[taeric]

My understanding was that if the host picks randomly, then you are still better swapping if a non-winning door is revealed. The catch is you can't switch to the winning door if it is revealed. So, going into the game, your odds are not as changed. However, at the point of possibly swapping, you are down to chance that the remaining door is a winner. Roughly 1/2. Compared to your initial chance of 1/3 on the first pick.

I think to enumerate the possibilities you'd have to see that if you picked the winning door, there are two ways the host could leave doors for you to swap to and lose.

If you picked a losing door, there is only a single way for the host to reveal a losing door.

So, at the point you are looking at a losing door and making a swap, there are 4 ways you could have gotten there. You picked the winning door, and the host showed either of the two losers. Or you picked either of the two loser doors and the host showed you the other loser. Four possibilities, two of them you win if you swap.

[dllthomas]

Your understanding does not jive with my simulation. Write the simulation. It is certainly possible that my simulation is in error, but as I said it surprised me so I looked closely for error, and I have several times heard people report independently reaching the same conclusion on writing their own simulations and never (yet?) the other.

[taeric]

Thought even more on this. Did not get a chance to run a simulation, but thought of it while driving around.

It finally jives with me that your odds at swap time are only 50%. Seems kind of obvious when you think of it as random events and you are at the end with it definitely behind one of two doors. Either door is clearly as likely. Now, your odds of getting to this point are vanishingly slim, the more doors there are. Which makes sense.

I think my intuitive block comes in in that your odds of winning the game are not increased in this scenario at all. Which, I knew. I think I even stated it at some point. Still a hard block to get around.

[taeric]

I'll try to write up a simulation this weekend. I'm not entirely sure where we are disagreeing, though. I'm not saying that you have 1/2 chance of winning the game. Only if you have the chance to swap, you win half of the time if you do. That seems to be what you said in a sibling thread.