The problem of finding an optimum, no-risk strategy for placing simultaneous win and place pari-mutuel bets is formulated in terms of a linear programming problem. For a basic feasible solution (i.e., a profitable schedule of bets) to exist, it is necessary for the win and place pools to weight the contestants differently. If the stake holder removes a fraction of the pool, then a solution is not guaranteed, but will exist if this difference in win-place weighting is sufficient. A simple example is presented
Optimum No-Risk Strategy for Win-Place Pari-Mutuel Betting
Willis, KE. (1964). Optimum No-Risk Strategy for Win-Place Pari-Mutuel Betting. Management Science, 10(3), 574-577.