Row 15371

Row ID: 15371 | Dataset Entry | Axioma AXP Content Repository

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This page contains data entry 15371 from the Axioma AXP content repository. The structured data below represents the complete record for this entry.

Do you understand why the answer to the Monty Hall question is "always switch"? I mean, really understand it?

If not, then start there. Go read about it, until it makes sense.

The important thing is, statistically, the other door on average is worth more than the one you picked. This is known, it has been tested, and it's just a fact.

*****

Now, before you open an envelope, there are an infinite number of possible values in each of them. You have no reason to prefer one over the other, and the two envelopes don't limit each other in any significant way.

Once you open one — and we will stick to $200 as our amount in the envelope — you are living in one of two universes, with a 50% chance each. You have no clue which one. Either the other envelope holds $100 or $400.

Forget about the fact that you could have chosen the other envelope. That's just confusion talking. You chose one with $200, so the other envelope is either $100 or $400, 50% chance each, average $250. So you switch.

It only works mathematically because the envelopes could have an infinite amount of money in them and are on a geometric distribution. Geometric distribution just refers to the fact that one envelope has twice as much as the other, so if you trade down, you only lose half, but if you trade up, you get double. So your bet is at 3-1 odds on a 50-50 chance.

If the higher envelope just always had $100 more than the lesser, then there would be no reason to switch. If there were a minimum and maximum X amount, then you could calculate the chance of whether you were at the bottom or the top of the distro and make the decision that way.

However, since you can't top out the distro, it's always a better bet that the other envelope has more.

FieldValue
text Do you understand why the answer to the Monty Hall question is "always switch"? I mean, really understand it? If not, then start there. Go read about it, until it makes sense. The important thing is, statistically, the other door on average is worth more than the one you picked. This is known, it has been tested, and it's just a fact. ***** Now, before you open an envelope, there are an infinite number of possible values in each of them. You have no reason to prefer one over the other, …
label r/chatgpt
dataType comment
communityName r/ChatGPT
datetime 2024-05-20
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url_encoded Z0FBQUFBQm5Lak9MM1psbEtlZU1BcVB0WDFKYjExR2tWS3lEcC1OTlcycVlBRmZpbU5uOHFkWXlubjlsSnlBbGEtdFR5TXEtTWlqRXR2OWs3TXc5c0V5amlhdi04Rmp1RGVoekowVW9wdjk5Sl9XUVZ4cTFWZWd0cXd0V1MzVWdXQldzLVpiZFF4RTI3UmJ3dE84WDFPaFNjbmpENThuMHNzN2JfRVFGM01LOU5xaGRzVDZvVnlwRG0ybktQS2tialM1Q1FZOG0tbmxTa3Jubi1uTjRWblNqSFRwYlZWM2R6Zz09

Raw Record

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  "text": "Do you understand why the answer to the Monty Hall question is \"always switch\"?  I mean, really understand it?  \n\nIf not, then start there. Go read about it, until it makes sense. \n\nThe important thing is, statistically, the other door on average is worth more than the one you picked. This is known, it has been tested, and it's just a fact. \n\n*****\n\nNow, before you open an envelope, there are an infinite number of possible values in each of them. You have no reason to prefer one over the other, and the two envelopes don't limit each other in any significant way. \n\nOnce you open one — and we will stick to $200 as our amount in the envelope — you are living in one of two universes, with a 50% chance each. You have no clue which one. Either the other envelope holds $100 or $400.  \n\nForget about the fact that you could have chosen the other envelope. That's just confusion talking. You chose one with $200, so the other envelope is either $100 or $400, 50% chance each, average $250. So you switch. \n\nIt only works mathematically because the envelopes could have an infinite amount of money in them and are on a geometric distribution. Geometric distribution just refers to the fact that one envelope has twice as much as the other, so if you trade down, you only lose half, but if you trade up, you get double. So your bet is at 3-1 odds on a 50-50 chance. \n\n\nIf the higher envelope just always had $100 more than the lesser, then there would be no reason to switch. If there were a minimum and  maximum X amount, then you could calculate the chance of whether you were at the bottom or the top of the distro and make the decision that way. \n\n\nHowever, since you can't top out the distro, it's always a better bet that the other envelope has more.",
  "label": "r/chatgpt",
  "dataType": "comment",
  "communityName": "r/ChatGPT",
  "datetime": "2024-05-20",
  "username_encoded": "Z0FBQUFBQm5Lakw4WkNXV0JKclBpaS1mMUNwQy1vMTRCQlU3MGRIbVpQMmhhQTVqY0pqYW90eG9vdHlFTmp5YWNGVUFYblZVN09XX05GcFZheVdObUVKMHFDTzZvZVMxWXc9PQ==",
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