what do you do about a slump?

[Boidhre]

When teaching statistics I explain that if everyone in the world tossed a hundred coins then there is a very good chance that someone would get 100 heads. If you were that person then I doubt very much that anyone could convince you it was simply by chance.

You'd have more issues convincing others that this person was using a fair coin. This is by far the real problem.

Well, that is actually how I put it to them, but in the current context the concept of a biased go board does not make sense.

Not a biased board, but sandbagger/gifted individual etc could apply as concepts.

[Boidhre]

When teaching statistics I explain that if everyone in the world tossed a hundred coins then there is a very good chance that someone would get 100 heads. If you were that person then I doubt very much that anyone could convince you it was simply by chance.

True, but go is not entirely a game of chance, right?

Perhaps not, but if the handicap and komi are set right then it should still be a 50-50 proposition.

Komi aren't set to match up individuals correctly, neither are handicaps. Even the EGF approach for ratings bears this out.

[speedchase]

I think you misunderstood my post slightly. If you play five games in a row, there is a just over 2% chance (ignoring that playing is never a coin toss) that you will win (or lose) all five. That doesn't mean that there isn't a better explanation.

[ez4u]

I think you misunderstood my post slightly. If you play five games in a row, there is a just over 2% chance (ignoring that playing is never a coin toss) that you will win (or lose) all five. That doesn't mean that there isn't a better explanation.

A timely comment from the speedster. Deja vu all over again. Let us not forget that we have had some discussion on this streak business before, kicked off by speedchase's famous 18-straight winners. In the end there may be some better explanations, but then again, there may not.

[Mike Novack]

I think you misunderstood my post slightly. If you play five games in a row, there is a just over 2% chance (ignoring that playing is never a coin toss) that you will win (or lose) all five. That doesn't mean that there isn't a better explanation.

Nitpicking, but 1/32 is more like 3%

What we are really talking about is knowledge, how we obtain certain forms of knowledge and our certainty about whether what we believe to be true is or is not true.

Let's say that we "know" 100 things each at the 95% confidence level. For any one of these things considered individually we might feel confident that its true knowledge. But at the same time, if we were correct about that confidence level calculation, we can be reasonably certain that we are mistaken about quite a few of those 100 truths.

So back to humans playing go and these are not coins but still ..... if we have 100 humans playing go and four of them experience a five game losing streak we can correctly conclude:
1) It is about as likely as not that there was a REAL REASON in the case of one of them. Maybe even in the case of two of them. But again about as likely as no no reason for any of them.
2) It is possible, but extremely unlikely, that there is a reason for all of them. The probability, were this purely chance, that none of 100 coins each flipped five times came up five tails is quite low.
Back to the example, if ten of those players experienced a five game losing streak we could properly conclude:
1) In the majority of those cases there was a reason as extremely unlikely if 100 coins were flipped five times there would be as many as ten of them coming up five tails.
2) BUT (a very big but) we have no way of knowing which.

How people think about these things has a bearing on how we operate in various fields of endeavor. Thus in the experimental social sciences, it is considered that the 95% confidence level is very adequate for publishing results. But thought of in a different way, out of 100 papers so published, much more likely than not 4-6 of them are total male bovine manure and we have no way of knowing which.

What the people talking about coin flipping are saying is not that human go players are coins but that we don't know if in this situation the outcome we are seeing is because "human, there is a reason" or "coin, there is not" and they are trying to distinguish by comparing against the expected results were they all coins.

[speedchase]

You seem intent on making my point for me. Would you disregard the bulk of scientific research humans have accrued because for each paper there is a 5% chance that is wrong? Similarly, is it reasonable to tell someone who is in a slump that it is more likely a chance occurrence than an actual slump? What if you consider that even a chance occurrence perceived as a slump could cause an actual slump purely by virtue of the psychology involved?

[SmoothOper]

You seem intent on making my point for me. Would you disregard the bulk of scientific research humans have accrued because for each paper there is a 5% chance that is wrong? Similarly, is it reasonable to tell someone who is in a slump that it is more likely a chance occurrence than an actual slump? What if you consider that even a chance occurrence perceived as a slump could cause an actual slump purely by virtue of the psychology involved?

Well, as far as modern research goes, so very little of it is repeated, that I feel fairly comfortable disregarding it, not to mention the fact that a majority of the research is trying to invent or market merchandise which has little redeeming social value, or medicine that is barely effacacious, so even if it is true, I have little motivation to regard it anyway.

[Mike Novack]

or medicine that is barely effacacious, so even if it is true, I have little motivation to regard it anyway.

Really? Maybe you should try applying a little "game theory" analysis (game theory is about the value of choices, not about games per se).

That the "payoff" if the drug is used and it does work is usually so much higher than if no drug is used is the reason that we tend to accept the results of medical research at so very much lower level of confidence. People don't bother publishing results in say Physics unless a couple of orders of magnitude more certain the results weren't chance. Rightly so.

The psychological consequences of experiencing a "slump" (unfavorable run) are another matter. So perhaps is the effort to seek a cause even though there might not be one if the cost of doing that isn't too high and the gain if there is a reason and it can be corrected is high enough. That's why the folks here who are saying the situation should be evaluated against chance.

[karaklis]

When teaching statistics I explain that if everyone in the world tossed a hundred coins then there is a very good chance that someone would get 100 heads. If you were that person then I doubt very much that anyone could convince you it was simply by chance.

This would be possible if the head appears in 80% of all throws.

[EdLee]

When teaching statistics I explain that if everyone in the world tossed a hundred coins then there is a very good chance that someone would get 100 heads. If you were that person then I doubt very much that anyone could convince you it was simply by chance.

This would be possible if the head appears in 80% of all throws.

No, I think he meant all coins are 50/50 even heads or tails.

[aconley]

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.

[C. Blue]

When teaching statistics I explain that if everyone in the world tossed a hundred coins then there is a very good chance that someone would get 100 heads. If you were that person then I doubt very much that anyone could convince you it was simply by chance.

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^^.)

[EdLee]

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).

Double checking...

The chance p of getting 100 heads is not about (1/2)¹⁰⁰; it is exactly (1/2)¹⁰⁰, isn't it ?

p = (1/2)¹⁰⁰

The chance q that a person does not get 100 heads in a row is exactly (1-p).

q = (1-p) ~= 0.999 999 999 999 999 999 999 999 999 999 21...

World Population Clock gives approx. 7.18 billion.

So, the chance n that nobody in the whole world gets 100 heads = approx. q^(7.18 x 10⁹).

n ~= q^(7.18 x 10⁹).

Finally, the chance c that at least 1 person gets 100 heads = (1-n).

c = (1-n).

(I have not checked the numeric calculations yet.)

n ~= q^(7.18 x 10⁹)
log(n) ~= log( q^(7.18 x 10⁹) ) ~= (7.18 x 10⁹) x log(q)
~= (7.18 x 10⁹) x log (0.999 999 999 999 999 999 999 999 999 999 21...)
~= (7.18 x 10⁹) x ( -3.426... x 10^-31 )
~= -2.4599... x 10^-21

n ~= 10^( -2.4599... x 10^-21 ) ~= 0.999 999 999 999 999 999 994 36...

c = (1-n) ~= 1 - 0.999 999 999 999 999 999 994 36...
~= 5.66 x 10^-21

Anyone else wants to double check the calculations ?

[EdLee]

When teaching statistics I explain that if everyone in the world tossed a hundred coins then
there is a very good chance that someone would get 100 heads.
If you were that person then I doubt very much that anyone could convince you it was simply by chance.

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 ?

Let's change the number of coin flips from 100 to 30:

The chance p of getting 30 heads in a row is (1/2)³⁰.

p = (1/2)³⁰

The chance q that a person does not get 30 heads in a row is exactly (1-p).

q = (1-p) ~= 0.999 999 999 068 677 425 384 521 484 375...

World Population Clock gives approx. 7.18 billion.

So, the chance n that nobody in the whole world gets 30 heads = approx. q^(7.18 x 10⁹).

n ~= q^(7.18 x 10⁹).

Finally, the chance c that at least 1 person gets 30 heads = (1-n).

c = (1-n).

n ~= q^(7.18 x 10⁹)
log(n) ~= log( q^(7.18 x 10⁹) ) ~= (7.18 x 10⁹) x log(q)
~= (7.18 x 10⁹) x log (0.999 999 999 068 677 425 384 521 484 375...)
~= (7.18 x 10⁹) x ( -4.044 682 552... x 10^-10 )
~= -2.904 082 072...

n ~= 10^{( -2.904 082 072... )} ~= 0.001 247 147 807...

c = (1-n) ~= 1 - ( 0.001 247 147 807... )
~= 0.998 752 852...
~= ( 99.875 285... ) %

Anyone else wants to double check the calculations ?

[EdLee]

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...) %