If, if, if, if ad infinitum. Shame!

"Yes, it is fundamental to the problem that Monty knows where the car is and makes an informed choice to open a door to reveal a goat. This gives you information (in the form of a probablity, not a certainty) about what is behind the door he chose not to open."

"NOT A CERTAINTY". It still boils down to ONE choice... between TWO doors. NO inference can logically be made about "switching" the first choice because there is NO switching... it is now simply, ONLY, a choice between TWO doors.

You ask me to play the game to prove your point? I could not be arsed to do so. If you consider that doing so is "proof" you really have too much time on yer hands.

Two doors. One choice. You may, in yer mind, THINK you have two choices... hit me or stick... but that is where your argument falls apart... they are the SAME. When you overlook that FACT you are throwing in another IF (which literally has no bearing on the logic on an even an empiracal level) and some of you don't seem to get that.

One last time... TWO doors... ONE choice. 50/50. If you don't believe me, flip a coin ten thousand times and report back your results. If you tell me picking heads wins 2/3 of the time, seek help.