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Finding the probability of going infinite with Nexus of Fate

frankkarsten Aug 6th, 2018 114 Never
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  1. package nexusoffate;
  2.  
  3. import java.util.Arrays.*;
  4.  
  5. public class NexusOfFate {
  6.  
  7.     public static void main(String[] args) {
  8.  
  9.         //Declare variables
  10.         int ExtraCardDrawPerTurn=2;
  11.         double[][][][] TransitionMatrix = new double[21][41][21][41];
  12.         int ExtraTurns; int CardsInDeck; int FROMExtraTurns; int FROMCardsInDeck; int TOExtraTurns; int TOCardsInDeck; int BETWEENExtraTurns; int BETWEENCardsInDeck;
  13.         boolean WeGoInfinite;
  14.         //Note that since we draw cards after casting Nexuses, we'll always have at least 4 cards in library at that point
  15.         //State with 0 extra turns, 0 cards in library => Absorbing, opponent took a turn
  16.         //State with 20 extra turns, 0 cards in library => Absorbing, we go infinite
  17.        
  18.         TransitionMatrix[0][0][0][0]=1;
  19.         TransitionMatrix[20][0][20][0]=1;
  20.        
  21.         for ( FROMExtraTurns=0; FROMExtraTurns<=10; FROMExtraTurns++){
  22.             for ( FROMCardsInDeck=4; FROMCardsInDeck<=40; FROMCardsInDeck++){
  23.                
  24.                 WeGoInfinite=false;
  25.                 if (FROMExtraTurns==20 || FROMExtraTurns*(1+ExtraCardDrawPerTurn)>FROMCardsInDeck) {WeGoInfinite=true;}
  26.                
  27.                 if (ExtraCardDrawPerTurn==1 && !WeGoInfinite){
  28.                     double ProbDrawFate1=4.0/FROMCardsInDeck;
  29.                     double ProbDrawFate2=4.0/(FROMCardsInDeck-1);
  30.                     TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][Math.min(FROMExtraTurns+1,20)][FROMCardsInDeck]=ProbDrawFate1*ProbDrawFate1;
  31.                     TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns][FROMCardsInDeck-1]=TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns][FROMCardsInDeck-1]+ProbDrawFate1*(1-ProbDrawFate1);
  32.                     TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns][FROMCardsInDeck-1]=TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns][FROMCardsInDeck-1]+(1-ProbDrawFate1)*ProbDrawFate2;
  33.                     if (FROMExtraTurns>0) {TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns-1][FROMCardsInDeck-2]=(1-ProbDrawFate1)*(1-ProbDrawFate2);}
  34.                     if (FROMExtraTurns==0) {TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][0][0]=(1-ProbDrawFate1)*(1-ProbDrawFate2);}
  35.                }
  36.                
  37.                if (ExtraCardDrawPerTurn==2 && !WeGoInfinite){
  38.                     double ProbDrawFate1=4.0/FROMCardsInDeck;
  39.                     double ProbDrawFate2=4.0/(FROMCardsInDeck-1);
  40.                     double ProbDrawFate3=4.0/(FROMCardsInDeck-2);
  41.                     //Hit-Hit-Hit
  42.                     TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][Math.min(FROMExtraTurns+2,20)][FROMCardsInDeck]=ProbDrawFate1*ProbDrawFate1*ProbDrawFate1;
  43.                     //Hit-Hit-Miss
  44.                     TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][Math.min(FROMExtraTurns+1,20)][FROMCardsInDeck-1]=TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][Math.min(FROMExtraTurns+1,20)][FROMCardsInDeck-1]+ProbDrawFate1*ProbDrawFate1*(1-ProbDrawFate1);
  45.                     //Hit-Miss-Hit
  46.                     TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][Math.min(FROMExtraTurns+1,20)][FROMCardsInDeck-1]=TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][Math.min(FROMExtraTurns+1,20)][FROMCardsInDeck-1]+ProbDrawFate1*(1-ProbDrawFate1)*ProbDrawFate2;
  47.                     //Miss-Hit-Hit
  48.                     TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][Math.min(FROMExtraTurns+1,20)][FROMCardsInDeck-1]=TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][Math.min(FROMExtraTurns+1,20)][FROMCardsInDeck-1]+(1-ProbDrawFate1)*ProbDrawFate2*ProbDrawFate2;
  49.                     //Hit-Miss-Miss
  50.                     TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns][FROMCardsInDeck-2]=TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns][FROMCardsInDeck-2]+ProbDrawFate1*(1-ProbDrawFate1)*(1-ProbDrawFate2);
  51.                     //Miss-Hit-Miss
  52.                     TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns][FROMCardsInDeck-2]=TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns][FROMCardsInDeck-2]+(1-ProbDrawFate1)*ProbDrawFate2*(1-ProbDrawFate2);
  53.                     //Miss-Miss-Hit
  54.                     TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns][FROMCardsInDeck-2]=TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns][FROMCardsInDeck-2]+(1-ProbDrawFate1)*(1-ProbDrawFate2)*ProbDrawFate3;
  55.                     //Miss-Miss-Miss
  56.                     if (FROMExtraTurns>0) {TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][FROMExtraTurns-1][FROMCardsInDeck-3]=(1-ProbDrawFate1)*(1-ProbDrawFate2)*(1-ProbDrawFate3);}
  57.                     if (FROMExtraTurns==0) {TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][0][0]=(1-ProbDrawFate1)*(1-ProbDrawFate2)*(1-ProbDrawFate3);}
  58.                }
  59.                
  60.                if (WeGoInfinite){
  61.                     TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][20][0]=1;
  62.                }
  63.  
  64.             }
  65.         }
  66.        
  67.         double[][] StartingDistribution = new double[21][41];
  68.         double[][] NewDistribution = new double[21][41];
  69.  
  70.         for (int StartingDeckSize=4; StartingDeckSize<=40; StartingDeckSize++){
  71.        
  72.            
  73.             for ( ExtraTurns=0; ExtraTurns<=20; ExtraTurns++){
  74.             for ( CardsInDeck=0; CardsInDeck<=40; CardsInDeck++){
  75.                 StartingDistribution[ExtraTurns][CardsInDeck]=0;
  76.                 NewDistribution[ExtraTurns][CardsInDeck]=0;
  77.             }}
  78.             StartingDistribution[2][StartingDeckSize]=1;
  79.  
  80.             for (int Turn=1; Turn<=60; Turn++){
  81.                 for ( FROMExtraTurns=0; FROMExtraTurns<=20; FROMExtraTurns++){
  82.                 for ( FROMCardsInDeck=0; FROMCardsInDeck<=40; FROMCardsInDeck++){
  83.                 for ( TOExtraTurns=0; TOExtraTurns<=20; TOExtraTurns++){
  84.                 for ( TOCardsInDeck=0; TOCardsInDeck<=40; TOCardsInDeck++){
  85.                     NewDistribution[TOExtraTurns][TOCardsInDeck]=NewDistribution[TOExtraTurns][TOCardsInDeck]+StartingDistribution[FROMExtraTurns][FROMCardsInDeck]*TransitionMatrix[FROMExtraTurns][FROMCardsInDeck][TOExtraTurns][TOCardsInDeck];
  86.                 }}}}
  87.  
  88.                 for ( ExtraTurns=0; ExtraTurns<=20; ExtraTurns++){
  89.                 for ( CardsInDeck=0; CardsInDeck<=40; CardsInDeck++){
  90.                     StartingDistribution[ExtraTurns][CardsInDeck]=NewDistribution[ExtraTurns][CardsInDeck];
  91.                     NewDistribution[ExtraTurns][CardsInDeck]=0;
  92.                 }}
  93.             }
  94.             System.out.println(StartingDistribution[20][0]);
  95.            
  96.         }
  97.        
  98.     }
  99. }
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