5 ms·

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 evidenc

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.

PhasmaFelis 6y ago
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.
- idolaspecus 6y ago
  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.
  - deleted 6y ago
    [deleted]
BenjiWiebe 6y ago
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.
- idolaspecus 6y ago
  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.
tromp 6y ago
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...
- idolaspecus 6y ago
  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.
GCA10 6y ago
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.
- rrobukef 6y ago
  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%.
- idolaspecus 6y ago
  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.

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.

PhasmaFelis 6y ago

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.

idolaspecus 6y ago
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.
- deleted 6y ago
  [deleted]

BenjiWiebe 6y ago

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.

idolaspecus 6y ago
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.

tromp 6y ago

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...

idolaspecus 6y ago
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.

GCA10 6y ago

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.

rrobukef 6y ago
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%.
idolaspecus 6y ago
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.