Probability of 5+ consecutive heads in 20 coin tosses

my bad, when i thought again, the sequential guessing implicitly makes P(right at i|wrong all before)=P(right at i) as wrong prior to i is a necessity rather than information for i event to happen.
P(right by n) =

 

For the record, the 1-100 guess game and its sim as follows

Code:

import java.util.Scanner;

/**
* Eck's book Chapter 4 PlayGame class
* @version 1.0
* @since 2019-11-1
*/

public final class NumberGuessingGame{

  static int totalPlay;
  static int totalWin;
  static int guessPermitted = 6; //# of guess permitted per game

  public static void main(String[] args){
    System.out.println("This game is very easy.");
    System.out.println("I will pick a number between 1 and 100, and you guess it.");
    System.out.println("If you don't get it within "+ guessPermitted + " times, you are a fucking loser.");
    System.out.println("Now, let's rock and roll baby!");
    boolean playAgain;
    String playAgainString;
  
    do{
      System.out.println("I rolled my dice. Let's see if you get it.");
      totalPlay++;
      PlayNumberGuessingGame();
      System.out.println("Play again?");
      Scanner scanner = new Scanner(System.in);
      playAgainString = scanner.next();
      playAgainString = playAgainString.substring(0,1).toUpperCase();
      playAgain = (playAgainString.equals("Y")) ? true : false;
    } while(playAgain);
  
    double expectedWinRatio = NumberGuessingGameSim.NumberGuessingGameSim(guessPermitted);
    double actualWinRatio = (double)totalWin*100/totalPlay;
    String performance = (actualWinRatio>expectedWinRatio) ? ("outperformed") : ("underperformed");
    System.out.println("You have won " + totalWin + " games out of the total of " + totalPlay + " games played.");
    System.out.println("Your win ratio is " + String.format("%.1f", actualWinRatio) +"%, which " + performance + " the average of "+expectedWinRatio+"%");  
    System.out.println("Thanks for playing. Have a fucking good day!");
  }

  static void PlayNumberGuessingGame(){
    int answer, guess, guessCount;
    answer = (int)(Math.random() * 100) + 1;
    guessCount = 0;
    while(guessCount < guessPermitted){
      Scanner guessScan = new Scanner(System.in);
      System.out.println("What's your guess?");
      guess = guessScan.nextInt();
    
      if (guess == answer){
        break;
      }
      else if (guess < answer)
        System.out.println("Wrong, guess is too low.");
      else System.out.println("Wrong, guess is too high.");
      guessCount++;
    } //at this point, either guessCount has reached the quota or the guess is right
    if (guessCount == 6)
      System.out.println("Sorry, you lost. My dice number was " + answer + ".");
    else {
      totalWin++;
      System.out.println("Congratulations! You got it in " + (guessCount+1) + " guesses. What a genius.");}
  }
}

    
            

Code:

import java.util.Scanner;

public class NumberGuessingGameSim{

  static int totalWin = 0;
  static int totalRun = 100000;

  public static void main(String[] args){
    int guessPermitted;
    Scanner guessScan = new Scanner(System.in); //getting # of guesses allowed in each game
    System.out.println("Enter the max # of guesses per game");
    guessPermitted = guessScan.nextInt();
    double winRatio = NumberGuessingGameSim(guessPermitted);  
    System.out.println("win ratio is " + winRatio+"%");
  }

  public static double NumberGuessingGameSim(int guessPermitted){
    int currentRun = 0; //counter
    while(currentRun<totalRun){
      currentRun++;
      PlayNumberGuessingGameSim(guessPermitted);
    }
    return ((double)totalWin*100/totalRun);
  }

  private static void PlayNumberGuessingGameSim(int guessPermitted){
    int answer, guess, guessCount;
    int lowerRange, upperRange;
    answer = (int)(Math.random()*100) +1;
    guessCount = 0;
    lowerRange = 1;
    upperRange = 100;
    while (guessCount < guessPermitted){
      guess = (upperRange - lowerRange)/2 + lowerRange;
    
      if (guess == answer){
        totalWin++;
        break;
      }
      else if (guess < answer){
        lowerRange = guess;
        guessCount++;
      }
      else {
        upperRange = guess;
        guessCount++;
      }
    }
  }
}
      

 

Simulating the Monty Hall game.
If someone can simplify the code, please comment.

Code:

import java.util.*;

public final class MontyHallGameSim{
 
  static int totalSwitchWin = 0;
  static int totalKeepWin = 0;
 
  public static void main(String[] args){
   
    int totalPlay = 10000;
   
    for(int iplay=0; iplay<totalPlay; iplay++){
      playMontyHallGame();
    }
   
    System.out.println("Out of total of " + totalPlay + " games, stay(no-switch) strategy won " + totalKeepWin + " times and switch strategy won " + totalSwitchWin + " times.");
    System.out.println("Win ratios are respectively " + String.format("%.2f",(double)(totalKeepWin*100/totalPlay)) + "% and " + String.format("%.2f",(double)(totalSwitchWin*100/totalPlay)) + "%.");   
  }
       
    private static final void playMontyHallGame(){
    Set<Integer> doorsSet = new HashSet<Integer>(); //declare and initialize the doors
    doorsSet.add(1);
    doorsSet.add(2);
    doorsSet.add(3);
    Set<Integer> emptyDoorsSet = new HashSet<Integer>();
    emptyDoorsSet.addAll(doorsSet);
    int prizeDoor = (int)(Math.random()*3 + 1); //generate U[1,3] for the prize door
    emptyDoorsSet.remove(prizeDoor); //remove the prize door from the set
    int initialChoice = (int)(Math.random()*3 + 1) ;//generate U[1,3] for the player's initial choice
   
    emptyDoorsSet.remove(initialChoice); //preparing for openable door set
    ArrayList<Integer> openableDoorList = new ArrayList<Integer>(emptyDoorsSet); //an openable door is one that is both empty and not chosen
    int openableDoorShown = openableDoorList.get((int)(Math.random()*emptyDoorsSet.size())); //depending on whether initial choice is correct, the openable door set can have 1 (if incorrect) or 2 (if correct) elements
   
    int finalKeepChoice = initialChoice;
    int finalSwitchChoice;
   
    doorsSet.remove(initialChoice); //identifying the sole remaining door to switch to, by removing the initially chosen and the shown doors
    doorsSet.remove(openableDoorShown);
    if (doorsSet.contains(1))
        finalSwitchChoice = 1;
    else if (doorsSet.contains(2))
        finalSwitchChoice = 2;
    else
        finalSwitchChoice = 3;
   
    if(finalKeepChoice==prizeDoor)
      totalKeepWin++;
    else if (finalSwitchChoice==prizeDoor)
      totalSwitchWin++;
  }
   
}