Default state (Add options) overrides my update options?

Question

I have a check box inside my admin page and the code looks like this (this code works and i can toggle my check box off and on and able to save changes)

add_settings_field(
    'my_checkbox_default',
    'Checkbox:',
    'my_default_checkbox_settings_function',
    'override_theme_display_options',
    'override_theme_display_options'
);

function my_default_checkbox_settings_function(){
    $options = get_option('override_theme_display_options');
    if(isset($options['my_checkbox_default'])) { 
        $checked = 'checked'; 
    } else { 
        $checked = '';
    }
    update_option('my_checkbox_default', $checked);
    echo "<input type='checkbox' name='override_theme_display_options[my_checkbox_default']' ".$checked." id='my_checkbox_default' />";
}

Now I want to add default state "checked" to my check box.

So my check box setting function looks like this:

function my_default_checkbox_settings_function(){
    $options = get_option('override_theme_display_options');
    //Added default state "checked" to my check box
    add_option('my_checkbox_default',$checked = 'checked');
    if(isset($options['my_checkbox_default'])) { 
        $checked = 'checked'; 
    } else { 
        $checked = ''; 
    }
    update_option('my_checkbox_default', $checked);
    echo "<input type='checkbox' name='override_theme_display_options[my_checkbox_default']' ".$checked." id='my_checkbox_default' />";
}

My check box now has "checked" state as default , but now I can't toggle my check box off and on anymore (it stays "checked" all the time no matter what I do), if I comment out my add_option() obliviously my default "checked" state will not be set but I will be able to toggle and save my check box states again.

How can I add "checked" state by default and still be able to toggle and save options for my check box?
I will be more than happy to add 50 bounty for solving this. THX!

Answer 1

If this is a plugin, you need to set the option for the first time with register_activation_hook. If a theme, use after_setup_theme.

There's an alternative technique for run_once described in this WPSE Answer that works quite well too.

Here's a working example ^{loosely based on yours and some Codex samples} using run_once. Note the use of the function checked().

add_action('admin_init', function() 
{
    // Change the "init_*" to anything else to `run_once` again
    if ( wpse_25643_run_once('init_checkbox_default') ) 
    {
        add_option('my_checkbox_default', true );
    }
    register_setting('media','my_checkbox_default');

    add_settings_field(
        'my_checkbox_default',
        'Checkbox:',
        'my_default_checkbox_settings_function',
        'media'
    );
});

function my_default_checkbox_settings_function() 
{
    printf( 
        "<input name='my_checkbox_default' id='gv_thumbnails_insert_into_excerpt' type='checkbox' value='1' class='code' %s /> Explanation text",
        checked( 1, get_option('my_checkbox_default'), false )
    );
}

function wpse_25643_run_once( $key )
{
    $test_case = get_option( 'run_once' );

    if ( isset( $test_case[$key] ) && $test_case[$key] )
    {
        return false;
    }
    else
    {
        $test_case[$key] = true;
        update_option('run_once',$test_case);
        return true;
    }
}