Really Lucky's statistic

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andykhang
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Really Lucky's statistic

Postby andykhang » Wed Nov 01, 2017 4:32 pm UTC

Got a question: At which point does we know for sure that a person is blessed rather than just being very lucky, and is there even a distinction? I would imagine that could be done with some statistic math with a chance of 1/10E100 or something.

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Re: Really Lucky's statistic

Postby gmalivuk » Wed Nov 01, 2017 4:36 pm UTC

You could never really know, you could only ever just state the statistics.

Without a prior probability of being blessed (i.e. "A randomly selected person has a 1 in N chance of being truly blessed"), we can't even say, "This lucky person has an M in N chance of being blessed."
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andykhang
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Re: Really Lucky's statistic

Postby andykhang » Wed Nov 01, 2017 4:40 pm UTC

That's what I thought too...so supposed the probability of a blessed person is 1/100 billion I.E Literally all the people who have ever live on earth, who would be blessed, based on propability of thing people considered good luck?

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Re: Really Lucky's statistic

Postby p1t1o » Wed Nov 01, 2017 4:53 pm UTC

This is one of those discussions where you need a really rigorous definition of "blessed".

To me, blessed and lucky mean the exact same thing.

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SDK
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Re: Really Lucky's statistic

Postby SDK » Wed Nov 01, 2017 5:28 pm UTC

Isn't "luck" meaningless in a world where "blessed" has real meaning? If there's a God that blesses certain individuals, then (according to most doctrine) he decides the outcomes of all random chance anyway. "Luck" doesn't exist. There's just a spectrum of how "blessed" you are.

But, of course, even if you're unlucky (unblessed?) he has a plan for you, so it's really for your own good, etc, etc.
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Re: Really Lucky's statistic

Postby gmalivuk » Wed Nov 01, 2017 5:48 pm UTC

p1t1o wrote:This is one of those discussions where you need a really rigorous definition of "blessed".

To me, blessed and lucky mean the exact same thing.
You would also need a specific definition of what counts as "lucky".

But if you have both definitions in terms of probabilities, then you just repeatedly apply Bayes' Rule.
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Re: Really Lucky's statistic

Postby LaserGuy » Wed Nov 01, 2017 8:25 pm UTC

andykhang wrote:Got a question: At which point does we know for sure that a person is blessed rather than just being very lucky, and is there even a distinction? I would imagine that could be done with some statistic math with a chance of 1/10E100 or something.


I don't know that even having an event with probability of 10-100 probability happen to you necessarily implies luck or blessing anyway. For example, the odds of a given person being born with a particular genetic code (even assuming fixed parents) is much, much smaller than 10-100. But the odds of reproductive success, on the whole, deal with fairly routine levels of probability.

More to the point, I think that both the concepts of blessing and luck deal not only with events that are particularly rare, but rare events happening to a person that are particularly and immediately favorable to their circumstances, and, in all likelihood, align in some way with an expressed desire of that person. Likewise, when someone is cursed/unlucky, this is normally due to low-probability events occurring that are immediately unfavorable to the person. If we don't account for the desires of the person into the consideration, we have no way of distinguishing between good luck and bad luck or blessings vs. curses.

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Eebster the Great
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Re: Really Lucky's statistic

Postby Eebster the Great » Thu Nov 02, 2017 4:04 am UTC

I think the basic answer the OP is hoping for is the one gmalivuk gave. If we know the prior probability of being blessed and both the probabilities of success at some predetermined task for a blessed person and for a person who is not blessed, we can use Bayes' Theorem to calculate the probability that a particular person is blessed based on their outcome. For instance, if the prior probability of being blessed is 10-100, the probability of a blessed person rolling six on a fair six-sided die is 1, and the probability of a person who is not blessed rolling six on a fair six-sided die is 1/6, then if you ask someone to roll a die 129 times, and every single roll is a six, then you can calculate that the probability of the person being blessed is almost 71%. If they roll 150 sixes in a row, then in fact the probability is about 99.999999999999998%.

Note that this type of analysis is only meaningful for cases where we could realistically know the prior probability. So for instance, rather than determining if someone is blessed with perfect dice rolls, we could use this to figure out if they are loading the die, since it is possible to get some grasp of the approximate prior probability of the person cheating.

LaserGuy's point is also important, because it is easy to look at a large set of data, discard most of it, and pick out only the most surprising point. To properly perform Bayesian analysis on that set, we would have to either use the entire set or a random sample of it, not a sample we hand-picked. That would be like deliberately choosing lottery winners out of the general population and then determining that those people must be psychic, because the probability of them winning would be so low otherwise.


Another way of looking at this is hypothesis-testing. We can test the hypothesis that the person has a 1/6 chance of rolling a six by having them roll a die a bunch of times and check how many sixes they rolled. If it is sufficiently different from 1/6 of the total number of rolls, we can reject that hypothesis. However, this approach will never conclude that someone is blessed, just that for some reason they roll sixes more or less than expected from chance alone. This is the same as the Bayesian approach above; if there are other reasons the probability of rolling a six might be greater than 1/6 (e.g. a loaded die), then the probability of a non-blessed person rolling a six is not in fact 1/6, and the equation changes.

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Re: Really Lucky's statistic

Postby andykhang » Thu Nov 02, 2017 10:50 am UTC

Alternatively, you could just give that person a bag with 150 dices, and test whether all of them that he throw return a six

Though yeah, that's an answer I was looking for. IMO though, a blessed person is basically carried a loaded dice in life anyway, just that the cause isn't clear (for instance, you could considered that a person who is the smartest, fastest,richest, strongest and the most beautiful to be blessed, but if you know he's the richest first, it's not hard to see the correlation)

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Re: Really Lucky's statistic

Postby gmalivuk » Thu Nov 02, 2017 12:21 pm UTC

Even if we could objectively define (and measure) all of those things, we'd still only end up with a probability.

And in this case, even if they were independent of each other (which they aren't), the probability of one person randomly ending up with all five traits is about 10^-40, which is still far too high compared to 10^-100 to tip the scale of thinking that person is blessed.
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andykhang
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Re: Really Lucky's statistic

Postby andykhang » Thu Nov 02, 2017 12:28 pm UTC

Yeah, it's more of a example only. A more accurate example would be a person being the fastest thing on the planet (meaning FTL, meaning Flash).

And a probability is fine, just wanna know to what rate would you considered "certain"

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Eebster the Great
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Re: Really Lucky's statistic

Postby Eebster the Great » Fri Nov 03, 2017 2:56 am UTC

Different people use different thresholds for significance. If you have 95% confidence in a fact, most people would call that significant, though obviously it's far from certain.

In most fields of science, the prior probabilities are not known, so we can't really do this type of Bayesian analysis. Instead, we can determine the probability that an outcome would have occurred if the hypothesis were false. So in this case, we would determine how likely it would be that a person who is not blessed would roll that many sixes in a row. In medicine, if this probability is less than 5% (written P < 0.05), that would commonly be considered significant, though obviously far from conclusive. In particle physics we have a different standard for significance, typically corresponding to a p-value of around 0.00003% (written p < 3×10-7 or σ > 5). There is no absolute right or wrong answer for where you draw the line.

In this case, we would want a very, very low p-value. The main reason is that the prior probability of blessedness is presumably very small. I don't know if 10-100 is really appropriate—that seems pretty exaggerated—but it should be tiny. The point of the Bayesian analysis is to show you how low of a p-value you need for it to actually be likely that the person is blessed. As measured above, for a prior probability of 10-100, you need to roll 129 dice for that to be the case, corresponding to p = 6-129 = 4.2×10-101).

A bigger problem here is that we don't even really know the probability that a non-blessed person rolls that many sixes in a row. Our calculation makes the explicit assumption that this probability is 6-n for n rolls, but for large n, that's probably not true, because some people may cheat or accidentally use unfair dice. And while that may be unlikely, it is probably far more likely than the person being blessed with a perfect dice-rolling hand. If we can't distinguish fakers from the real deal, this test will never be able to get us anywhere.

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Re: Really Lucky's statistic

Postby arbiteroftruth » Fri Nov 03, 2017 4:47 pm UTC

If we consider being 'blessed' as not just "being a statistical outlier", but as an actual property with causal influence on the world, then we can estimate upper bounds on the probability of a randomly selected person being blessed.

If being blessed has actual influence on the probabilities in a person's life, then it amounts to otherwise fair dice becoming suddenly weighted just because the blessed person cares about the outcome. If that's true, it means the gambler's fallacy is not a true fallacy. A run of luck at the roulette table constitutes evidence that the table might be under the influence of a blessed person and thus that the run is more likely to continue than it would be at a fair table. If the gambler's fallacy is sometimes true, we should be able to observe that fact. The stronger the effect, the more common blessedness must be to explain it. The weaker the effect, the less common blessedness must be in order to not be more obvious.

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Eebster the Great
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Re: Really Lucky's statistic

Postby Eebster the Great » Sat Nov 04, 2017 7:46 am UTC

Technically, that is the reverse gambler's fallacy (the gambler's fallacy is expecting a run of luck to change). But yes, there would in principle be a detectable effect. But again, if we assume it is very rare, it would be practically impossible to distinguish from other, more common effects.


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