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Comment by texan2945 | Hacker News Reader

It's no more/ less probable than any other combination, right?

Only if the lottery works as advertised.

Such a sequence, assuming a low total number of draws, is pretty strong evidence in favor of the theory that the balls were put in sequentially and were supposed to be randomized but the randomization didn't actually happen.

If the probability distribution gives equal weight to all the numbers, then yes. But the fact that a sequence that is semantically meaningful to humans (in such a profound way) came up should raise some questions, because there may be some funny business going on. At the very least, it you want to audit the lottery just to give people confidence it isn't rigged.

if you're a completely logic person then yes. I guess the problem here is that a lot of people will always think this was a scam as they do not understand that 1 2 3 4 5 6 7 8 9 is as likely to happen as 2 1 3 4 5 6 7 8 9. And there's there's the other step... if we can make people have this kind of thinking then very easily this kinds of games would end as people would figure out it's just a waste of money.

I believe that the lottery in question picks a combination, not a permutation, and writes the combination in ascending order. But it's not particularly clear from the documentation.

I don't think you're correct. Imagine you code a random number generator and run it ten times and get the same number every time. A "completely logical" person would probably assume there's a bug in their program. In fact, this is basic Bayesian reasoning.

No, but the sum you win will be significantly less than normal lottery win. 1/20 in this case.

How often does the computer ticket "quick pick" system generate this combination?

Yes, but the outcome 5 6 7 8 9 10 is also evidence that something is amiss. If you can discern some structure in some random sequence of numbers, that's evidence that it's not random.

It's kind of the opposite: if a random number generator never produces "pretty" sequences, that's evidence that it's not truly random.

If it produces pretty sequences at significantly greater than expected rates, that would be suspicious.

Your comment is basically correcet, but not as a refutation of mine. Your point is the same as mine: certain "special" outcomes at certain rates are evidence of implementation flaws in our random number generator even though they're not any more or less likely given an actually perfect RNG.

Not really, no. Humans are good at spotting patterns, even when none exist. AND.... Given a truly random number generator, there WILL be patterns in various subsets of the numbers.

The thing is that the lottery is not a truly random number generator. It's a physical process implemented by humans, subject to design flaws. So how can we detect whether or not the random number generator we've built has any flaws? By using sound Bayesian reasoning and experiment. If we run the process and it gives us the same number 100 times in a row in the first 100 results, we should adjust our priors and assume what we've built is not in fact a random number generator.

In a long enough random sequence of numbers, small scale patterns are inevitable, as their absence would in itself constitute a (large scale) pattern. The small scale is only logarithmic in the sequence length though...

Of course. In this case I think it's plenty likely that in fact the 5678910 sequence is in fact just a random event. It's not strong evidence, it's just evidence.

I'm looking at the first 100,000 digits of pi. Lo and behold, 00000 shows up once. So does 11111. What are the odds of each of those happening? It's 1:100,000!

Absolutely astonishing.

As an aside, the inevitability of weird flukes in large sample sizes really sinks in if you've ever wasted part of a year multi-tabling online poker. You'll see some hands play out in totally WTF fashion, as 1:100 and 1:1,000 probabilities come good.

The lesson, of course, is that when you play thousands of hands, encountering such oddities with your money at stake is no longer nearly impossible. It's moved into the zone of nearly certain.

Assuming pi is normal, the odds are 59.3% for any run of 5. The odds of two specific runs of 5 in 100,000 digits is (rough guess) between 3.5% and 10%.

This snarky response unfortunately misses my point, and your point is trivial to anybody who has taken even a remedial course in probability. The key detail is that we know the "RNG" in question might be flawed. If I tell you I implemented a RNG and you run it and find that it imediately spits out the ASCII codes for DONTBEADOUCHE in binary, you might rightly assume you've been duped.

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