Timeline for Five pirates splitting gold with a twist
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| May 4, 2015 at 22:40 | history | edited | Lawrence | CC BY-SA 3.0 |
Propagate P's fever-free status through the answer to leave 4 states, not 5.
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| May 3, 2015 at 17:30 | comment | added | Lawrence | @Lopsy Good point. The probabilities aren't going to be nice and simple fifths. | |
| May 3, 2015 at 15:39 | comment | added | Lopsy | But once the first pirate proposes that uneven split, all the other pirates know that he isn't the one with the fever, so all the fever probabilities change to 1/4. Also, whenever a proposal is voted no, the result of the vote may give some pirates information about who might have the fever. | |
| May 3, 2015 at 14:34 | history | edited | Lawrence | CC BY-SA 3.0 |
Reformatted for clarity, clarified how expected earnings is calculated.
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| May 2, 2015 at 9:37 | comment | added | Lawrence | @JS1 "as if they know exactly who has the fever" - they don't know who has the fever. However, they can consider each possibility and weight the payouts by the probability of it happening, which produces the "expected number". | |
| May 2, 2015 at 9:28 | history | edited | Lawrence | CC BY-SA 3.0 |
Elaborated on the use of "expected number".
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| May 2, 2015 at 9:20 | comment | added | JS1 | I don't think you can calculate expected earnings based on future proposals that can never actually happen. I think the flaw is that you are making each person do their proposals as if they know exactly who has the fever. | |
| May 2, 2015 at 9:16 | comment | added | Lawrence | @JS1 I think the answer holds at R. The $269:31:0$ split is conditional on RS being both fever-free. If S has the fever, R's proposal would be an even split. Of course, R doesn't know who has the fever, so the calculations up to QRST are only for the purpose of calculating the expected earnings. Only P makes an actual (single) proposal. | |
| May 2, 2015 at 9:09 | history | edited | Lawrence | CC BY-SA 3.0 |
added 183 characters in body
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| May 2, 2015 at 9:03 | comment | added | JS1 | I don't think R can propose 269:31:0. Because what if S has the fever, then R will get killed. I think R's motivation must be to survive first, grab more coins second. | |
| May 2, 2015 at 8:49 | history | edited | Lawrence | CC BY-SA 3.0 |
deleted 127 characters in body
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| May 2, 2015 at 8:44 | history | answered | Lawrence | CC BY-SA 3.0 |