Some constant-sum $n$-stage sequential game version of 

best-choice problems under Winning Probability (WP) 

maximization are investigated and the explicit solutions 

are obtained. The essential feature contained in 

these sequential games is the fact that 

the players have their own weights 

by which at each stage, player's desired decision 

may be taken away by an opponent as an outcome of 

drawing a lottery. The game is, essentially, 

a generalization of the ``horse game'' first investigated  

by Enns and Ferenstein [2]in 1985.