Following up on Emil's excellent answer, "you can open the popup on click and manipulate it later when the callback fires". I used this implementation.

$('#attackButton').click(function() {

New code here

    var win = window.open('');
    window.oldOpen = window.open;
    window.open = function(url) { // reassignment function
        win.location = url;
        window.open = oldOpen;
        win.focus();
    }

end new code

    $.ajax({
        url: baseurl + '/index.php',
        data: { 'gameid': 618 },
        type: 'POST',
        success: function(data) {
            window.open('some url'); // will call reassignment function above 
        }
    });

    return false;
});