When first confronted with this, I wrote a simulation in GW-Basic on a PC with an orange monochrome monitor and ran it a bunch of times to convince myself switc

When first confronted with this, I wrote a simulation in GW-Basic on a PC with an orange monochrome monitor and ran it a bunch of times to convince myself switching was the right thing to do, statistically. I came up with another way to visualize it that made more sense than increasing the number of doors, but it requires that one accept the fact that your chances of winning are 1/3 if you don't switch, and you know Monty always shows a losing door.