Do you think our Lord and Savior would have been crucified if Judas hadnt betrayed Him?

I think so. I love Jesus with all my heart and soul but I feel that the betrayal was like a vital move in a chess game. Even though our Lord was hurt very badly and it pains me to realize that it also makes me happy to know one Being sacrificed Himself and went through all the human pains and tortures one could go through so that a bunch of people can make it to Heaven. Whats your opinions?