Notice: Undefined property: wpdb::$current_post What can be wrong?

There are problems with this part:

 ++$GLOBALS['wpdb']->current_post

There’s no current_post property of the wpdb class, here you’re most likely confusing the wpdb class with the WP_Query class.

Also we wouldn’t want in general to modify the current_post property of the global WP_Query, it could surely “bite us” if we mess with the globals 😉

Note that the current_post property of WP_Query is already doing the counting for us with $this->current_post++; inside next_post(), that’s called within the_post(). See here. So there’s no need to increase it manually (++) within the loop.

Here’s an example using the post_class filter, with the help of a static variable:

add_filter( 'post_class', function( $classes ) 
{
    static $instance = 0;

    if( in_the_loop() )
        $classes[] = ( 0 === $instance++ % 2 ) ? 'even' : 'odd';        

    return $classes;
} );

where we target post classes in the main query loop. Just remember to modify the even/odd classes and other restrictions to your needs.

Using the post_class filter could mean better re-usability for our template parts.

Update

It looks like you’re using the first version of @toscho’s one-liner answer, creating a custom current_post property (for counting) of the global wpdb object. He suggested then to use the prefixed custom property, like wpse_post_counter. But it looks like it needs an initialization to avoid the PHP notice.

@kaiser did post a great answer here that uses the current_post property of the global $wp_query (probably not the global $wpdb).

Since I gave a promise here, regarding anonymous functions and global variables, I should rewrite it to: See my edit here
– where we use the use keyword to pass on the global $wp_query object.

Update

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