And I think what Karaklis is trying to say is that, for 50/50 coins, there is basically no chance that somebody would get 100/100 heads if everyone in the world tossed 100 coins.

The chance of getting 100 heads is about (1/2)^100 ~ 8 x 10^(-31). There are only 6 billion people in the world, so the chance of 1 of those people getting 100 heads is still only 5 x 10^(-21). Thats... not good.

If the coins are severely biased, so that 80% of the time they give heads, then the odds of getting 100 heads is (8/10)^100 ~ 2 x 10^(-10), which indeed means that there is a pretty good chance of at least one person out there getting 100 heads.

But for an unbiased coin, you would be right to think the coins are biased if even one of those 6 billion people got 100 heads.

Not sure ~0.00000000000000000063% qualifies as "very good". >_>
(Edit: Doh, aconley was faster. Should read whole thread before replying I guess. I assumed 8 billion people for this example btw^^.)

DrStraw, karaklis, aconley, C. Blue,

I think if you reduce the original 100 coin flips to 30,
you'd get about 99.88% chance at least one person would get 30 heads in a row.

The original idea was sound, but the number 100 turned out to be too ambitious,
underestimating the power of exponentiation.

Could you double check these calculations ?

Do not underestimate the power of exponentiation.

(Others please double-check the calculations.)

If we increase the coin flips from 30 to merely 35,
the chance of someone getting all (35) heads already drops from about 99.88 % to only about 18.86 %.

At 40 coin flips, the chance drops to only about 0.65 %.

At 45 flips, chance ~= 0.02 %.

At 50 flips, chance ~= ( 0.000 6377...) %

Really?
We are down to discussing the math of coin flipping in relation to slumps in somebody's play?

Back to the topic:

Slumps happen, and you can usually feel when they do. There can certainly be losing streaks without slumps, but there are seldom slumps without loosing streaks, so it is certainly one of the symptoms. Personally - I think you can tell it when you are in the slump. You see yourself making more mistakes, and bigger mistakes, maybe have harder times to concentrate, or something like that. You lose your games and you lose your drive and you use your will. I think the best thing in such case is simply to step back for a while, until you get 'hungry' and 'fierce' again. When you come back you might be slightly weaker, but you will get back and above fast.

Its all a matter of mind-set. What worked for me good in the past was to play chess for a while, until my need for Go grew back.
For me, chess and Go are perfect companions, for exactly this reason - chess is a great therapy for Go slumps, and it still keeps your mind sharp. But YMMV.

An important point here is not to mix a slump with your average losing streak. They are not synonymous.
If you feel you are playing as well as usual, with the same greed for good moves and a win, you are probably not in a slump. Its just one of those things - play and you start winning again, just a matter of time. Maybe this is where the coins come in, although I really think it is a silly analogy.

_________________
- Bantari
______________________________________________
WARNING: This post might contain Opinions!!

Pretty sure you meant checking your reasoning and not the raw numerical data, but anyways, here's some GNU bc code which gives the same figures you get.

Here l(x) is the natural logarithm and e(x) is the exponential function.


The likelyhood of losing-streaks without an actual "slump" being the cause of it is not entirely off topic.


edit: gave the "result" variable a more readable name.

DrStraw's illustration has interesting implications.

Variation thought experiment: suppose we were able to make an instant clone of every person on earth.
And each person plays a game of Go with their own instant-replica.
( The idea is to approximate the 50/50 coin flip of each game's outcome. )

This means for 30 games, there's a ~99.88% chance at least one person will
beat their own clone for 30 games in a row. (Likewise, the clone will have lost
all 30 games in a row.)

In isolation, that person might be tempted to think they have just gained
at least one stone or two on their own clone. (Likewise, for the clone
to think they have just dropped one or two stones.)

leichtloeslich, Thanks for checking. No, I meant exactly to check the numerical data,
because I only have the Windows calculator, so I did everything "by hand".
I'm pretty sure my reasoning was correct.

This .. is such a horrible mangling of the way statistics in published papers is supposed to be interpreted

Apparently the best way out of a slump is to read a thread on statistics that will scare you back to tsumego!

So go straight to the heart of the matter instead.

_________________
Dave Sigaty
"Short-lived are both the praiser and the praised, and rememberer and the remembered..."
- Marcus Aurelius; Meditations, VIII 21

Now I want to publish a paper entitled, "Why this research finding is false".

_________________
be immersed

I was curious if this was written by a scientist or by a journalist who took a class about statistics in college. The about the Author section was empty.

http://en.wikipedia.org/wiki/John_P._A._Ioannidis

There was some criticism.

EdLee:

karaklis, Thanks!

This .. is such a horrible mangling of the way statistics in published papers is supposed to be interpreted [/quote]

Why do you find that disturbing? The differences about "truth" and "knowledge of truth" and "certainty" are all relevant.

I believe ten things to be true. I have reason, much stronger* reason than my reason to believe in the truth of any of those ten, to believe that of that ten at least five are true. But I have no reasons to support a belief that I could tell which.

In my example, I was describing the meaning of saying "a confidence level of X" when a population was involved (in this case, a population of research papers). To say that "if X is the confidence level of each of the papers then our expectation is that at least Y of them were wrong" is NOT an argument that can be used against any one of those papers.

Saying that of 100,000 people age Y we can expect ~300 to be dead before a year has passed does not say anything about who shall live and who shall die. (and if my example seems morbid, I used to write software for the life insurance industry).


* In fact, close to certainty. We're talking about "mathematical truth" in this case.

Mike, the quality of a paper is not determined by its significance. That a paper finds a statistically significant finding erroneously does not make the paper itself bovine manure, nor does a marginally non-significant finding on an issue later determined to be a real effect (resolving power aside) make it bovine manure.

The quality of the paper often has little or nothing to do with the statistical power of the results.

On top of that, statistical significance is _not_ a precursor to publishing results. It is appalling publication bias to only allow positive papers into publication.

I suspect in both cases it was just a poor choice of wording, but it made my eye twitch enough that I had to comment

I think I touched off this statistical sidetrack, but the point I was trying to make isn't particularly numerical: sometimes you feel like a slump when you are not in a slump. All this stuff about randomness and statics maybe obscures the point: a game of go is unpredictable. When two players of similar ability sit down to play, you cannot predict who will win or how the game will go. Your opponent is also trying to win, and to learn, and I think even the best players can be surprised by the turns a game will take.

So if you lose a game, does that mean your play has gotten worse? Maybe your opponent has gotten better, or just played a great game. Maybe this is someone you've never played before, whose style catches you unprepared. Maybe you were distracted at a key moment, or tried something new that didn't work. If any of that can be true for one game, it can surely be true for two, or three, or four.

If two friends/rivals sit down for an afternoon and play four games of go together, and one friend wins all four, can you say that the other friend is in a slump? Maybe. I would certainly be frustrated in that situation (and have been). But it almost feels like that takes something away from the friend who won four games in a row.

Sometimes you are learning, and playing your best, and improving, and you still lose. That is go.