We use game theory techniques to automatically compute improved lower bounds on the competitive ratio for the bin stretching problem. Using these techniques, we improve the best lower bound for this problem to 19/14. We explain the technique and show that it can be generalized to compute lower bounds for any online or semi-online packing or scheduling problem. We also present a lower bound, with value 7/6, on the expected competitive ratio of randomized algorithms for the bin stretching problem.