In chess, "busted" refers to an opening or a position that has been rendered completely untenable by one's own or the opponent's moves.
Some chess openings previously considered sound have been busted by players finding effective counters that render the opening unplayable. In this sense, "busted" is significantly worse than "dubious"; a dubious opening can still be played, but a busted opening is now worthless, unless a counter to the counter can be discovered at some point down the road.
Similarly, a player's position on the chess board is said to be "busted" if a blunder by the player or a brilliancy by the opponent renders the position completely indefensible without yielding checkmate or a massive loss of material. Once a position is busted, a resignation usually follows in short order.