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>> The game would be reduced to "does Monty feel like gifting you a car or a goat today". But, in fact, that is the way the real show worked. He was more like

>> The game would be reduced to "does Monty feel like gifting you a car or a goat today". But, in fact, that is the way the real show worked. He was more likely to give you a car when he hadn't given away any cars for a while. And Marilyn's description of the problem included no information about whether or not Monty offered to swap doors rarely, frequently, or always, or about the previously observed outcomes depending on whether or not the contestant took the bait. And she surely did not say that Monty was a robot and had no interest in what happened on his show. The way the game actually worked is like how poker and life work until proven otherwise. Every high-stakes game has a sucker, and if you do not know who is the sucker, it is you. Read the story in which a NY Times reporter interviewed Monty about the controversy and you will learn how it really worked.

harshreality 3y ago
If you're playing the game as stated, and if the host opens a door revealing a goat, you must switch for the best odds. The offer to switch doors is part of the problem statement. You can't justify your decision based on the possibility in the real game that you might not get the offer to switch (which would mean that when you do it might be an intentional red herring). Even if there's a 50% chance there are all goats, or a 75% chance, you still switch. That reduces the overall probability of a win, but it doesn't affect the relative probability from switching. The only reason you might not want to switch is if the first choice had been forced, such that there was an above-random chance that your first pick was the car.
- grogers 3y ago
  The person you are responding to is pointing out that if the host doesn't offer you to switch all the time, then it isn't the best strategy to always switch when you are given the option. For example, knowing that everyone switches when given the option, the host might only offer to switch when you've picked the correct door. In that case, not switching would be better. Hence the poker aspect.
  - lucas_membrane 3y ago
    I'll admit that it might be a little more complicated than that. Does life require that we make default assumptions? Is the default assumption that when we are seeing and playing a game for the first time, we should assume that the other players are following the simplest and most impartial strategy that can explain their behavior a good default assumption? Implicit default assumptions are rampant in human efforts to resolve the hard problems of life. Can anyone recommend ways to identify them, to find alternative default assumptions, choose good ones, and to be aware of their impact on conclusions.

harshreality 3y ago

If you're playing the game as stated, and if the host opens a door revealing a goat, you must switch for the best odds. The offer to switch doors is part of the problem statement. You can't justify your decision based on the possibility in the real game that you might not get the offer to switch (which would mean that when you do it might be an intentional red herring). Even if there's a 50% chance there are all goats, or a 75% chance, you still switch. That reduces the overall probability of a win, but it doesn't affect the relative probability from switching. The only reason you might not want to switch is if the first choice had been forced, such that there was an above-random chance that your first pick was the car.

grogers 3y ago
The person you are responding to is pointing out that if the host doesn't offer you to switch all the time, then it isn't the best strategy to always switch when you are given the option. For example, knowing that everyone switches when given the option, the host might only offer to switch when you've picked the correct door. In that case, not switching would be better. Hence the poker aspect.
- lucas_membrane 3y ago
  I'll admit that it might be a little more complicated than that. Does life require that we make default assumptions? Is the default assumption that when we are seeing and playing a game for the first time, we should assume that the other players are following the simplest and most impartial strategy that can explain their behavior a good default assumption? Implicit default assumptions are rampant in human efforts to resolve the hard problems of life. Can anyone recommend ways to identify them, to find alternative default assumptions, choose good ones, and to be aware of their impact on conclusions.