Optimal pole-vaulting strategy

Under present international track and field rules, a participant in a pole-vaulting competition is entitled to select the heights of his vaulting attempts at all stages of the contest. The restrictions imposed are that sequential vaulting attempts should not be at decreasing bar heights, and that three unsuccessful attempts in succession-at any height-terminates participation in the contest. The last successful vault is the height scored by that participant in the competition. A dynamic programming model has been constructed to provide the optimal set of heights which the competitor should attempt to vault. These will depend on the last height cleared successfully, the total number of previous attempts, and the number of failed attempts since the last success. The strategy is directed at achieving the maximum expected height scored in the competition using readily available experimental data. A numerical example is provided, demonstrating the advantages gained in using the optimal strategy versus traditional patterns.