Look at it from actual door, first guess door pairs -- which are the random uncorrelated events: 1,1 - switch loses (host may have shown door #2 or #3) 1,2 -

Look at it from actual door, first guess door pairs -- which are the random uncorrelated events: 1,1 - switch loses (host may have shown door #2 or #3) 1,2 - switch wins (host showed door #3) 1,3 - switch wins (host showed door #2) 2,1 - switch wins (host showed door #3) 2,2 - switch loses (host may have shown door #1 or #3) 2,3 - switch wins (host showed door #1) 3,1 - switch wins (host showed door #2) 3,2 - switch wins (host showed door #1) 3,3 - switch loses (host may have shown door #1 or #2) The choice of which door to show you is not a random event and is highly dependent upon the events which preceded it, because the host cannot show you the door it is actually behind, or the door that you picked.