So you're saying that you can make n amount of measurements and the chance of the spin being positive or negative will be about 1/2n (50%). And that P1spin=P2spin at the time of measurement?
How do we know that a random variable isn't being produced at the time of entanglement? What makes this different than both particles following a function?
Nothing is different. They both follow the same wave function. That's why they are entangled.
Edited:
But the important question is this: can it bypass the lightspeed limit?
No. You still have to share the time of measurment between the "readers" .
That enables both readers to read the same information.
This technique is used to create uncrackable encryption.
The readers read the two particles at the same time or with a MINIMAL lag since changing the spin for example also takes some time. In the end they read the same information and use this as the key to encrypting data.
Now they can easily exchange the encrypted date and noone else can read it since only those two know the key.
The key is not crackable either since it's generated randomly from the quantum status of the two particles while reading.
It even goes further.
Let's say someone is between both and knows the exact time of the reading and reads an entangled 3rd particle.
The reading itself would also influence the other measurements and thus change the results. So you'll always see if someone tried to read your "time" after comparing the keys.