The comments here led me to realize that I didn't really understand, either. Thank you. To save you some searching, I found the answer here [1]. The crux is th

The comments here led me to realize that I didn't really understand, either. Thank you. To save you some searching, I found the answer here [1]. The crux is that Alice and Bob don't know which row/column the other is filling, and they are given symbol-selection rules which would contradict each other if used to fill the whole square, preventing a pre-ordained strategy (e.g. a pre-seeded RNG) with 100% success rate. So a 100% strategy would intuitively need some way of communicating _after_ they are given their row and column, and the math shows that the quasi-communication granted by entanglement is sufficient. I'm sure my explanation is also insufficient, but there should be enough information at the link to convince you if you're curious. [1] https://en.wikipedia.org/wiki/Quantum_pseudo-telepathy#The_Mermin%E2%80%93Peres_magic_square_game https://en.wikipedia.org/wiki/Quantum_pseudo-telepathy#The_M...