Last time I claimed this was the correct answer, I was linked to the Monty Crawl problem. https://www.probability.ca/jeff/writing/montyfall.pdf
Years ago, the Monty Fall variation was mentioned on a local telnet forum I visited. The "consensus" of the thread was the solution of Monty Fall is the same as that of Monty Hall: switching gives you 2/3 chance to win.
That was when I realized many people just memorize the Monty Hall's solution without understanding it, a.k.a. "standardized tests".
That's fine, but given the parameters of the problem change with the Monty Crawl variant, it's not the same problem, and doesn't invalidate the answer of the base variant.