Seems more like Rob is insuring random rolls by having a chaotic surface.[quote=“FerrisWheeler, post:102, topic:93124”]
, the only proper way to measure estimation would be to build a roll-bot. Load the die 1-side up, , tumble them for 10 seconds, then release them into a chute at fixed height from the table surface (e.g., 8 inches). Have the roll bot roll onto a steel surface from a consistent height.
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The roll bot would test whether the dice roll fair when rolled by the roll bot under those specific conditions.
Well, yes and no. If all you want to do is determine if the dice are fair then you should eliminate as many variables as possible. We would want to see if the dice roll as expected not if the table causes them to do so. Same with the hand that rolls the die, we would want to control the casting so that there’s no variance between rolls.
In this case, however, I believe @Beschizza just wants to engage in some pallet-table-ren-faire-wankery to which I advise that he keeps plonking away at it. Also, a sufficiently large sample size would probably shake out most biases.
Yes, one wants to eliminate uncontrolled variables to test the dice in relative isolation. However, you also need to confirm the results hold up under real world circumstances as you may have accidentally eliminated key factors in how dice behave in the real world. Do you want to determine if the dice are “theoretically” fair when laboratory tested? Or if they are actually fair when used in real life? I think both types of test have their place.
I definitely am. I don’t know chaotic noise from chaotic evil But I’m also ignorantly confident that if you want to know if dice are going to be biased under the conditions they are used in then the best test is under the conditions they are used in I’ve not seen a rejoinder that disproves that contention.
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\r?\n would get you both Windows formatted newlines and UNIX formatted newlines (I’ve had horrible files where the two were mixed ). Unless you’re trying to remove the newline character(s), it’s easier to use $.
RegEx is a real pain for HTML anyway. I mean more of a pain than RegEx usually is.
If you use the chi-squared this way, you can say that both dice are (possibily) not not fair.
If you use a chi-squared test, you test AGAINST the null-hypothesis that the numbers the dice roll are equally distributed, that each number will be rolled with the same probability. The alternative hypothesis (which normally is your idea you want to see proven in the data) would be “Certain numbers are rolled with higher probability than others”. If the chi-squared test gives you a result which has a probability below the significance level you agreed upon (in general 0.05 or 5%), you claim the alternative hypothesis seems to be “true”, if the result is larger than the significance-level, you stick with the null-hypothesis (“not significant… boohoo”).
However, in this case you should revert the hypotheses: Your alternative hypothesis (the one you claim) should be “All number roll with the same probability”, and your null-hypotheses (which is all that the alternative hypothesis is not) should be: “Some number roll with a higher probability”. That is not what the chi-squared test is made for as it tests the other way aorung. A hands-on-solution would be to take the hypothesis as reported above and adapt the level of significance: Increase it to make it harder to get a result which is higher than the significance level, e.g. to 30% oder 0.30. In this case the reported numbers of p=.126 and p=.172 (which I agree upon) are below the significance level, and we would assume with the alternative hypothesis: The distribution of numbers is not fair.
Perhaps what’s going wrong with the dice is that statistics is simply no longer going to apply in the Trump age? The dice are sensitive to the coming turmoil and are already diverging from ‘fair’ outcomes. If you repeat the experiment periodically in the run-up to midday on the 20th Jan, you’ll find progressively larger deviations from a uniform distribution, until one dice (and in fact 99% of all dice) rolls ‘1’ all the time, and the remaining roll consistent 6’s
Careful there, the sum should approximate a normal distribution (as should the average since a normal distribution divided by an integer is still a normal distribution). Also, the count of any of the possibler esults will approach a normal distribution (the number of 7’s rolled will be go towards a normal distribution around 1/6 the number of rolls as the number of rolls goes to infinity). The law of large numbers only works on sums.
The distribution of the rolls of a pair of dice is known and easy to calculate. You should expect 1/36 rolls to be snake eyes. If the results were normally distributed with a mean of 7 and a standard deviation of close to 2.04 just over 1/20 rolls would be snake eyes.
But you still can’t do this without reference to the manufacturing process. The distribution of number is unlikely on a fair die, but if the chance of the manufacturing process producing fair dice was 99.9999% then that would heavily outweigh the observed data - the data isn’t convincing enough to make me think I got the 1 in 1,000,000 die that isn’t fair. Of course we would never guess that hand forged dice have such a low defect rate. But if they were casino dice, I don’t think these rolls would give us much of a reason to think they were unfair.
Do you want to determine if the dice are “theoretically” fair when laboratory tested? Or if they are actually fair when used in real life? I think both types of test have their place.
I’ve not seen a rejoinder that disproves that contention.
). Unless you’re trying to remove the newline character(s), it’s easier to use $.
