So, take the usual Monty Hall setting - 3 doors and one car, 2 goats. I can reveal a door once you've chosen yours.

Then extend it to a situation, where,if you SWITCH, the door you switched from is deleted. And then you go on and on....

how would you model this formally?

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    $\begingroup$ How does the game goes 'on and on' after I've switched ? Don't you just open the door I've just switched to and I go away with two thirds of a car and one third of a goat ? In classical Monty Hall at least you may or may not delete the door I've switched from, the game is over. $\endgroup$ – Evargalo Jul 27 '17 at 7:30
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    $\begingroup$ I agree with @Evargalo - as I understand it, you start with 3 doors, and you choose one. A random other door is then opened. You are given the choice of switching or sticking with your door, having seen the contents behind the opened door. The door you choose is opened. If you delete a door after switching from it, then you are left with one closed door and one open door. Your only option is to open the closed door and receive the item behind it... $\endgroup$ – lioness99a Jul 27 '17 at 7:51

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