You are applying the math, informed or otherwise, to 2 consecutive guesses. That doubles Monty's chances.After 17 pages you still have it 100% wrong. Just because there are 2 choices doesn't make it 50-50 because the 2 choices do not have an equal chance of being the winner. Your original door has a 1/3 chance of being the winner and the other door has a 2/3 chance of being a winner.