This YouTube video explains the error in the math of the paper most commonly cited to disprove “heating up”. I absolutely cannot wrap my head around it. Are there any math people here that are able to explain it?

The section of the video that deals with the math is titled “A Coin Flip Simulation.” It starts at 10:40. The guy mentions that it’s a version of the Monty Hall Problem, which I do understand, but I can’t intuit how the two problems are similar.