A coin is tossed repeatedly, and a payoff of 2n dollars is made, where n is the

Question

A coin is tossed repeatedly, and a payoff of 2n dollars is made, where n is the number of the toss on which the first Head appears. So TTH pays $8, TH pays $4 and H pays $2. Write a program to simulate playing the game 10 times. Display the result of the tosses and the payoff. At the end, display the average payoff for the games played. A typical run would be:

TTTH       You win $16.00
TH            You win $4.00
TH            You win $4.00
H               You win $2.00
TTTTH      You win $32.00
TH             You win $4.00
H               You win $2.00
H               You win $2.00
TH             You win $4.00
TH             You win $4.00

The average payout was $7.40

Explanation / Answer

The logic is same in any language. You did not specified language so I wrote it in java.

import java.util.Random;
import java.util.Scanner;


public class TossPayout {
   public static void main(String []args){
      
       Random rand = new Random();
       int total = 0;
       //simulating tossing for 10 times
       for(int i = 0; i < 10; i++) {
           //In each iteration coin is tossed till head turns up
           int count = 0;
           String output ="";
           
           int num = -1;
           do {
               num = rand.nextInt();
               //System.out.println(" count = "+count+", num = "+num);
               count++;
              

//Generating a random number, if it is divisble by 2 its Head, otherwise its tail
               if(num % 2 == 0) {
              
                   //payoff = 2n dollars is made, where n is the number of the toss on which the first Head appears
                   total = total + 2 * count;
                   output += "H              You Won $ "+(2 * count);
                   System.out.println(output);
                   break;
               } else {
                   output += "T";
               }
              
           } while(num % 2 != 0);
       }
      
       System.out.println("The average payout is $ "+ (float) total/10.0);
      
   }
}

-----------------------------output--------------------------

H              You Won $ 2
TTH              You Won $ 6
TTH              You Won $ 6
H              You Won $ 2
TTTTH              You Won $ 10
H              You Won $ 2
TTTTTTH              You Won $ 14
H              You Won $ 2
H              You Won $ 2
H              You Won $ 2
The average payout is $ 4.8

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