A sequential game can be broken into a decision tree. If the game is meaningful, that is the tree's depth is finite, and every leaves of the tree can be either A win, or B win, or tie, and not all of the leaves are tie. Once this tree is computed, both players picked the best move, and the best the losing side can do is to prolong the inevitable lost.
A sequential game is not meaningful is that there isn't an ultimate winer. Either the decision tree's depth is infinite, or the best move always lead to tie.
To answer your question, if the decision tree can be computed, and the game is meaningful, one side, either the one that move the first, or the last, will always win.