[HN Gopher] The Surprising Predictability of Long Runs (2012) [pdf]
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The Surprising Predictability of Long Runs (2012) [pdf]
Author : alexmolas
Score : 37 points
Date : 2024-10-11 14:40 UTC (2 days ago)
(HTM) web link (www.csun.edu)
(TXT) w3m dump (www.csun.edu)
| nuancebydefault wrote:
| I once saw on some website a chart with distribution of flat tire
| events. Often one does not encounter it in 10 years and suddenly
| 2 or 3 times in a year. Mathematically, chances of such
| distribution are quite high.
| fastaguy88 wrote:
| One of the major breakthroughs in Bioinformatics was the
| recognition that local similarity scores (which can be thought of
| as runs of positive sequence similarity) are extreme-value
| distributed.[0] The logic of that discovery uses almost exactly
| the same mathematical argument as this paper [1], indeed I
| recognized some of the same equations.
|
| It is difficult to overstate the importance of this discovery for
| biology, as today, the vast vast majority of protein functional
| inferences for newly sequenced genomes are based on the
| statistics of long runs of sequence similarity.
|
| [0] https://www.ncbi.nlm.nih.gov/BLAST/tutorial/Altschul-1.html
| [1] https://www.pnas.org/doi/epdf/10.1073/pnas.87.6.2264
| wenc wrote:
| This is an interesting finding. There are two takeaways from the
| paper.
|
| 1. The length of streaks L for an independent Bernoulli process
| with success probability p (with q = 1-p) over n trials can
| easily be calculated.
|
| L = log_{1/p} (n*q)
|
| 2. This estimate becomes more accurate as p decreases. Because
| the distribution of L is an extreme value distribution which gets
| more concentrated as p decreases.
|
| This means for low values of p, L becomes more predictable and
| accurate.
|
| I don't know how this result will change my life, but at least
| now I know that I can predict streaks if I know p.
| jonathan_landy wrote:
| First thing it makes we want to do is qualify success rates
| among individuals. Eg investors. Some are quite successful, but
| more so relative to what you'd expect give equal randomness?
| treetalker wrote:
| Long streaks, not runners' long runs (which are also surprisingly
| predictable).
| mcswell wrote:
| Unless of course a streaker does a long run.
| DiscourseFan wrote:
| Interesting but the paper suffers in certain respects within its
| methodology by conflating real probabilities vs theoretical
| probabilities.
|
| Roulette, for instance, is only _theoretically_ 38 /1, but in
| actuality all roulette tables have imperfections such that
| certain numbers almost always get hit more than others; even
| certain colors, under extraordinary circumstances.
|
| One could say: well, but isn't this the case for all
| probabilities? Not so: in the case of the lottery, the spread of
| numbers people tend to choose may not be so random, but the
| drawing itself is as close to random as possible. A run on the
| lottery is very different from a run on a roulette table and a
| run in baseball, or even a run in elections: there are forces,
| even if they aren't necessarily measurable, that determine these
| things and strict probabilistic analysis has no hold on these
| forces. It's almost certainly the case that a hurricane will hit
| Florida in September of 2025, even though nobody can precisely
| predict it, nobody would bet against it. It's just the same way
| with almost all chance in society, except for that which is
| already controlled from the outset.
| notahacker wrote:
| > actuality all roulette tables have imperfections such that
| certain numbers almost always get hit more than others; even
| certain colors, under extraordinary circumstances
|
| Seems unlikely these imperfections are enough to shift it
| _significantly_ from 1 /38, based on both the variation in the
| geometry of roulette tables that's small enough to be non-
| obvious being tiny in comparison with the variation in croupier
| action, and the likelihood of casinos _noticing_ any very long
| run deviation in the size of their edge (which is contingent
| upon customers hitting the zero pocket(s) with a certain
| frequency)
| conformist wrote:
| Yes, but it's potentially more subtle - there's a competition
| between professional players and casinos, in particular
| online. There's an interesting bloomberg story on this: https
| ://www.bloomberg.com/news/newsletters/2023-04-06/meet-n...
| SoftTalker wrote:
| Randomness doesn't look random.
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