Improbably Frequent Lottery Winners

Good points, but continuing with the thought experiment, I think you fail to consider what might be a reality for your psychics. What if the psychics don't have perfect information, nor perfect control, but have, perhaps varying on the psychic in question, some amount of power that lets them see or control future numbers with some amount of probability, but not certainty?

In that case, they might win more often, but not every time. Given that so many things in nature follow a power curve or a bell curve, I think your presumed psychic abilities, we can assume, follow the same curves, and if most of your psychics then have "some ability" to predict these numbers, but not a certainty, then I think they are more likely to be frequent smaller winners.

For example, if you have an ability that let's you see a 4/8 of the future numbers, with 33% certainty, then one time out of three, you will win 4/8 of the numbers, and sometimes more than 4/8 if you're lucky.

TL;DR -- your presumed psychic abilities probably exist on a spectrum ( bell / power curve ) and likely most of your psychics do not have "perfect" future information.

PS - I have a feeling that psychics would prefer to play the stock market, than lottery. I just sense their expected payoff is higher in that case, probably because there are a lot more factors that affect a stock price, so even partial information across a lot of these seems to provide a better advantage, than partial information on 1 single list of numbers.

Yeah, that was a whole other story. Initially, the family jumped to MJ's defence in the local press, then when the lawsuits started happening, they filed one too, saying that the son had been interfered with (!) - it was all really surreal and odd. Lost touch completely with that family now - no idea what they are up to, but I hope they lost that infatuation with winning prizes and accolades and are happily settled somewhere...

Oh wow, I did not know that:

>The North American lottery system is a $70 billion-a-year business, an industry bigger than movie tickets, music, and porn combined.

The parent poster is "serious" in the sense that I bet literally every person reading this had the idea of psychics briefly cross their mind as they read it.

The problem is that psychics don't exist and the people who believe in them are unscientific. So it is the same as asking "Could God have favored these winners? Could it be divine providence"?

That has no place in the article.

If there were even half a sentence in the article stating something like:

    Are they psychics
    ------------------
    
    As a fanciful aside we analyzed whether the winners involved could be psychics.
    The effect is not strong enough for that: a psychic could win 3 or 4 lotteries in a
    row, for example.  A 1 in 10 million * 1 in 300 million is still much weaker than
    what a psychic could produce.  The improbability is not strong enough to show psychc
    ability.

    Less fancifully, prediction of the results through some other means outside of psychic
    ability (such as by predicting the random number generator used), would show the same
    effect, also not present.

The problem is that this validates "psychic ability" (which does not exist), in much the same way as a paragraph about God does.

Imagine if the article had written:

   Is it Allah's will?
   -------------------

   We asked our statistician whether the statistics show this may simply be the will of
   Allah.  Our statistician stopped replying to our mail at that point, so that this
   analysis is inconclusive.

The reason the statistician would stop replying to mail at that point is that nobody wants to mix statistics with religious beliefs. It just completely derails the conversation.

I don't think that this HN thread will end up completely derailing anything, but just for your information, psychics don't exist, nobody in the world is psychic to any extent.

(Some people are very good at reading information that is very subtle, however, and making inferences. Obviously this does not translate to predicting lottery numbers.)

Lightning is not 100% random as many people don't go out in storms which changes the odds.