In the
Monty Hall problem, there is a correct door and with Monty's inadvertent help you are improving your chance of ending up with that correct choice.
With Bell's inequality, you have two measurement stations and for each particle pair, each station randomly selects one those three possible measurements.
After repeating the Monty Hall experiment 9000 times, you will either end up with 3000 goats and 6000 Cadillacs or 6000 goats and 3000 Cadillacs.
After repeating Bell's experiment 9000 times, you will have:
3000 measurements that were made at the same angle and they all showed the particle pairs with opposite spins (0% the same);
2000 measurements that were made at angles 30 degrees apart with 268 with the same spin (13.4%); and
4000 measurements that were made at angles 15 degrees apart with 136 with the same spin (3.4%).
After Monty carefully examined the results of your Bell experiment, he would deduce:
1) From the 3000 measurements at the same angle, he would discover that the particles in any particle pair had opposite spins;
2) That a 15-degree change in the measurement would result in a 3.4% difference in the measuring result;
3) That two 15-degree changes could not possibly result in more than double that difference, ie 6.8%;
4) That since your 30 degree measurements showed 13.4% (large than 6.8%), you are a chronic cheater and must be banned from winning any goats or Cadillacs.
