Is this what you expect from expectations? -2

The daily problem for Feb 27 asks which of two special dice (1,1,3,3,5,5) and (2,2,2,2,5,5) has a better chance of winning if both dice are rolled simultaneously and the higher roll wins (In case of a tie, you roll both dice again.)

Notice that both dice have the same expected value.

Suppose we have two six-sided dice, A and B, whose faces have integers between 0 and 100 (inclusive).

You are not told what numbers are on the individual faces, but you are told that the probability that A wins is at least 1/2. (And hence the probability that B wins is at most 1/2)

Let $E_A$ and $E_B$ be the expected values of the rolls of A and B respectively.

Which of the following is true?