Ask HN: Could we make a decision based on a random measured value?

Let's have a set of two actions { goLeftOpenDoor, goRightRiseFlag }, and a deterministic algorithm to pick one action given a completely random input.

Alice and Bob are both aware of this algorithm, but they are very far from each other.

Alice and Bob each receives one particle from an entangled pair (A,B).

Alice makes a measurement on her particle, and so does Bob.

They now both also share a meaningless random value.

But, since they previously agreed on a way to _do something_ based on a random input, Bob actually picks _goRight_ and he goes right, and raises the flag.

Could then Alice know that the flag has been raised ? If so, why isn't it considered as an actual information ?

Note : I think I'm really wrong somewhere here (and probably have "divided by zero" several times)... just correct me if/where it's the case.