I feel like there is some overthinking of the monty problem here. The answer no makes the most sense. Consider this, what is behind the doors is predetermined, right? So either the smallest number of people you can hit is 0 or 5. The most is 10. Chosing either a or c guarentees at least 5 people hit. Choosing B limits the number who can be hit to 5 (if they’re behind the door). So you should always choose B and always keep the choice.
Overthinking it is exactly what leads to the solution “no” imo. If you say no every time, then you can only possibly be correct 1/3 of the time since it’s a 1/3 chance of picking the correct door. Hence 2/3 of the time you picked incorrectly and hence should switch. By design if you pick incorrectly then the switched door will be the correct solution
