Dar -- I hardly think you need my blessing, but I agree with your definition of p(k). I ran some numbers through Wolfram Alpha, and it looks like even for 100 item lists the probability of the first item being sorted to the first spot is about 0.015, or 1.5 times what it should be if sorted by random(the number of items).
Of course, that's not the overall probability that the list is mal-sorted. That probability is much higher, and I'm not sure how to calculate it (hanging my head in shame), but roughly: Say you have a set of 100 items where each gets a unique random number to sort by except for the first two, which both get 1. They *should* be able to come out either A,B or B,A, but they can only come out A,B. Note that this does not depend on what common number they get -- even if they both got 100, then although both of them would be moved to a different spot in the output, there should be two possible outcomes, but there is only one. Hence the probability under this circumstance of having an improper shuffle is 0.5. Likewise, if three items had the same random number, there would be only one possible outcome when there should be 3*2*1 = 6 possible outcomes, so there is a 5/6 or roughly 0.83 probability of a bad shuffle. This goes up, obviously, as the number of dupes increases. Further, there can be more than one duplicated number. If two items have 99, and three others have 23, then the probability of an improper shuffle is 1 - 1/2 * 1/6 = 1 - 1/12 = about 0.92. My failure comes in aggregating all the various possible sets of duplicates. Of course, the goal is achieving success, not calculating failure. I did the math (okay, Wolfram Alpha did the math) and using: sort lines of myList by random(999999999) & random(999999999) For a list 1 million lines long has a probability less than 1 in a million of having even a *slightly* non-random order (within the bounds of the random number generator). That seems good enough for me. For shorter lists the concatenation would be unnecessary. I commented on the feature request. I think this would be an excellent application of the new language features once they are available. gc _______________________________________________ use-livecode mailing list use-livecode@lists.runrev.com Please visit this url to subscribe, unsubscribe and manage your subscription preferences: http://lists.runrev.com/mailman/listinfo/use-livecode
