This description greatly helped in making the problem "click" for me, thanks! The fact that they can't know which row/column they're going to be assigned makes

This description greatly helped in making the problem "click" for me, thanks! The fact that they can't know which row/column they're going to be assigned makes it impossible to know with more than 8/9 certainty what the correct move would be. Even if they agree ahead of time what the values should be, the fact that they only know half of the information makes it impossible (classically) to win more often than 8/9 of the time. They have no control over and no way of knowing which row/column the other was given. If I'm understanding correctly, the "quantum version" lets you increase that precision arbitrarily depending on how many measurements you make, up to 99.9999999...% Really neat stuff