Moscow parks : Tsaritsino (Царицыно)

One of the nicest park that we can find in Moscow is Tsaritsino. This park is situated at the south side of Moscow. I have been there already many times and enjoyed all of them. The Tsaritsino park is very well maintained, large enough to walk for several hours, and has a mixture of historical monuments together with nice natural spots. I strongly recommend to visit the park earlier than noon because in the afternoon, specially during the weekends and when the weather is sunny, there are tons of people coming to visit. In the summer, there is some refreshing fontains dancing under some soviet-style chill-out music.

There are tons of pictures on the internet of this park : you can find few on wikipedia (along with history) and in Mikhail Fursov's folder of pictures. I am sharing here a couple of pictures I made.

The first one is a general view of the park. This photo and the one below were made in end of october 08. There is a large lake in the park with a couple of neat islands which are full of ducks because no one can get on these islands to bother them!



This second picture shows nice contrasts between the blue sky and the "blue" water. It was taken from one of the corners of the park.



This third picture shows another view on the lake. The photo as well as the two following ones, were taken in the summer, in the period of July. As you can see, there is a lot of green...!



The following two pictures were made close to the Tsaritsino Museum. This is one of the bridge leading to the park.


This is a picture of a small artificial lake made to decorate the park.

Decrypting the chess DNA

The subject of how much chess is complex has been in my mind since I have started to play chess. I will try to give here a good view on the complexity of chess and to assess how long it will take to finally decrypt this game, using some simple mathematics.

When will chess be solved ? Imagine that the opening theory reaches the level of endgame tablebases that we already have. In other words, we would know with 100% accuracy, for every chess position, moves that lead to a draw, winning moves and losing moves. At such a level, we might even discover some opening lines that would give a forced win for white (what I call "golden lines"). So to answer that question we need first to answer the question : how many total possible chess positions do we have ?

A first answer can be found in wikipedia :

http://en.wikipedia.org/wiki/Shannon_number

So, our mathematiciens, estimate it roughly to be equal to 64! / 32!(8!)²(2!)⁶, or roughly 10⁴³.

First we have to mention that this number corresponds to the exact number of possible position of 32 chess pieces (16 black + 16 white) on the chess board. However, there are all the intermediate possible piece combinations : 31 pieces on the board, 30 pieces down to only two kings on the board. From this point of view, we can think that this number is under-estimated.

On the other hand, this number does not take into consideration all the forbidden type of positions. Below a list of them :
1) Two kings cannot be adjacent.
2) Pawns do not exist on the first and last rank.
3) Bishops do only exist on half of the board.
4) Some pawn configurations are not possible, for instance a position where all 8 white pawns are located on 7th rank and all 8 black pawns are located on the 2nd rank. This is, I think, the part that is the most difficult to assess.

We can redo the same calculation that Shannon did. We will first start with the calculation of the space used by the bishops. They can only exist on half the board (64/2=32) :

Pos.Bishops = (32!/30!) * (32!/30!) = 32*31*32*31

There are 4 bishop units in total. For pawns, we will assume that all the bishops are limiting the space of existence of the pawns. That is to say, that none of the bishops is on the first and last rank. This is already an approximation, which reduces a bit the number of possibilities. Therefore, the pawn space of existence, becomes 48 (from 2th rank till 7th = 6*8) minus the four squares occupied by bishops : 48-4=44. In the case of pawns, we have to exclude all the dual positions, this is why we divide the result by 8! for white pawns and 8! for black pawns. In this calculation, we did not take into account remark 4) above because it adds a lot of complexity.

Pos.Pawns = (44!/28!) / (8!*8!) = (44*43*42*41*40*39*38*37)*(36*35*34*33*32*31*30*29)/(8!*8!)

Finally, the last piece with space of existence limitations is the king. We have now 64 minus four squares occupied by bishops minus 16 squares occupied by pawns equal 44 squares remaining for the king to choose from. The second king can only be placed in squares that are not neighboring the first king. Therefore, we will have :

Pos.Kings = 44 * (44-9)

Finally for the rest of the pieces, all the 42 remaining squares are free and can be used without exception. Each time duals have to be taken out :

Pos.Queens= 42*41
Pos.Knights= (40*39*38*37) / (2*2)
Pos.Rooks = (36*35*34*33) / (2*2)

Therefore, the total number of legal chess positions, assuming 8 pawns for black and white; 1 queen for black and white; 2 knights, 2 rooks and 2 bishops for black and white, is :


Chess Possible 32 pieces = Pos.Bishops x Pos.Pawns x Pos.Kings x Pos.Queens x Pos.Knights x
Pos.Rooks
= 2.71 x 10³⁹

This is already ten thousand times less than Shannon !
There are many possibilities for position including less pieces : for 31 pieces, we have already 10 possible piece combination (32 pieces - 1 black pawn or 1 white or 1 black bishop or 1 white bishop or 1 black rook or 1 white rook or 1 black knight or 1 white knight or black queen or white queen). For every of these piece combination, the total number of possible chess positions will decrease. For instance, if we have 32 pieces without 1 white rook :

Pos.Rooks = (36*35*34) / (2)

The total number of positions decreases to 1.64 x 10³⁸ , which sixteen times less.
So the sum of all the variations with 31 pieces, will result in an order of magnititude of 1 x 10³⁹
For 30 pieces, there will be even more piece combinations, but because we have less pieces, there are also less possible chess positions. Without getting in all the detailed calculations, we can presume that the sum of all the additional positions coming from less pieces than 32, we will not exceed 10⁴⁰ possible chess positions.

Another question araises : how relevant are these positions ? Because many of them will never occur in real chess games although they are fully legal. See my post about chess 960, where I show some of other possible starting positions that would allow to explore this large part that does never happen in classical chess. Very roughly, we can guess that the number of chess possible positions based on the standard starting position is in the range of 10²⁰ to 10³⁰.

Now, let's estimate the total amount of memory needed for storing a 32-men tablebases :

A 6-men tablebase, requires about 1000 GB = 8 x 10¹² bits (see here for details). The number of chess positions in a 6-men tablebase is smaller than 64!/58! = 64*63*62*61*60*58 = 3.10¹². We can deduce a ratio of 10bits/position. With such a ratio, 32-men tablebases will require about 10⁴¹ bits to be stored. This also means that we need to increase our current storing capabilities by 10^41-12 = 10²⁹ assuming that 1000 GB is a typical storage capability today.

Now we have to take a look at what is called "Moore's law".




Gordon Moore is the co-founder of Intel, the current biggest semiconductor corporation in the world. This law states that every two years, the density of transistors on our chips is doubled. This law would be better called Intel's law, because Intel has been driving and maintaining this speed of transistor densification. It is not clear how Moore's law will do when the semiconductor industry will reach to atomic scale (after nanotechnology, angstr-technology). It is also possible that due to some new technology, moore's law would be accelerated.

Assuming Moore's law will continue to be applicable as it has already been for the last 40 years : since 2 power 99 is about 10²⁹, we can deduce that we will 99 x 2 years to reach that increase in storage capacity. Therefore :

By year 2200, 32-men tablebases will be available and the DNA of chess will be totally and finally decrypted.

See you then!

No more choco

Today, a new Succhess puzzle to illustrate the Spy technical capabilities. The puzzle is very simple when you know Succhess rules.

White mates in 5

To see the solution, highlight the text below.


" Solution :

The material balance is clearly in favor of Black. However Black pieces are totally inactive. The rook and queen are stuck on the last column. The spy is prisoner on the a9 square.

Some tempting moves here :
1. Rxb9 : this is not real threat for black. Black releases immediately the pressure with ...Rj1. White's b8 pawn is not a real threat because the spy on a9 will immediately block the b10 square. And then only White's king can succeed in getting the pawn to queen but in the mean time Black's army would be unleashed and White will lose the game.

2. Nxi6 : this looks like a winning move at first sight. White gets Black's queen. But the truth is that it leads to most likely draw. Black's reply is simple ...Rj5 and after Nxj8 Rxi5+ Ke6 ixj8 Rxb9+ Ki10 Kd7 the position is very drawish because white king will succeed to chase away the spy on a9 but Black can simply exchange his rook against the b-pawn. And with a spy and three pawns against rook and spy, Black has a draw at least especially given the distant position where White's king will end up. May be Black is even winning.

So instead of these attacking moves, the very simple and passive looking Spy move is winning on the spot :

Sj5

After this move, Black is totally paralyzed because only black's king or queen can attack the spy. There is nothing Black can do apart from moving the rook and the queen in the j6-j7-j8 squares and waiting for the hammer to fall on its head. White win becomes very easy :

Rj6 Ng6 (and certainly not pawn takes rook!) Qj7 Nf8 Qj8 Nh9 Rj7 Rj10# "

And here is the animated GIF, that starts after the spy has moved to j5 to block black's army from moving :





PS. About the title of the post, it's just that my doctor is telling me to drop eating chocolate to improve my metabolism. So does White in this puzzle, the theme is don't eat any of Black chocolate pieces !

First Succhess Puzzle

Below the first Succhess puzzle that came to my mind :

White to move and win

Highlight the text below to see the solution

" The solution to this puzzle is very simple but requires to know Succhess rules. The situation is as following : White queen is pinned by the bishop on b8. In addition to that, Black is on the edge of queening with his c2 pawn, that is protected by the rook on c8. The position looks desperate for white. But there is only one winning move.

The solution is just to push the queen with the hero :
Hg3&Qg4+

This is an example of an amazing Hero move. He saves the queen from the pin and at the same time, the queen checks the black king winning not only a tempo but also the black rook and killing the queening potential of the c2 pawn. Note that the "&" symbol is used to represent the fact that two pieces are moving simultaneously

Ki7
Qxc8 1-0 "

You can see the solution animated below

Succhess Story

Today is a great day,

After a long period of work and investigation, I am finally very proud to release on this day of July 3rd 2008 the Millenium chess variant : SUCCHESS. What is SUCCHESS ? It stands for Super Creative Chess and it defintely opposes the french word for chess (echecs) that means failure in french.

The level of complexity is increased significantly by the size of the board (10x10), by several new pieces introduced and several group pieces also. Contrary to many other chess variants, the new pieces introduced remain simple enough for the brain to swallow them easily. Below a nice snapshot of a Succhess position :




I have made all the SUCCHESS rules available on the chess variants web page. Below a link to the Succhess rules :

SUCCHESS RULES

For those who have the software Zillions of Games, you can just download the game here and play Succhess. The required screen definition is 1280x1024.

http://users.skynet.be/fb419844/SUCCHESS.zip

If you don't have Zillions of Games, you can download a demo version but you won't be able to play my chess variant. I am looking into implementing Succhess under linux but this is for the future.

http://www.zillions-of-games.com/demo/


Enjoy playing and let me know what you think !

Chess and culture

Today, I am not posting another of my patzer games commented but I am posting some interesting chess links.

First, a link to the very nice chess diary of Tim Krabbe. I really enjoy reading parts of it and one can really feel that Tim has writing skills (he is by the way book author). That's the link to the beginning of his diary.

http://www.xs4all.nl/~timkr/chess2/diary_1.htm

And that's a link to all his web content :

http://www.xs4all.nl/~timkr/chess/chess.html


Now after you've read all of Tim's interesting material ;-) , you might find time to review these very interesting chess pages. The french speaking author of these pages has mixed a selection of chess problems with classic paintings. You will find paintings from Van Gogh, Rembrandt, Da Vinci, Dürer...as well as some modern art paintings and pictures of Kandinsky, Edmaier, Grunewald....I really like the idea and the spirit behind this webpage. I think the site would become even greater if he would add a piece of classical music to each theme. Beware that for every author of chess problems there are many chess puzzles (you need to click on the name of the theme being displayed and a scrolling menu will appear). And every puzzle has a painting or picture associated to it.

http://www.jmrw.com/Chess/Chess_Curiosities1.htm

Enjoy reading and watching.

King Gambit Accepted : Rosenthal variation

I am posting another analyzed game in the King Gambit Accepted (KGA) line. Since it is my favorite opening with white this will probably not be the last game.

The game analyzed below features the Rosenthal variation in the Kiezeritsky line (C39). The diagram below shows the Rosenthal variation. It is also called the Stockwhip variation.


From my experience, the Rosenthal line allows black to avoid the very complicated lines of the KGA and to directly jump into a rather safe endgame.

Below a beautifull position reached at move 35 in this game.


The complete analysis is on the link below :

http://users.skynet.be/fb419844/Rosenthal1/KGA_Rosenthal.html

Chess 960 or much more?

Bobby Fischer, one of the most brilliant and controversial chess player of 20th century has stated that he was not interested anymore in classical chess. The heavy opening preparation in standard chess has become a burden to creative chess. Today, opening preparation is reaching easily the 20th move in some top level games. We can state safely that :

The deeper the chess opening knowledge is, and the more likely draws will be.

This is why Fischer turned his attention to shuffle chess. Chess 960 or Fischer random chess is the alternative to classical chess that should put aside opening preparation. For those who are not familiar with it, below a link to wikipedia :

http://en.wikipedia.org/wiki/Fischer_Random_Chess

It is interesting to notice that the people that have won the Mainz Chess 960 Open are very strong classical chess players (Aronian, Svidler, Bacrot...). This shows that even though opening preparation is very important, it is still chess thinking that matters. And for the moment, the best chess thinkers are still within the top classical chess players.

Looking further into this, I realized that there is a large number of additional starting positions already in chess 960. Instead of making the classical mirror symmetry over the middle of the board line, one could make a central symmetry over the center of the board (point in green in the diagram). The diagram below shows the standard starting position with the central symmetry. Suddenly the fact that the black king position is swapped with the black queen makes the position even more equal. Castling king side with black will finally feel the same way as when castling king side with white.



There is no reason not to play this position. And this position could be considered part of Fischer random chess. By the way, it will not be anymore chess 960 but 960x2=1920 because every chess 960 starting position has a dual position with a central symmetry. Chess 1920 is funnier and more complex. It can also be called Fischer random chess extended.

So while thinking about this, I discovered on the board another interesting position.



Basically I am extending shuffle chess to different sides. I do not know if this is new. I called it Mixed Shuffle Chess or Mixu-Chess. Mixu-Chess is chess starting positions with pieces of opposite side colors standing on the same side of the board. I shall remark that in this first diagram castling is still possible (the Fischer way) but in other positions, it won't be.

Is the position neutral enough to be a possible new starting position ?
It seems that White has a small edge. My computer estimates it to between +0.2 and +0.5.
So this might make a difference for two strong computers playing each other but for most humans it won't. It might be fair and may be exciting to let such positions be played as draw odds. White starts but if there is a draw, black wins.

Actually the question is also fully relevant to chess 960 or chess 1920 : are all 960 or 1920 starting positions equal enough ?

I would not be surprised if in some of them White has some edge.
Below a couple of other Mixu-Chess starting positions :


This rook based Mixu-Chess position is considered very equal by the computer. Below a rather weird Mixu-Position, also quite equal :


However the following very interesting position that could be called Mixu-Chess Extended (because of the central symmetry used like Chess 1920), White seems to have an edge (+0.5).



Finally, my chess wandering brought me to a new chess variant : Cubic Chess. The idea of using the central symmetry allows some very interesting starting positions. Below an example of cubic chess :




The computer says that white has a slight edge but I do not believe here my computer assessment. In Cubic-Chess, the position of the pieces can vary inside the starting cube as much as wanted provided it gives equal chances for both sides. There is a total of about 1.3 billion of possible starting positions in cubic chess, however probably only a very small part of it is really equal. It might be that cubic chess is only playable with draw odds although it is very difficult to assess this.

There are many other possible starting positions that can be equal enough. May be in the future when 32-men tablebases are available, precise equal starting positions can be generated just before the match starts. And the players would discover the board. This would allow to discover the large continent of chess possibilities that is today only being investigated in chess studies.

I will be posting some mathematical analysis of chess possibilities in the future.

Analysis of not famous chess games

I will be posting links to the analysis of some chess games, mostly mine. If you have an amazing and original game to share, please send it to me, I might try to analyse it.

I realized that my chess was improving a lot by performing a post-mortem analysis of my games. Also I have to admit that I am tired of finding the analysis only of GM level games. Their games are sometimes very complicated and intermediate level players do not learn always from that.

First day / Первый день

Welcome !
Добро пожаловать !