The Bahncard is a railway pass of the German Decutsche Bundesbah.Such cards have become a popular marketing mode,however the consumer can not make the optimal opportunity to buy a card.There- fore,this paper,based on the limited foreknowledge,establishes a risk-reward model,solved by the competi- tive algorithms,and finds the optimal TSUM strategy and PSUM strategy,together with their competitive ratios.A numerical example is illustrated to explain such model and strategies.