Refer to the divide-and-choose method for two players presented in Section 4.1. Referen...

Refer to the divide-and-choose method for two players presented in Section 4.1.

Reference:

DIVIDE-AND-CHOOSE METHOD FOR TWO PLAYERS

Two players, X and Y, are to divide a cake.

STEP 1: Player X divides the cake into two pieces that he or she considers of equal value. (We call player X the divider.)

STEP 2: Player Y picks whichever of the two pieces he or she considers to be of greater value. If player Y also considers the pieces to be of equal value, then he or she can pick either piece. (We call player Y the chooser.)

STEP 3: Player X gets the piece that player Y did not select.

In the divide-and-choose method for two players, will the divider always receive a division that is worth one-half of the total value? Explain.