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 Post subject: Re: 10 games match Lee Sedol vs Gu Li
Post #61 Posted: Mon Jul 28, 2014 5:50 am 
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paK0 wrote:
Does anyone know what happens if there is a draw or a 6-x lead?


They split the prize money if they draw. I believe the match ends immediately if one person wins six games.

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 Post subject: Re: 10 games match Lee Sedol vs Gu Li
Post #62 Posted: Tue Jul 29, 2014 10:54 am 
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From the standpoint of intuitive probability Sedol has basically secured his non-defeat. It's impossible to envision Sedol losing 4 games out of the remaining 4 games. I'd even go so far as to say that Li won't win 3 out of 4, so Sedol will win. You heard it here fist :).

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 Post subject: Re: 10 games match Lee Sedol vs Gu Li
Post #63 Posted: Tue Jul 29, 2014 10:59 am 
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Pippen wrote:
From the standpoint of intuitive probability Sedol has basically secured his non-defeat. It's impossible to envision Sedol losing 4 games out of the remaining 4 games. I'd even go so far as to say that Li won't win 3 out of 4, so Sedol will win. You heard it here fist :).

however, just prior to his last win, he had in fact lost 4 in a row against Gu Li... just not all in the same event. So it is indeed possible.

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 Post subject: Re: 10 games match Lee Sedol vs Gu Li
Post #64 Posted: Tue Jul 29, 2014 7:14 pm 
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Pippen wrote:
From the standpoint of intuitive probability...


A.k.a bulls**t


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 Post subject: Re: 10 games match Lee Sedol vs Gu Li
Post #65 Posted: Wed Jul 30, 2014 8:59 am 
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Well, Lee Sedol has currently won 22 out of 44 games vs. Gu Li, exactly 50%. If we leave out the one triple ko game then it's 51%. If each player has a 50% chance of winning each upcoming game then the odds are now:

Lee Sedol Wins: 68.75%
Draw: 25%
Gu Li Wins: 6.25%

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 Post subject: Re: 10 games match Lee Sedol vs Gu Li
Post #66 Posted: Wed Jul 30, 2014 9:26 am 
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True.. under the added assumption that the outcomes of the games are uncorrelated. Which probably isn't true. But with only 44 games between them, there's no way there's enough data to extract solid information about the correlations, so emeraldemon's calculation is probably about as good as you are going to get.

It does make me wonder if there have been enough n-game matches out there to build a better model, though.

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 Post subject: Re: 10 games match Lee Sedol vs Gu Li
Post #67 Posted: Sat Aug 30, 2014 4:46 pm 
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Tonight,

http://www.usgo.org/news/2014/08/myungw ... day-night/

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 Post subject: Re: 10 games match Lee Sedol vs Gu Li
Post #68 Posted: Sun Aug 31, 2014 1:28 am 
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7th game,

Lee Sedol defeated Gu Li by resign.

Lee Sedol vs Gu Li 5:2


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 Post subject: Re: 10 games match Lee Sedol vs Gu Li
Post #69 Posted: Sun Aug 31, 2014 1:47 am 
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emeraldemon wrote:
Well, Lee Sedol has currently won 22 out of 44 games vs. Gu Li, exactly 50%. If we leave out the one triple ko game then it's 51%. If each player has a 50% chance of winning each upcoming game then the odds are now:

Lee Sedol Wins: 68.75%
Draw: 25%
Gu Li Wins: 6.25%


Now that Lee Sedol has won game seven, it looks like this:

Lee Sedol Wins: 93.75%
Draw: 6.25%
Gu Li Wins: 0%

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 Post subject: Re: 10 games match Lee Sedol vs Gu Li
Post #70 Posted: Sun Aug 31, 2014 6:51 am 
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No, because now Sedol has won 23 out of 45.
BTW could one of the players improve his odds in this jubango given the score by changing his style? I obviously don't mean by playing better go but something like playing risky or unexplored moves/fuseki.

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 Post subject: Re: 10 games match Lee Sedol vs Gu Li
Post #71 Posted: Thu Sep 04, 2014 4:19 am 
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Joaz Banbeck wrote:
Now that Lee Sedol has won game seven, it looks like this:


Lee Sedol Wins: 93.75%
Draw: 6.25%
Gu Li Wins: 0%



cyclops wrote:
No, because now Sedol has won 23 out of 45.


Even assuming 50% chance each of winning a game, isn't the odds on a draw 12.5% rather than 6.25%? Gu Li needs to win 3/3, which is presumably 1/8 chance (at 50% probability per game.)

Also, clyclops - are you suggesting a purely frequentist approach to updating the winning probablities? In the abstract, I prefer a Bayesian method, since a frequentist approach produces silly answers if the lifetim score were, say 2-0 to one player or the other.
It's slightly off topic, but it seems to me that Bayesian probability theory is on far sounder theoretical basis than the frequentist approach.

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 Post subject: Re: 10 games match Lee Sedol vs Gu Li
Post #72 Posted: Thu Sep 04, 2014 5:15 am 
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The problem is more fundamental than the difference between "frequentist" and Bayesian theory. Related to whether or not belief in the independence of the outcomes of each game.

Thus the belief that Gu Li has zero chance of winning is based on the belief that result of the last few games means that the probability of the next game is no longer 50% (the 50% being based on their game history over long time).

So if we have been flipping a coin for a while, and the result prior to the current match had been 53 heads to 47 tails (no reason to suppose not 50-50 out of 100 trials) but the results so far in a current set of ten trials was two heads followed by seven tails expecting the tenth try to be more likely a tail (because of the previous seven tries).

That is disbelief in "independence of the events" (and would affect Bayesian thinking as well as frequentist).

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 Post subject: Re: 10 games match Lee Sedol vs Gu Li
Post #73 Posted: Thu Sep 04, 2014 5:24 am 
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Thank you for the edifying and informative lecture Mike, but
Mike Novack wrote:
Thus the belief that Gu Li has zero chance of winning is based on the belief that result of the last few games means that the probability of the next game is no longer 50%
is not true, it's that to win the Jubango he needs to win 6 games, has won 2 so far, and there are 3 games left: 6 - 2 = 4. 4 > 3. QED


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 Post subject: Re: 10 games match Lee Sedol vs Gu Li
Post #74 Posted: Thu Sep 04, 2014 6:07 am 
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Mike - I didn't deny the chances of Gu Li winning were 0! My post was on the odds of a draw.

A time varying binomial model has a lot more complexity than a simple binomial model. It's not immediately apparent to me how one would go about working out the time weighting.

Furthermore, the model could also become arbitrarily complex quite quickly. For example, it is intuitively pluasible to weight towards more recent games. This acknowledges that P(winnning) is actually changes over time. However, it could also be affected by other things such as:
    Time limits
    Location
    Prize money
    Colour played
    Amount of komi, and other changes in rule-sets
    Amount of beer drunk the night before a game

The issue is that the data set is relatively small, and insufficient to give any confidence in a very granular model.

According to go4go, since the jubango started, the score in all games is 6-4 to Lee Sedol. (Gu Li won a couple not in the jubango, and Lee Seedol won 1 not in it.) This may or may not be sufficient evidence to abandon the 50% hypothesis. You could argue that the jubango games are the best evidence for P(winnning) in the jubango - that acknowledges that some of the other factors on my list could be in play.

On a side note, a friend (who is a go player) has set up a Markov Chain Monte Carlo prediction model for the English football leagues. This features time-varying parameters and a (presumably) Bayesian updating approach. I believe he assigns attack and defence scores to each team, and the scores are updated after each result is received. Maybe something along those lines could be set up for Go.
http://www.archduke.org/footballpreds/

Edited to add: The MCMC approach would presumably take all known games as input, and assume games against other players gives useful information for games between the two.

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 Post subject: Re: 10 games match Lee Sedol vs Gu Li
Post #75 Posted: Fri Sep 05, 2014 1:12 pm 
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drmwc wrote:
According to go4go, since the jubango started, the score in all games is 6-4 to Lee Sedol. (Gu Li won a couple not in the jubango, and Lee Seedol won 1 not in it.) This may or may not be sufficient evidence to abandon the 50% hypothesis.


While most of the modeling you all are talking about sounds too complex for me to make any comment on, I feel confident in saying this: Lee Sedol winning 6/10 games cannot possibly invalidate a 50% null hypothesis. That's only 1 more than expected!

In fact, the chance of getting exactly 5/10 wins (assuming a null hypothesis that each game is a coin toss) is only 24.6%. So there's over a 75% chance of getting a skew of 6/10 or more towards one or the other of them.

Applying the same reasoning towards just the Jubango games: Even with the null hypothesis that every game is a coin toss, the chance of one player being ahead at 5/7 or more is a whopping 45.3%! So this result really isn't too surprising even if you believe Gu Li and Lee Sedol are exactly evenly matched.

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 Post subject: Re: 10 games match Lee Sedol vs Gu Li
Post #76 Posted: Sat Sep 06, 2014 8:15 am 
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Shawn Ligocki wrote:
drmwc wrote:
According to go4go, since the jubango started, the score in all games is 6-4 to Lee Sedol. (Gu Li won a couple not in the jubango, and Lee Seedol won 1 not in it.) This may or may not be sufficient evidence to abandon the 50% hypothesis.


While most of the modeling you all are talking about sounds too complex for me to make any comment on, I feel confident in saying this: Lee Sedol winning 6/10 games cannot possibly invalidate a 50% null hypothesis. That's only 1 more than expected!

In fact, the chance of getting exactly 5/10 wins (assuming a null hypothesis that each game is a coin toss) is only 24.6%. So there's over a 75% chance of getting a skew of 6/10 or more towards one or the other of them.

Applying the same reasoning towards just the Jubango games: Even with the null hypothesis that every game is a coin toss, the chance of one player being ahead at 5/7 or more is a whopping 45.3%! So this result really isn't too surprising even if you believe Gu Li and Lee Sedol are exactly evenly matched.



But you have to divide by two. It is not 'one player' that is ahead. It is one particular player. So the odds of this happening randomly are only about 23%.

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 Post subject: Re: 10 games match Lee Sedol vs Gu Li
Post #77 Posted: Sat Sep 06, 2014 8:52 am 
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Joaz Banbeck wrote:
But you have to divide by two. It is not 'one player' that is ahead. It is one particular player. So the odds of this happening randomly are only about 23%.


Are you sure we wouldn't be having this same conversation if Gu Li was 5:2 up?

Richard Feynman wrote:
You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won't believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!


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 Post subject: Re: 10 games match Lee Sedol vs Gu Li
Post #78 Posted: Sat Sep 06, 2014 10:11 am 
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 Post subject: Re: 10 games match Lee Sedol vs Gu Li
Post #79 Posted: Sat Sep 06, 2014 12:38 pm 
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So if it goes 5-5, that's just it, right? There's no tie breaker?

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 Post subject: Re: 10 games match Lee Sedol vs Gu Li
Post #80 Posted: Sat Sep 06, 2014 5:02 pm 
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see above

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