I'm trying to pass a nullable bool to my controller. But when I pass the bool value from my view to the controller, it's being passed null all the time regardless of the value it has in my view.

Here is my view:

@model Cars.Models.Car

@using (Html.BeginForm("Index", "Home", FormMethod.Post,
new { id = "CategoryFormID"})) {
    <label>Convertible:</label>
    <input type="checkbox" id="ConvertibleID" name="convertible"/>
    <button type="submit" name="submit" value="search" id="SubmitID">Search</button>
}

And my controller:

[HttpPost]
public ActionResult Index(bool? convertible){
    var cars = from d in db.Car
               select d;

    if (convertible.HasValue)
        {
            cars = cars.Where(x => x.Convertible == convertible);
        }

    return View("SearchResult", cars);
}

I also have other fields such as drop down lists and text fields, but they're being passed flawless. Any help would be really appreciated.

Update: Thank you for your fast responds. However, I did try giving it a value="True" as you guys suggested. There is only 2 options now: null and true. But my intention is to use nullable bool to have three options: null (when user doesn't touch the checkbox), true(checked) and false(unchecked). I know it sounds not smart and silly, but I'm just trying to figure out how nullable bool is working, and what is the intention of having such a thing in C# (I'm new with C#). I was wondering if it is possible to do so with just checkbox and without the use of dropdownlist or radio buttons.