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Very Hot Topic (More than 25 Replies) When do players start learning "exotic" endgames? (Read 17869 times)
Zwischenzugzwang
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Re: When do players start learning "exotic" endgames?
Reply #33 - 05/04/12 at 09:30:28
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When I'm joking, I'm taken serious (http://www.chesspub.com/cgi-bin/yabb2/YaBB.pl?num=1326464525/7#5), and when I'm serious, people think I'm joking --- what am I doing wrong??  Sad

Here's a picture of the Logistic Function, together with some description: http://www.google.de/imgres?imgurl=http://upload.wikimedia.org/wikipedia/commons....

Gilchrist is a legend wrote on 05/03/12 at 20:19:17:
...
And how about an exponential function, is that also possible since as rating increases, it might be more possible that a higher rated player knows these endgames faster than a linear regression.

The following quote is from the Wikipedia page the link above is refering to:
Quote:
More quantitatively, (...) the logistic curve shows early exponential growth for negative t, which slows to linear growth of slope 1/4 near t = 0, then approaches y = 1 with an exponentially decaying gap.

Jupp53 wrote on 05/04/12 at 07:30:05:
...
As every chess player should have a hobby - why not science which starts with mathematics?

That's a good one!  Grin

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Zwischenzugzwang
  

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Re: When do players start learning "exotic" endgames?
Reply #32 - 05/04/12 at 07:30:05
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Smyslov_Fan wrote on 05/03/12 at 23:32:51:
I thought Zwischenzugzwang was joking. I certainly found it amusing. But since others are taking his formula seriously, maybe he wasn't joking.



As every chess player should have a hobby - why not science which starts with mathematics?
  

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Gilchrist is a legend
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Re: When do players start learning "exotic" endgames?
Reply #31 - 05/04/12 at 01:33:14
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Well equations like the logistic equation can also concern subjects such as squirrel population density, so why not have mathematics to model endgames in chess as well?
  

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Re: When do players start learning "exotic" endgames?
Reply #30 - 05/03/12 at 23:32:51
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I thought Zwischenzugzwang was joking. I certainly found it amusing. But since others are taking his formula seriously, maybe he wasn't joking.

  
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Re: When do players start learning "exotic" endgames?
Reply #29 - 05/03/12 at 20:19:17
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Does anyone use a formula during a tournament game to calculate if they should resign or play on in one of these endgames? Smiley

And how about an exponential function, is that also possible since as rating increases, it might be more possible that a higher rated player knows these endgames faster than a linear regression.
  

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Zwischenzugzwang
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Re: When do players start learning "exotic" endgames?
Reply #28 - 05/03/12 at 16:03:48
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I don't take my formula too serious, cf. the problems I mentioned four posts ago.

What you are talking about is the possibility that players know the correct mating procedure not "completely", but only to a certain percentage. Whereas your brother might reach 100%, you only reach 99%  Smiley:
Stefan Buecker wrote on 05/03/12 at 09:02:12:
...
It was more interesting with me, sometimes my flag fell.
...

Brown and Epishin are maybe 75% ...

My assumption of knowledge either being 0% or 100% also runs into another problem [Attention! Now some mathematics!]:

The "Logistic Function", which provides the aforementioned S-curve follows the formula y = 1 / (1 + ez). If we take z = mx + b and do some calculation, we get ln ((1 - y) / y) = mx + b (with "ln" being the natural logarithm). With this formula it's easy to calculate a linear regression if the values for the x's and y's are known.
The problem with my assumption of y either equal 0 or equal 1 is that (1 - y) / y = ∞ for y = 0 and that ln ((1 - y) / y) = -∞ for y = 1, as the Logistic Function neither reaches 0 nor 1 (it just approximates those values). If I try to replace 0% by, say, 1%, and 100% by 99%, I can perfom my calculation, and get values for m and b. The same goes for 0.01% and 99.99%, and so on. Now the problem is that my results for the m's and b's don't converge the closer I get to 0% and 100% respectively. Just the shape of the resulting curve changes: Whereas it's quite smooth with a moderate gradient with, say, 10% and 90% resp., it becomes like a "sharp" step with 0.01% and 99.99%.  Undecided

So I still have to think about that ...
  

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Re: When do players start learning "exotic" endgames?
Reply #27 - 05/03/12 at 13:51:06
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Zwischenzugzwang wrote on 05/03/12 at 12:17:32:
Stefan Buecker wrote on 05/03/12 at 09:02:12:
About 1980, I used to play 1-minute matches against my older brother Peter (both 2350), practicing KBN vs K.
...

Taking these data into account would change virtually nothing in my results, as they predict the likelihood of a 2350 player to know KBN vs. K to be almost 100% (cf. x1) Wink

But your formula doesn't explain the failures of Epishin or Browne (e.g. http://mail.redhotpawn.com/board/showthread.php?threadid=118256&page=2 )

Players with blitz practice need to know it. Strong players who are rarely playing blitz, not so much.
  
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Zwischenzugzwang
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Re: When do players start learning "exotic" endgames?
Reply #26 - 05/03/12 at 12:17:32
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Stefan Buecker wrote on 05/03/12 at 09:02:12:
About 1980, I used to play 1-minute matches against my older brother Peter (both 2350), practicing KBN vs K.
...

Taking these data into account would change virtually nothing in my results, as they predict the likelihood of a 2350 player to know KBN vs. K to be almost 100% (cf. x1) Wink
  

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Re: When do players start learning "exotic" endgames?
Reply #25 - 05/03/12 at 09:02:12
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About 1980, I used to play 1-minute matches against my older brother Peter (both 2350), practicing KBN vs K. Playing with BN, he needed in average 30-35 seconds for delivering the mate. It was more interesting with me, sometimes my flag fell. - When I have to do with opponents known as Blitz experts, Podzblitz or such, I'd automatically assume that they know this kind of things.
  
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Zwischenzugzwang
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Re: When do players start learning "exotic" endgames?
Reply #24 - 05/03/12 at 07:42:01
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Here I'm quoting myself:
Quote:
Some minutes ago, I sent an email to 15 of my clubmates, ranging from 1200 - 2200 DWZ, asking them if they would consider themselves to be able to win KBN vs. K.

I've got four answers yet, adding myself I have five data points. I set "knowledge" to either 0 or 1, and I count my own knowledge as "0".

From the data so far, I calculated the following linear trend:
y = 0,0015x - 2,53

where "x" is the rating (in DWZ) and "y"  is the likelihood of the particular player to know how to play KBN vs. K.
Two points of interest are: Where is the likelihood of knowledge equal 0 (x0), and where is it equal 1 (x1)?
From my data, I get:
-  x0 = 1685 DWZ,
-  x1 = 2352 DWZ.

Of course, there are heaps of flaws in this calculation: 5 data points are definitely not enough, a model with "knowledge is either 0 or 1" is too restrictive, and especially the assumption of a linear trend is highly implausible, not least because it gives impossible values for the ranges below 1685 (likelihood of knowledge < 0%) and above 2352 (likelihood of knowledge > 100%). A S-curve model is much more appropriate, but I have to find out how to calculate that (can somebody tell me how to do that in Excel?)

But despite all these flaws, I find the results given above (x0, x1) not too implausible. What do you think?

Best regards,

Zwischenzugzwang
  

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Re: When do players start learning "exotic" endgames?
Reply #23 - 05/02/12 at 10:57:55
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Zwischenzugzwang wrote on 05/02/12 at 08:47:54:

A quite similar question: Did any of you ever have a position with K + N vs. K + P (rook's pawn) on the board, where the Knight's side can mate, because the Pawn's King is stuck between his own pawn and the edge of the board?


Once in a tournament game on the board, twice in the background not coming to the surface.

This is the main point about knowing this endgames imo. If you know how to treat them your life over the board is much easier in the middlegame and in other endgames.
  

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Re: When do players start learning "exotic" endgames?
Reply #22 - 05/02/12 at 08:47:54
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TN wrote on 05/01/12 at 00:02:08:
...
Speaking of which, have any of you had the drawn endgame with Knight and Rook's Pawn against a lone King, with the stronger side's king trapped in the corner? e.g. W: Ka8, Pa7, Nd6 B: Kc7; White to move.

A quite similar question: Did any of you ever have a position with K + N vs. K + P (rook's pawn) on the board, where the Knight's side can mate, because the Pawn's King is stuck between his own pawn and the edge of the board?
Nunn in his "Understanding Chess Endgames" (p. 49) gives as example the game Nogueiras-Gongora Reyes, Las Tunas Cuba ch 2001, where Black resigned in the following position:

* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*
It would follow 1.Nc1 a2 2.Nb3#.

This endgame is definitely not "exotic" material-wise, but rather "procedure-wise".
  

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Re: When do players start learning "exotic" endgames?
Reply #21 - 05/02/12 at 08:14:10
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Quote:
...
On the second time, I resigned at once without allowing my opponent to blunder. 

Very generous. I think I wouldn't behave like that - if somebody doesn't know his/her endgame therory, he/she might need some motivation to learn it, I think!? And if he/she knows it, why withhold the pleasure of showing his/her skills?

------------------------

Some minutes ago, I sent an email to 15 of my clubmates, ranging from 1200 - 2200 DWZ, asking them if they would consider themselves to be able to win KBN vs. K. I wonder how many will answer!?
If or when I get some results, I'll publish them here (as I wrote in my initial post, I mastered that endgame some years ago, but don't feel confident about me succeeding at the moment).

Best regards,

Zwischenzugzwang

Addendum (11:07 CEST): I got the first answer: Yes, he can (o.k., he's rated about 2200 DWZ). As I have to play him on Friday, he suggested we might test it then: We cancel opening and middlegame, and just try B + N vs. K. Very clever! But I probably won't agree to that!  Cool

Addaddendum: I would agree to that if I would get the bishop and the knight. That would be a good motivation!
« Last Edit: 05/02/12 at 09:18:26 by Zwischenzugzwang »  

What do people mean when they say "Chess is the pawn of the soul"?
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Re: When do players start learning "exotic" endgames?
Reply #20 - 05/01/12 at 19:56:40
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a great theme with the parity of colours, I remember learning it in a Paris chess club along with Marcello Mastroianni. OTB I had twice the much commoner theme of a bare King defending on the h-file against a h-pawn, Knight and distant King (the stronger side wins if he doesn't push on the seventh too soon). On the first time I waited, waited and finally the pawn was pushed one square too far : I had the draw but felt somewhat ashamed. On the second time, I resigned at once without allowing my opponent to blunder.
  
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Re: When do players start learning "exotic" endgames?
Reply #19 - 05/01/12 at 00:02:08
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LeeRoth wrote on 04/30/12 at 22:14:58:
Years ago, I had an opponent who resigned after a time-scramble flurry of exchanges reduced down to Bishop and wrong-color rook pawn.  One of the spectators ran over to tell my opponent that it was a draw and that he shouldn't have resigned.  When my opponent shot him a dirty look and walked away from the board, the spectator grew even more agitated.  He turned to me and told me I had gotten lucky.  It was only then that I was able to point out to him that the enemy king couldn't make it back in time to catch the pawn.

      


Grin

Speaking of which, have any of you had the drawn endgame with Knight and Rook's Pawn against a lone King, with the stronger side's king trapped in the corner? e.g. W: Ka8, Pa7, Nd6 B: Kc7; White to move.
  

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