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> It's always impossible to tell, for any given sequence, whether it was produced by a fair die. There's nothing an experimental subject can do to make the impo
by HWR_14 5y ago
> It's always impossible to tell, for any given sequence, whether it was produced by a fair die. There's nothing an experimental subject can do to make the impossible more impossible.
That's just not true.
Or feel free to play a game with me. We'll roll a 20 sided die. If it comes up 20, you give me a ten. If it comes up any other number, I'll get you a dollar. Nice EV on that!
Oh, the die has come up 20, 20, 20, 20, 20, 20, 20 the last seven times. Do you play?
- mmoll 5y agoYou’re comparing apples to oranges. The correct analogy is: you pick any other sequence of numbers between 1 and 20 and then tell me you’re more likely to win because your sequence is more random.
- Ygg2 5y agoIt can still be a fair die. The context implies it's not, but it's only unlikely, not impossible. See https://youtu.be/8Ko3TdPy0TU https://youtu.be/8Ko3TdPy0TU It introduces a 10 billion human second century i.e. 3.1 x 10^19. If your chance times it is greater than 1 then it's definitely plausible to be done by someone, somewhere.
- denton-scratch 5y agoI would; would you? The Gambler's Paradox says you shouldn't (I'm assuming your 20-sided die isn't crooked). Incidentally, you haven't made your case that you can ever tell whether a given sequence was produced by a fair die. You've just asserted it, and then suggested a game that doesn't illuminate anything.
- dtech 5y agoIt would be incredibly stupid to take the bet, as it's way more likely that the sequence was not produced by a fair die than that it was (i.e. the dice is rigged in the example) Just because it's impossible to know for certain, doesn't mean you can't make a prediction with very high chance of being correct.
- denton-scratch 5y agoI'm not really a gambling man, but I'd expect a crooked 20-sided die to produce a biased sequence, not a running straight. I don't know if it's possible to make a die that always rolls the same, and I'd expect any such die to fail a superficial inspection (all sides but one bulge; one side is larger than the others; the die has a weird magnetic field; the die is heavily weighted on one side). So I'd still expect a running straight to be rare, even with a crooked die. Of course, if I watched the die produce 7 20s in a row, and was then asked to bet on the next roll NOT being 20, I'd be stupid to assume the die was fair without inspecting it. All this is beside the point; the instructions invite the subject to produce a sequence that they think will convince people it was produced by a roll of dice. But there is no sequence that SHOULD have that power to convince.
- baobabKoodaa 5y ago> All this is beside the point; the instructions invite the subject to produce a sequence that they think will convince people it was produced by a roll of dice. But there is no sequence that SHOULD have that power to convince. If you genuinely believe that, we can easily set up a sequence of bets where you will win infinite amounts of money from me. But of course, you don't genuinely believe that, so you aren't interested in making bets around your supposed "beliefs".
- denton-scratch 5y agoI guess my "supposed" beliefs must be the beliefs you suppose I have. Whatever. If you're offering me a bet, and you can easily set it up, then what bet are you proposing? You haven't been very specific. I'm no Turf Accountant[0], but I can spot a three-card-trick when I see one. [0] https://en.wikipedia.org/w/index.php?title=Turf_accountant https://en.wikipedia.org/w/index.php?title=Turf_accountant
- baobabKoodaa 5y agoFine. You made this statement: > the instructions invite the subject to produce a sequence that they think will convince people it was produced by a roll of dice. But there is no sequence that SHOULD have that power to convince. Let's gather a random sample of people 20 people. I will produce 10 manually generated sequences of dice rolls and 10 actual dice roll sequences. The sequences are added to a list and the list is shuffled. We will present each person with a sequence from the list (sampling without replacement), and the person should guess whether the sequence was manually generated or produced with a dice roll. For each person who correctly identifies a manual sequence as a manual sequence, I will pay you $1. For each person who mis-identifies a manual sequence as an actual dice-roll sequence, you will pay me $1000. As you said, you believe no sequence should have the power to convince a person of such a thing, you will obviously never have to actually pay me $1000, you would just collect 20 x $1 from me. I'd be happy to continue this up to infinity in batches of 20, so you will eventually get infinite dollars from me. I will need escrow.
- alisonkisk 5y ago
- whatever1 5y agoB-but statistics taught me that the events are independent! Take my 10!
- geysersam 5y agoIt's just a question about what we perceive as random. It has nothing to do with the probability of the sequence being produced by a die, only with the probability of the sequence being produced by a human. A 20 20 20 sequence is not less random, it's just more likely to be produced by someone with incentive to cheat. How did the researchers measure the "randomness" of a particular sequence in this experiment? > Formally, the algorithmic (Kolmogorov-Chaitin) complexity of a string is the length of the shortest program that, running on a universal Turing machine (an abstract general-purpose computer), produces the string and halts. Oh, interesting.
- dorgo 5y agoI think we want (and expect) RNGs to produce sequences with high algorithmic complexity (which we regard as "random") and ignore the (almost impossible) possibility that they fail to do so. An impossible to create modified RNG which always produces sequences with high algorithmic complexity would better meet our expectations of randomness, but would be less random because it could not produce uniform sequences (among others).
- photochemsyn 5y agoThe obvious thing to do is then conduct a physical test on the die, for example trying to spin it on an axis with the 20 face near the top of the axis. An obviously loaded die will not be mass-symmetrical and will not spin well. In general this is called an independent test for systematic bias and it's something often left out of statistical arguments.
- xphos 5y agoYeah except that can happen. Its vanishingly a small probability but it's not impossible. I would feel that the die is crooked but feelings are not proof
- denton-scratch 5y agoHey, out of curiosity, why did you choose a 20-sided die? I assume it was just to match the "ten bucks" bit. I'm not snarking, I just began thinking about 20-sided dice. I do not believe there is a solid with 20 faces, and all faces congruent (I haven't checked). So we end up with a solid that is roughly ball-shaped, with faces of different sizes and shapes. [Edit] I checked; I suspected I'd made a fool of myself. An icosahedron has 20 congruent faces, of course. A ball-shaped die is much more likely to topple, and so more likely to be influenced by small differences in weight distribution, selective corner-shaving, whatever. I can't think of a way of judging the fairness of a 20-sided die other than casting it many times, and analysing the results. I'd be much more confident in my ability to judge by inspection the fairness of a 6-sided die.
- squeaky-clean 5y ago> Oh, the die has come up 20, 20, 20, 20, 20, 20, 20 the last seven times. Do you play? If you let me float the die in a cup of water and spin it to determine its not weighted so the 20 comes up, or have some magical means of assuring me the die is not weighted 100% yes I would play. It's entirely possible that a fair die rolls 20 7x in a row, but it's more probable that you're cheating.