FROMExtraTurns==20 || FROMExtraTurns*(1+ExtraCardDrawPerTurn)>FROMCardsInDeck) {WeGoInfinite=true;}

                if (ExtraCardDrawPerTurn==1 && !WeGoInfinite){
                    double ProbDrawFate1=4.0/FROMCardsInDeck;
                    double ProbDrawFate2=4.0/(FROMCardsInDeck-1);
                    TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][Math.min(FROMExtraTurns+1,20)][FROMCardsInDeck]=ProbDrawFate1*ProbDrawFate1;
                    TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns][FROMCardsInDeck-1]=TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns][FROMCardsInDeck-1]+ProbDrawFate1*(1-ProbDrawFate1);
                    TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns][FROMCardsInDeck-1]=TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns][FROMCardsInDeck-1]+(1-ProbDrawFate1)*ProbDrawFate2;
                    if (FROMExtraTurns>0) {TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns-1][FROMCardsInDeck-2]=(1-ProbDrawFate1)*(1-ProbDrawFate2);}
                    if (FROMExtraTurns==0) {TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][0][0]=(1-ProbDrawFate1)*(1-ProbDrawFate2);}
               }

               if (ExtraCardDrawPerTurn==2 && !WeGoInfinite){
                    double ProbDrawFate1=4.0/FROMCardsInDeck;
                    double ProbDrawFate2=4.0/(FROMCardsInDeck-1);
                    double ProbDrawFate3=4.0/(FROMCardsInDeck-2);
                    //Hit-Hit-Hit
                    TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][Math.min(FROMExtraTurns+2,20)][FROMCardsInDeck]=ProbDrawFate1*ProbDrawFate1*ProbDrawFate1;
                    //Hit-Hit-Miss
                    TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][Math.min(FROMExtraTurns+1,20)][FROMCardsInDeck-1]=TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][Math.min(FROMExtraTurns+1,20)][FROMCardsInDeck-1]+ProbDrawFate1*ProbDrawFate1*(1-ProbDrawFate1);
                    //Hit-Miss-Hit
                    TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][Math.min(FROMExtraTurns+1,20)][FROMCardsInDeck-1]=TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][Math.min(FROMExtraTurns+1,20)][FROMCardsInDeck-1]+ProbDrawFate1*(1-ProbDrawFate1)*ProbDrawFate2;
                    //Miss-Hit-Hit
                    TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][Math.min(FROMExtraTurns+1,20)][FROMCardsInDeck-1]=TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][Math.min(FROMExtraTurns+1,20)][FROMCardsInDeck-1]+(1-ProbDrawFate1)*ProbDrawFate2*ProbDrawFate2;
                    //Hit-Miss-Miss
                    TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns][FROMCardsInDeck-2]=TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns][FROMCardsInDeck-2]+ProbDrawFate1*(1-ProbDrawFate1)*(1-ProbDrawFate2);
                    //Miss-Hit-Miss
                    TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns][FROMCardsInDeck-2]=TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns][FROMCardsInDeck-2]+(1-ProbDrawFate1)*ProbDrawFate2*(1-ProbDrawFate2);
                    //Miss-Miss-Hit
                    TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns][FROMCardsInDeck-2]=TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns][FROMCardsInDeck-2]+(1-ProbDrawFate1)*(1-ProbDrawFate2)*ProbDrawFate3;
                    //Miss-Miss-Miss
                    if (FROMExtraTurns>0) {TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns-1][FROMCardsInDeck-3]=(1-ProbDrawFate1)*(1-ProbDrawFate2)*(1-ProbDrawFate3);}
                    if (FROMExtraTurns==0) {TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][0][0]=(1-ProbDrawFate1)*(1-ProbDrawFate2)*(1-ProbDrawFate3);}
               }

               if (WeGoInfinite){
                    TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][20][0]=1;
               }

            }
        }

        double[][] StartingDistribution = new double[21][41];
        double[][] NewDistribution = new double[21][41];

        for (int StartingDeckSize=4; StartingDeckSize<=40; StartingDeckSize++){


            for ( ExtraTurns=0; ExtraTurns<=20; ExtraTurns++){
            for ( CardsInDeck=0; CardsInDeck<=40; CardsInDeck++){
                StartingDistribution[ExtraTurns][CardsInDeck]=0;
                NewDistribution[ExtraTurns][CardsInDeck]=0;
            }}
            StartingDistribution[2][StartingDeckSize]=1;

            for (int Turn=1; Turn<=60; Turn++){
                for ( FROMExtraTurns=0; FROMExtraTurns<=20; FROMExtraTurns++){
                for ( FROMCardsInDeck=0; FROMCardsInDeck<=40; FROMCardsInDeck++){
                for ( TOExtraTurns=0; TOExtraTurns<=20; TOExtraTurns++){
                for ( TOCardsInDeck=0; TOCardsInDeck<=40; TOCardsInDeck++){
                    NewDistribution[TOExtraTurns][TOCardsInDeck]=NewDistribution[TOExtraTurns][TOCardsInDeck]+StartingDistribution[FROMExtraTurns][FROMCardsInDeck]*TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][TOExtraTurns][TOCardsInDeck];
                }}}}

                for ( ExtraTurns=0; ExtraTurns<=20; ExtraTurns++){
                for ( CardsInDeck=0; CardsInDeck<=40; CardsInDeck++){
                    StartingDistribution[ExtraTurns][CardsInDeck]=NewDistribution[ExtraTurns][CardsInDeck];
                    NewDistribution[ExtraTurns][CardsInDeck]=0;
                }}
            }
            System.out.println(StartingDistribution[20][0]);

        }

    }
}