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.
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.
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.
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".
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
> 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.
Payment only happens for the manual sequences here.
> you would just collect 20 x $1 from me.
So they'd only get 10 x $1 per batch.
You promised me "infinite amounts of money", I only stand to win 20 bucks.
Also, you have specified that these are 20 random people; so I guess I don't get to brief them in advance that they MUST say manual each time. So you have replaced me, the bettor, with a panel of 20 people whose average IQ is 100, and who don't have my interests at heart. Why would I take that bet?
If my random panel say manual each time, you stand to lose.
But as I say, I don't bet often. Only once a year, only on gee-gees, and only as much as I'm willing to lose (because I always lose).
I made a statement about a simple bet, using a fair 20-sided die, on the outcome of the 8th roll after the die has just come up 20 seven times. I'll take the bet that it doesn't come up 20 on the 8th roll. This scenario with 20 random people and 10 sequences appears to be a different scenario. I'm not sure how the odds work in that scenario, and I don't fancy that bet. That's all.
How is this related to the topic at all? Our disagreement concerns the ability of humans to produce numbers that look random, our disagreement doesn't concern the ability of a fair die to produce numbers that look random. Of course a fair die is going to produce numbers that look random, that's not related to this discussion at all!
"The topic" is whether the challenge faced by the experimental subjects makes any sense. It doesn't; the challenge is to produce a string of six symbols that others can't distinguish from randomness. There is no such string. Your contrived betting scenario doesn't illuminate the issue; it's an attempt to distract attention, and IMO it's not in good faith.
I strongly disagree with that statement. On a surface-level inspection, some strings appear to have more entropy than others ("can be distinguished from randomly generated strings"). This absolutely is a real thing, and it's measurably real. If you genuinely believe what you say, then we can easily wager on it and find out who's right.
> Your contrived betting scenario doesn't illuminate the issue; it's an attempt to distract attention, and IMO it's not in good faith.
You asked me to produce a specific betting scenario, and I did my best to entertain you with that. I crafted the scenario in good faith insofar as I tried my best to answer to your request. I suppose you can still argue that it's not in good faith because I never had any expectation that you would take the wager. But like I said before, that's because there is no way to formulate our disagreement as a betting scenario that you would accept, because you don't genuinely believe the claim you are making here, so you will simply weasel out of any wager.
I call on you to withdraw your claim that my remarks were made in bad faith.
I still don't know why you felt the need to contrive a complicated betting scenario, when we were discussing a "simpler" scenario that already involved an icosohedral die. If we're using betting scenarios to model good faith, then aren't simple scenarios more useful than complex ones? Ergo, coin-toss is the most appropriate.
But trying to talk about this stuff in terms of physical things like coins or dice inevitably turns into discussion about unfair coins and crooked dice, or whether the caster can influence the outcome; so argument by analogy quickly leads to dead ends, in this area.
I don't want to offend you, but I still do not think you believe the claim you are making. If you actually do believe it, we should be able to formulate our disagreement in the form of a wager and use the scientific method to determine which one of us is correct.
> I still don't know why you felt the need to contrive a complicated betting scenario, when we were discussing a "simpler" scenario that already involved an icosohedral die. If we're using betting scenarios to model good faith, then aren't simple scenarios more useful than complex ones? Ergo, coin-toss is the most appropriate.
The die scenario you formulated is not suitable, because it is unrelated to our disagreement. We're looking for a wager that illustrates the disagreement, e.g. you would be taking one side of the wager and I would be taking the other side of the wager. Your die scenario is not like this, because both of us would be taking the same side of the wager in that scenario; it has no connection to our disagreement at all.
I tried my best to formulate a simple scenario that would illustrate our difference and allow us to wager on which one of us is right. Sure we could use coin-toss instead of dice. Feel free to formulate a scenario.
> But trying to talk about this stuff in terms of physical things like coins or dice inevitably turns into discussion about unfair coins and crooked dice, or whether the caster can influence the outcome; so argument by analogy quickly leads to dead ends, in this area.
The disagreement concerns whether a person can produce a sequence of numbers in a way such that another person will/will not not be able to determine whether that sequence of numbers was manufactured or generated by a random process. A generator like coin toss or dice roll is very appropriate here.
The easiest way would be to put the same number on every side, which would probably fail a superficial human inspection (but might pass a surprising number of machine inspections).