Checkbox with false value in form

I need send with post false value of checkbox witch is not checked by default. My checkbox is defined like this:

<label><input type="checkbox" id="rez" name="rezerwowanie" value="false" />Rezerwowanie</label>

And after submit I use that code to check if checkbox is checked or not:

$Reservation = $_POST['rezerwowanie'];
    if ($Reservation == false) {
        $Reservation = 0;
    } else
    {
        $Reservation = 1;
    }

It work when I check the checkbox but with not checked it don't work. What's the problem here?