3 ms·

The question is phrased ad-hoc. We know the host picked a goat in both scenarios. Decision time. Do we switch or no? It didn't ask: "On an infinite timeline whe

by skizm 12y ago

The question is phrased ad-hoc. We know the host picked a goat in both scenarios. Decision time. Do we switch or no? It didn't ask: "On an infinite timeline where the host might not always pick the goat, should we switch and if so when?" Which I think is what op was trying to say.

Cushman 12y ago
No. Even in the case of a single trial, it matters. If the host picks randomly, and the host picks a goat, and you switch, your odds of a car are 1/3, just as if you'd stuck. There's no point. If the host always chooses a goat, and the host picks a goat, and you switch, your odds are 2/3 in favor of now having a car. You should always switch. Intuition suggests this. Statistics proves it. If you implement this in software, you will see it happening to you in black and white, right before your eyes.
- dllthomas 12y ago
  "If the host picks randomly, and the host picks a goat, and you switch, your odds of a car are 1/3, just as if you'd stuck. There's no point." 1/2, once you see the goat. One of 1/3, 2/3, and 1/2 beforehand, depending on what happens when Monty shows a car: whether you automatically win, automatically lose, or start over from the top, respectively.
  - Cushman 12y ago
    Right, to be clear, that's your total chance of walking away from the show with a car. Switching doesn't change it.
    - dllthomas 12y ago
      Right.
dllthomas 12y ago
It matters why the host picked the goat. (Or, more precisely, what the odds were of him doing otherwise when he picked). That we're looking at a goat doesn't tell us everything. Again, write the simulation. Either the switch strategy will win 2/3 of the time or 1/2 of the time, depending on how you write Monty. Only one of those approaches matches the results we saw IRL - Monty never revealed the car (so far as I'm aware) - but either is consistent with many phrasings of the question, and OP correctly specified the other case above.
- skizm 12y ago
  you keep telling me to write a simulation. It won't matter. the code is the same for both questions since they are asking the same thing.
  - dllthomas 12y ago
    That's not true, but we'll pick it up under the code jayvanguard supplied.

by skizm 12y ago

Cushman 12y ago

No. Even in the case of a single trial, it matters. If the host picks randomly, and the host picks a goat, and you switch, your odds of a car are 1/3, just as if you'd stuck. There's no point. If the host always chooses a goat, and the host picks a goat, and you switch, your odds are 2/3 in favor of now having a car. You should always switch. Intuition suggests this. Statistics proves it. If you implement this in software, you will see it happening to you in black and white, right before your eyes.

dllthomas 12y ago
"If the host picks randomly, and the host picks a goat, and you switch, your odds of a car are 1/3, just as if you'd stuck. There's no point." 1/2, once you see the goat. One of 1/3, 2/3, and 1/2 beforehand, depending on what happens when Monty shows a car: whether you automatically win, automatically lose, or start over from the top, respectively.
- Cushman 12y ago
  Right, to be clear, that's your total chance of walking away from the show with a car. Switching doesn't change it.
  - dllthomas 12y ago
    Right.

dllthomas 12y ago

It matters why the host picked the goat. (Or, more precisely, what the odds were of him doing otherwise when he picked). That we're looking at a goat doesn't tell us everything. Again, write the simulation. Either the switch strategy will win 2/3 of the time or 1/2 of the time, depending on how you write Monty. Only one of those approaches matches the results we saw IRL - Monty never revealed the car (so far as I'm aware) - but either is consistent with many phrasings of the question, and OP correctly specified the other case above.

skizm 12y ago
you keep telling me to write a simulation. It won't matter. the code is the same for both questions since they are asking the same thing.
- dllthomas 12y ago
  That's not true, but we'll pick it up under the code jayvanguard supplied.