My game is written differently, but I think it still works. Can someone check it for me?

alert('Let\'s play a game!');  // Alert 1st Program BEGIN.
console.log('BEGIN 1st Program.');  // Log 1st Program BEGIN.

var input = prompt('Choose a number.');  // Entered userNumber.
var userNumber = parseInt(input); // Convert userNumber.
console.log(userNumber); // Log userNumber.

alert('Now, think of a number in between 1 & the number you just chose.');
alert('And now, I\'ll try to guess the number you\'re thinking of.');

var randomNumberOne = Math.random() * userNumber + 1;  // Select randomNumberOne.
console.log(randomNumberOne); //Log randomNumberOne.

document.write('<h2>Was ' + parseInt(randomNumberOne) + ' the number you were thinking of?</h2>');

alert('Thanks for playing.');  // Alert 1st Program END.
console.log('END 1st Program.');  // Log 1st Program END.

alert('Let\'s play another game!');  // Alert 2nd Program BEGIN.
console.log('BEGIN 2nd Program.');  // Log 2nd Program BEGIN.

var input1 = prompt('Again, choose a number.');  // Entered bottomNumber.
var bottomNumber = parseInt(input1); // Convert bottomNumber.
console.log(bottomNumber); // Log bottomNumber.

var input2 = prompt('Now, choose a larger number.');  // Entered topNumber.
var topNumber = parseInt(input2); // Convert topNumber.
console.log(topNumber); // Log topNumber.

alert('Now, think of a number in between the 2 numbers you just chose.');
alert('And again, I\'ll try to guess the number you\'re thinking of.');

var randomNumberTwo = Math.random() * (topNumber - bottomNumber + 1) + bottomNumber;  // Select randomNumberTwo.
console.log(randomNumberTwo); //Log randomNumberTwo.

document.write('<h2>Was ' + parseInt(randomNumberTwo) + ' the number you were thinking of?</h2>');

alert('Thanks for playing.');  // Alert 2nd Program END.
console.log('END 2nd Program.');  // Log 2nd Program END.