Both the if statement and the else if statements run

I am newer to java programming and have been working on a hangman 'game' of sorts. This was an exercise proposed by my instructor and after completing the basic version, I wanted to make one that is more advanced. So far I have found that the problem in the code is that both the if statement and the else if statements run. To try to fix this, I added some break statements. It did help with one problem but both statements still run.

Here is the if else statement that is faulty:

                if (guess.equals(letters[i])){
                    wordi[i] = guess.charAt(i);
                    System.out.println("Included");
                    break;
                }
                else if (!guess.equals(letters[i])){
                    wordi[i] = '*';
                    wrong_guess++;
                    num_guess ++;
                    System.out.println("Not included");
                    break;

Here is the full code if it helps:

import java.util.Scanner;

public class Test {
    public static Scanner input = new Scanner(System.in);
    @SuppressWarnings({ "unused" })
    public static void main(String[] args) {

        String[] words = new String[10];
        words[0] = "chair";
        words[1] = "apple";
        words[2] = "bear";
        words[3] = "word";
        words[4] = "table";
        words[5] = "cow";
        words[6] = "cabbage";
        words[7] = "food";
        words[8] = "computer";
        words[9] = "mouse";

        int cap_guess = 6;
    int wrong_guess = 0;
    int n = (int)(Math.random()*10);
    String word = words[n];
    String out_word = "";
    int num_guess = 1;
    for(int count = 0; count < word.length(); count ++){
        out_word += "*";
    }
    boolean success = false;
    String guess = "";
    String[] letters = new String[word.length()];
    for (int i = 0; i < letters.length; i++){
        letters[i] = word.substring(i,i+1);
        System.out.println(letters[i]);
    }

    while (num_guess <= cap_guess){
        display(wrong_guess);
        System.out.println(out_word);
        System.out.print("Enter a guess: ");
        guess = input.nextLine();
        guess = guess.trim();
        guess = guess.toLowerCase();
        System.out.println("Guess: " + guess);

        char[] wordi = out_word.toCharArray();
        if (guess.length() == 1){
            for (int i = 0; i < word.length(); i++){
                if (guess.equals(letters[i])){
                    wordi[i] = guess.charAt(i);
                    System.out.println("Included");
                    break;
                }
                else if (!guess.equals(letters[i])){
                    wordi[i] = '*';
                    wrong_guess++;
                    num_guess ++;
                    System.out.println("Not included");
                    break;

                }
            }
            out_word += wordi;

        }
    }

    /*System.out.println(word);
    System.out.println(out_word);*/

}
public static void display (int wrong_guess){
    if (wrong_guess == 0){
        System.out.println("_____________________");
        System.out.println("    *----------,     |");
        System.out.println("    |          |     |");
        System.out.println("               |     |");
        System.out.println("               |     |");
        System.out.println("               |     |");
        System.out.println("               |     |");
        System.out.println("               |     |");
        System.out.println("               |     |");
        System.out.println("               |     |");
        System.out.println("               |     |");
        System.out.println("               |     |");
        System.out.println("______________/-\\____|");
        System.out.println("");
    }
    if (wrong_guess == 1){
        System.out.println("_____________________");
        System.out.println("    *----------,     |");
        System.out.println("    |          |     |");
        System.out.println("   /=\\         |     |");
        System.out.println("  |. .|        |     |");
        System.out.println("   \\-/         |     |");
        System.out.println("               |     |");
        System.out.println("               |     |");
        System.out.println("               |     |");
        System.out.println("               |     |");
        System.out.println("               |     |");
        System.out.println("               |     |");
        System.out.println("______________/-\\____|");
        System.out.println("");
    }
    if (wrong_guess == 2){
        System.out.println("_____________________");
        System.out.println("    *----------,     |");
        System.out.println("    |          |     |");
        System.out.println("   /=\\         |     |");
        System.out.println("  |. .|        |     |");
        System.out.println("   \\-/         |     |");
        System.out.println("    |          |     |");
        System.out.println("    |          |     |");
        System.out.println("    |          |     |");
        System.out.println("    |          |     |");
        System.out.println("               |     |");
        System.out.println("               |     |");
        System.out.println("______________/-\\____|");
        System.out.println("");
    }
    if (wrong_guess == 3){
        System.out.println("_____________________");
        System.out.println("    *----------,     |");
        System.out.println("    |          |     |");
        System.out.println("   /=\\         |     |");
        System.out.println("  |. .|        |     |");
        System.out.println("   \\-/         |     |");
        System.out.println("    |          |     |");
        System.out.println("    |\\         |     |");
        System.out.println("    | \\        |     |");
        System.out.println("    |          |     |");
        System.out.println("               |     |");
        System.out.println("               |     |");
        System.out.println("______________/-\\____|");
        System.out.println("");
    }
    if (wrong_guess == 4){
        System.out.println("_____________________");
        System.out.println("    *----------,     |");
        System.out.println("    |          |     |");
        System.out.println("   /=\\         |     |");
        System.out.println("  |. .|        |     |");
        System.out.println("   \\-/         |     |");
        System.out.println("    |          |     |");
        System.out.println("   /|\\         |     |");
        System.out.println("  / | \\        |     |");
        System.out.println("    |          |     |");
        System.out.println("               |     |");
        System.out.println("               |     |");
        System.out.println("______________/-\\____|");
        System.out.println("");
    }
    if (wrong_guess == 5){
        System.out.println("_____________________");
        System.out.println("    *----------,     |");
        System.out.println("    |          |     |");
        System.out.println("   /=\\         |     |");
        System.out.println("  |. .|        |     |");
        System.out.println("   \\-/         |     |");
        System.out.println("    |          |     |");
        System.out.println("   /|\\         |     |");
        System.out.println("  / | \\        |     |");
        System.out.println("    |          |     |");
        System.out.println("   /           |     |");
        System.out.println("  /            |     |");
        System.out.println("______________/-\\____|");
        System.out.println("");
    }
    if (wrong_guess == 6){
        System.out.println("_____________________");
        System.out.println("    *----------,     |");
        System.out.println("    |          |     |");
        System.out.println("   /=\\         |     |");
        System.out.println("  |x x|        |     |");
        System.out.println("   \\-/         |     |");
        System.out.println("    |          |     |");
        System.out.println("   /|\\         |     |");
        System.out.println("  / | \\        |     |");
        System.out.println("    |          |     |");
        System.out.println("   / \\         |     |");
        System.out.println("  /   \\        |     |");
        System.out.println("______________/-\\____|");
        System.out.println("");
    }
}
}

Thanks in advance for any help.