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CFJ 1577 |
1578 → |
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============================== CFJ 1577 ============================== The Registrar has not legally resolved the Rebellion that occurred on December 15th, 2005. ======================================================================== Caller: Sherlock Judge: Quazie Judgement: Judge: OscarMeyr Judgement: FALSE ======================================================================== History: Called by Sherlock: 17 Dec 2005 13:27:57 GMT Assigned to Quazie: 01 Jan 2006 01:31:43 GMT Quazie recused: 23 Jan 2006 00:00:00 GMT Assigned to OscarMeyr: 13 Feb 2006 08:45:52 GMT Judged FALSE by OscarMeyr: 13 Feb 2006 20:03:35 GMT ======================================================================== Caller's Arguments: Registrar OscarMeyr used a roll of 1 - 12 to determine the success of the Rebellion. However, per eir own admission, there were only 11 registered players at the time of Rebellion. Rule 1079 (Definition of "Random") is fairly clear that the choice has to made between the "possible outcomes": (a) When a Rule requires a random choice to be made, then the choice shall be made using whatever probability distribution among the possible outcomes the Rules provide for making that choice. If the Rules do not specify a probability distribution, then a uniform probability distribution shall be used. By Agoran rules, 12 was not a possible outcome of Rebellion, so it should not have been included as a possible roll in the determination, regardless of whether the Registrar would have ignored it as a result. ======================================================================== Judge OscarMeyr's Arguments: The result of my random determination (selecting a random number from 1 to 12, and trying again on a result of 12) to resolve the rebellion was mathematically equivalent to selecting a random number from 1 to 11. Goethe posted eir proof of this in http://www.agoranomic.org/cgi-bin/mailman/private/agora-business/2006-January/ 005505.html. ======================================================================== Judge OscarMeyr's Evidence: Judge's evidence, the aforementioned post by Goethe: Quazie wrote: >> Would u mind submitting your math you menitioned doing as evidence >> on CFJ 1577? Gratuitous Evidence for CFJ 1577, by request: Part 1. Math. The algorithm used is: Roll 1d12, and re-roll on every 12 (forever if needed), until a 1 through 11 comes up, terminating the process with the last number. What are the odds of a 1 coming up in the terminus? Odds are 1/12 of rolling a 1 on the first roll, terminating. Odds are 1/12 * 1/12 of rolling a 12 on first roll, then a 1 on the second roll, terminating. Odds are 1/12 * 1/12 * 1/12 of rolling 12-12-1, terminating. Odds are (1/12)^4 of rolling 12-12-12-1, terminating. Etc. Since the above sequences are mutually exclusive, the probabilities can be added, giving the probability of rolling a 1 as: SUM[k=1...inf](1/12)^k = (1/12) / (1-(1/12)) = 1/11 (proof ommitted, see equation 9 at http://mathworld.wolfram.com/GeometricSeries.html ) So there's a 1/11 chance of terminating the process with a 1 (or a 2, or 3 or ... or 11). Of course, as Maud pointed out, if the only allowable outcomes are 1 to 11, and there's no reason to bias any one of those, so the math isn't really needed to make the same argument. Part 2. Why this doesn't matter As I said before, my play of Not Your Turn http://www.agoranomic.org/cgi-bin/mailman/private/agora-business/2005-December /005464.html "took back" one Rebel Rabble, and changed the odds. So the odds should have been 9/11 of failure, not 10/11. So OscarMeyr chose from the wrong distribution. E pointed out that eir roll of "10" would have been a failure under either distribution, so e shouldn't be required to re-roll. This IMO is a more interesting reason to consider this CFJ. =Goethe ========================================================================