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I see this posted a lot but it doesn't click with me. It only feels obvious once I know how the probabilities work - meaning I have to get the base case first.

by IanCal 3y ago

chefandy 3y ago
Picture, in your mind or maybe draw on paper, 20 brightly lit doors in a row where 19 are labeled L and one is labeled W. Out of those 20 doors, one door gets randomly selected. It's almost certainly going to be an L. After choosing it, the lights go out above 18 of the other L doors so only the W door, and the L door you probably chose, remained lit. If you stayed with your existing selection— one of two doors that remains lit— you've still almost certainly got an L door. If you switch to the one other door, with all of the other L doors eliminated, the only way it's not the W door is if you chose the W to begin with.
- IanCal 3y ago
  Two things about this 1. It requires that I already get the point about the probabilities. 2. You don't get a benefit in Monty hall if the host picks randomly - the description requires that they deliberately leave the winning door available. Any situation that gives you the same intuition but you just picture as happening without intent has given you the wrong feeling. I don't find that increasing the number of doors makes it feel any different.
  - latexr 3y ago
    > You don't get a benefit in Monty hall if the host picks randomly But the host doesn’t pick randomly, they always pick a goat. That is an integral part of the Monty Hall problem. Picking randomly wouldn’t make sense. You’d pick a goat, then the host could randomly reveal the car and the game would end anticlimactically.
    - chefandy 3y ago
      Exactly— the entire point is that the host always eliminates every losing answer that you didn't choose unless you chose the right answer initially. If you keep your pick, you have a 1 in 3 chance of winning, and if you switch, you have a 1 in 3 chance of losing.
      - IanCal 3y ago
        Yes, it is this point (and reinforcing it) that explains the problem to me. Simply increasing the number of doors doesn't help - and it shouldn't.
        chefandy 3y ago
        I didn't simply increase the number of doors— I created a visual of a more extreme version of the problem without making it so extreme that it's abstract. That sort of thing helps a lot of visual thinkers and I'm not sure why you're being so pissy about it not helping you. Frankly, I'm sorry I tried.
        IanCal 3y ago
        I'm not being pissy about it, I'm explaining why this approach doesn't click for me. I'm not sure why, after being told that this type of explanation doesn't work for me and being told exactly why, you are surprised when I say that again. I'll try and help explain why in more detail. The point is that for me the key bit of information is yet again missing from your explanation. > Picture, in your mind or maybe draw on paper, 20 brightly lit doors in a row where 19 are labeled L and one is labeled W. Out of those 20 doors, one door gets randomly selected. It's almost certainly going to be an L. After choosing it, the lights go out above 18 of the other L doors so only the W door, and the L door you probably chose, remained lit. It's extremely important the reasoning behind why the 18 other doors are picked is highlighted. The game show deal or no deal has basically this, but with 20 or 25 or something boxes. At the end they get to switch - and it doesn't make a difference. It wouldn't make a difference if the host opened the boxes or the contestants. It wouldn't make a difference if the host opened them and knew what was inside. What would make a difference is if the host opens the boxes while deliberately avoiding opening the jackpot. Lets reframe deal or no deal in a way that highlights the key part for me: There are 25 boxes with sums from 1p to £1M in them. Nobody knows what's in them. You pick one randomly, and the others are placed in a pile. You now get to choose one of two things: 1. Keep the box you chose randomly 2. Take the highest value box out of the pile of 24 What if there were 24 boxes worth nothing and one with £1M in, does your strategy change? What if there were 23 boxes with nothing and one with £1M in, does your strategy change? What if there were just three boxes?

I see this posted a lot but it doesn't click with me. It only feels obvious once I know how the probabilities work - meaning I have to get the base case first.

by IanCal 3y ago

I see this posted a lot but it doesn't click with me. It only feels obvious once I know how the probabilities work - meaning I have to get the base case first.

chefandy 3y ago

Picture, in your mind or maybe draw on paper, 20 brightly lit doors in a row where 19 are labeled L and one is labeled W. Out of those 20 doors, one door gets randomly selected. It's almost certainly going to be an L. After choosing it, the lights go out above 18 of the other L doors so only the W door, and the L door you probably chose, remained lit. If you stayed with your existing selection— one of two doors that remains lit— you've still almost certainly got an L door. If you switch to the one other door, with all of the other L doors eliminated, the only way it's not the W door is if you chose the W to begin with.

IanCal 3y ago
Two things about this 1. It requires that I already get the point about the probabilities. 2. You don't get a benefit in Monty hall if the host picks randomly - the description requires that they deliberately leave the winning door available. Any situation that gives you the same intuition but you just picture as happening without intent has given you the wrong feeling. I don't find that increasing the number of doors makes it feel any different.
- latexr 3y ago
  > You don't get a benefit in Monty hall if the host picks randomly But the host doesn’t pick randomly, they always pick a goat. That is an integral part of the Monty Hall problem. Picking randomly wouldn’t make sense. You’d pick a goat, then the host could randomly reveal the car and the game would end anticlimactically.
  - chefandy 3y ago
    Exactly— the entire point is that the host always eliminates every losing answer that you didn't choose unless you chose the right answer initially. If you keep your pick, you have a 1 in 3 chance of winning, and if you switch, you have a 1 in 3 chance of losing.
    - IanCal 3y ago
      Yes, it is this point (and reinforcing it) that explains the problem to me. Simply increasing the number of doors doesn't help - and it shouldn't.
      - chefandy 3y ago
        I didn't simply increase the number of doors— I created a visual of a more extreme version of the problem without making it so extreme that it's abstract. That sort of thing helps a lot of visual thinkers and I'm not sure why you're being so pissy about it not helping you. Frankly, I'm sorry I tried.
        IanCal 3y ago
        I'm not being pissy about it, I'm explaining why this approach doesn't click for me. I'm not sure why, after being told that this type of explanation doesn't work for me and being told exactly why, you are surprised when I say that again. I'll try and help explain why in more detail. The point is that for me the key bit of information is yet again missing from your explanation. > Picture, in your mind or maybe draw on paper, 20 brightly lit doors in a row where 19 are labeled L and one is labeled W. Out of those 20 doors, one door gets randomly selected. It's almost certainly going to be an L. After choosing it, the lights go out above 18 of the other L doors so only the W door, and the L door you probably chose, remained lit. It's extremely important the reasoning behind why the 18 other doors are picked is highlighted. The game show deal or no deal has basically this, but with 20 or 25 or something boxes. At the end they get to switch - and it doesn't make a difference. It wouldn't make a difference if the host opened the boxes or the contestants. It wouldn't make a difference if the host opened them and knew what was inside. What would make a difference is if the host opens the boxes while deliberately avoiding opening the jackpot. Lets reframe deal or no deal in a way that highlights the key part for me: There are 25 boxes with sums from 1p to £1M in them. Nobody knows what's in them. You pick one randomly, and the others are placed in a pile. You now get to choose one of two things: 1. Keep the box you chose randomly 2. Take the highest value box out of the pile of 24 What if there were 24 boxes worth nothing and one with £1M in, does your strategy change? What if there were 23 boxes with nothing and one with £1M in, does your strategy change? What if there were just three boxes?