Then, someone hands you a huge number of KCBS pentagrams, but at first, all of the colorings are hidden. You're told you can only uncover 2 vertices at most, and only if they share a common edge. So, for each pentagram, you randomly pick an edge and uncover the colors on its vertices. This random choice is necessary because if the pentagram producers had been able to guess your choice for each pentagram in advance, he could have "conspired" to fool you. You find no matter which edge you choose, you find blue-blue with a probability of 1 − − 2 5 , red-blue with 1 5 , and blue-red with 1 5 . So, the expectation value of the sum of mismatches is 2 5 ≈ ≈ 4.47 > 4 .