dyadiccounterpoint wrote:
...changes the odds because patterns emerge when you draw sequences.
Firstly, a little bit of an apology - I may have led things astray a little bit with the word "sequences". A winning lottery ticket has a "set" of numbers, but not a "sequence", because whether you win or not doesn't depend on the order that the numbers get drawn in. Whether or not patterns emerge in the drawing depends on what pool of things you're drawing from and how you select them. In this case, there's no reason that any patterns should form
in theory, but it is possible if the random number generators are not designed well enough.
Drawing the numbers one at a time is in practice no different than shuffling all of the numbers into a completely random order, then picking a bunch all in one go - very like cutting a well shuffled pack of cards. The probabilities work out exactly the same as doing it one at a time (but not so dramatic on TV, of course!) Not sure if that helps for you, but it's clearer to me why there are no mathematical patterns if I think of it that way, somehow.
What you say about the number properties, and your 'photon' example are perfectly reasonable, there certainly are plenty of predictions you can make about how different ways of generating random numbers will spread the results out. Ironically, the engineering/programming to get the ideal, but totally boring, "likely to go everywhere" result can be fiendishly difficult; but you can bet your bottom dollar that the guys who designed the lottery machine got a bit fat paycheck for stopping gamblers from exploiting any weaknesses! (history trivia: the worlds first electronic lottery machine, "ERNIE", was based on the famous Colossus computer that cracked the WWII Nazi Enigma codes, and designed by the same boffin.)
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