Life In 19x19

uPWarrior wrote:... games should get more important (or "heavier") the farther from the expected outcome one gets. The 5th win in a 5win streak should increase one's rating more than a win after a win-lose-win-lose scenario.

Bayes' Theorem describes exactly how much you should change a probability in response to new evidence, which is why the word "Bayesian" keeps showing up in these rating discussions. if you want to join the Bayesian Conspiracy with shapenaji, Redundant, and me, read this: http://yudkowsky.net/rational/bayes

If you search for the phrase "In front of you is a bookbag", you'll see an example relevant to this discussion, although it won't make much sense unless you've read the prior examples.

In the terms used there, every game you win is a few decibels of evidence that you're under-ranked, and every loss is an equal amount of evidence that you're over-ranked (the amount of evidence should be scaled for the strength difference, of course).

People find a lot more patterns in random data than is actually there. The whole point of the rating system is to figure out if your 5 recent wins are enough evidence of improvement to counteract your average prior performance. I'd expect WHR (which is a Bayesian system) to do much better at making sense of such runs than systems that just add on an arbitrary bonus for runs (is WLWWWWLW really worse than LLWWWWWW? I think it depends a lot on time elapsed between the games). WHR assumes your strength changes over time. I'm not aware of another system that does.

Redundant wrote:

jts wrote:

Redundant wrote:Yes! 10 heads in a row is starting to be good evidence that you aren't dealing with a fair coin.

If the ten flips were HTHTHTHTHT, would you consider that evidence that it was a trick coin?

That is some small amount of evidence that the coin alternates heads and tails. If you can't tell, I'm very much a bayesian.

And if the ten flips were HTTHHHTTTT, would that be some small evidence that the next five flips would be HHHHH?

jts wrote:And if the ten flips were HTTHHHTTTT, would that be some small evidence that the next five flips would be HHHHH?

Can you get to your point here? Any seeming structure in the result of a trial is evidence for nonrandomness. The strength of the evidence relies on the improbability of the result.

Redundant wrote:

jts wrote:And if the ten flips were HTTHHHTTTT, would that be some small evidence that the next five flips would be HHHHH?

Can you get to your point here? Any seeming structure in the result of a trial is evidence for nonrandomness. The strength of the evidence relies on the improbability of the result.

My point is, that after ten penny flips, you are going to have some highly improbably sequence of heads and tails, on which you can happily impose some ridiculous structure. If you start with a set of priors that is significantly different from the data-generating process, Bayes' rule will give you silly results.

I heard the Rev. Bayes' ghost will torment you in your sleep if you blame him for your horrible priors...

jts wrote:My point is, that after ten penny flips, you are going to have some highly improbably sequence of heads and tails, on which you can happily impose some ridiculous structure. If you start with a set of priors that is significantly different from the data-generating process, Bayes' rule will give you silly results.

The sequence doesn't really matter for Bayes,

But you're right, It really comes down to the strength of your prior.

The only reason why people believe that after 10 heads in a row, that the next flip is 50-50 is because they have strong confidence in the prior of the coin. They don't believe in an unfair coin, so therefore it doesn't matter how much evidence arrives to support that conclucsion.

Tweaking your prior is important, if you don't think 5 heads in a row is enough to change the bias of the coin much, then by-all-means, make the prior strong enough to absorb 5 heads in a row.

There's nothing silly about the results, the only silly part is your choice of prior.

Just to throw this out there: Bayes' theorem is just a fact of probability. It is the particular ideas about assigning priors and updating via conditionalization that are philosophically/mathematically controversial.

It seems like my comment on a possible alternative with a volatility factor was completely ignored and the discussion quickly focused on the oversimplistic 5win streak.

The example I provided is not related to Bayes' theorem nor to patterns.

uPWarrior wrote:The example I provided is not related to Bayes' theorem nor to patterns.

yes it is, actually