How do we know the universe hasn't decided?

You and I decide to test whether or not the universe has decided. We have Nabisco mail us quantum oreos, three at a time and we each choose randomly to measure one of them (this is analogous to measuring the spin of an electron in a randomly-chosen axis).

Now, if we're measuring them three at at time, there are only two plausible possibilities: one of us has all three cremes (this happens 2 out of every 8 trials) or one of us has two cremes (this happens 6 out of every 8 trials). If one of us has all the cremes, it doesn't matter which one each of us independently chooses to measure; we will both have the same outcome. If one of us has only two of the cremes (e.g., [M]e has two and [Y]ou have one), we agree 5/9ths of the time

      M M Y
    M 1 1 0
    M 1 1 0
    Y 0 0 1

If we run this experiment many, many times, we should converge upon (2/8 * 9/9) + (6/8 * 5/9) = 2/3 of the time our measurements agree. This would be consistent with a model of "preprogrammed" quantum Oreos. This is not what we see in practice. When we actually run this experiment, our measurements agree exactly 50% of the time which can only be explained if the quantum Oreos are not preprogrammed.