Winning Strategies in Multimove Chess (i,j)

We propose a class of chess variants, Multimove Chess (i,j), in which White gets i moves per turn and Black gets j moves per turn. One side is said to win when it takes the opponent's king. All other rules of chess apply. We prove that if (i,j) is not (1,1) or (2,2), and if $i \geq \min(j,4)$, then White always has a winning strategy, and otherwise Black always has a winning strategy.