Move Move Chess

Consider a chess game in which every player is allowed to move twice per turn. Show that Black does not have a winning strategy.

SOLUTION

Assume Black has a winning strategy. Then if White plays Kb1-Kc3 and Kc3-b1 on his first turn, the game basically will start all over again, but with Black moving first. Therefore White will have a winning strategy, which is a contradiction.

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