PHP If / Else statement going directly to the Else without waiting for form input

Ok so I have a form with 1 input and a submit button. Now I am using an if/else statement to make three acceptable answers for that input. Yes, No, or anything else. This if/else is working the thing is the code is kicking out the else function as soon as the page is loaded. I would like there to be nothing there until the user inputs then it would show one of three answers.

Welcome to your Adventure! You awake to the sound of rats scurrying  around your dank, dark cell. It takes a minute for your eyes to adjust to your surroundings. In the corner of the room you see what looks like a rusty key.
<br/>
Do you want to pick up the key?<br/>


<?php

//These are the project's variables.

$text2 = 'You take the key and the crumby loaf of bread.<br/>';

$text3 = 'You decide to waste away in misery!<br/>';

$text4 = 'I didnt understand your answer. Please try again.<br/>';

$a = 'yes';

$b = 'no';


// If / Else operators.

if(isset($_POST['senddata'])) {

    $usertypes = $_POST['name'];

}

if ($usertypes == $a){

    echo ($text2);
}

elseif ($usertypes == $b){

    echo ($text3);
}

else {

    echo ($text4);
}

?>

<form action="phpgametest.php" method="post">
         <input type="text" name="name" /><br>
         <input type="submit" name="senddata" /><br>
</form>