a device capable of measuring quantum levels events

The brain doesn't do this,

You don't know that, since no one does.

Dice are deterministic.

You don't know that either. A number of random number generators have enough sensitivity to initial conditions to reach the quantum level.

Chaotic behavior != indeterminism

Confusing phrased. Classical chaos could exist in a deterministic universe, but it can also exist in an indeterministic universe where classical behaviour is a high level approximation. In that kind of universe, classical chaos acts ad a natural amplifier.