The Logic
The Monte Hall problem is frequently misunderstood as just a probability problem, but in reality, it is an information game. With a minimum of 3 doors, there is a 1/3 chance you pick the correct door on the first try and a 2/3 chance it's in the other set of doors. Not bad odds either way, but you should switch. Here's the reasoning without getting too math-y:
Door A (your pick) - Chance of correctness 1/3
Doors B and C (other doors) - Chance of correctness 2/3
Reveal - C is open and empty
The probability of each group remains unaffected as above, BUT the group with 2 doors has revealed critical information. Your choices of doors again:
Door A - 1/3
Door B (C is a guaranteed loss) - 2/3
About 66% of the time, switching will result in finding the cat. Increasing the number of doors increases the probability of success on switching, although good odds are not a guarantee. Try the visualizer yourself and see if you can beat the odds.
