Endgame tablebase

Endgame databases have complete endgame knowledge about chess positions with a few stones. There are now final DVDs with nearly all types of positions up to six stones, such as the important rook endgame is " king, rook and two pawns against king and rook " fully analyzed before. A query of the database shows this in any position, whether at both sides best play White or Black wins and which one is the "best" train, or whether the position is drawn, and which trains get the draw.

2012 reported the Moscow University that the databases are created completely with seven stones. They include about 140 terabytes.

• 6.1 Examples

• 9.1 Basic principles of endgame databases
• 9.2 Clarification of the theory by endgame databases

Basics

There are different ways to set a target for a specific position. The American computer scientist Ken Thompson has the matte and the transition into another won endgame set ( by hitting a figure or by conversion ) as equivalent. In a position against Lady tower ( without figures) was for him the beating of the tower ( without a subsequent loss women ) as part of destination as well as the immediate Matt. (Defined by Nalimov and previously also other developers ) Today is the Matt in the shortest number of moves the goal, either with or without regard to the 50 - move rule.

Apart from programming errors and small exceptions, the results of endgame databases generated by the computer are fully and accurately. The possibility of programming errors can be virtually eliminated because many playoffs already calculated in different ways and the results have been tested against each other. However, an exception is, for example, castling, which is not considered in endgame databases in most cases.

By endgame databases in the course of centuries grown chess endgame theory development could be clarified. The Five Steinem was noteworthy that the previously considered as draw final " king and two bishops against king and knight " can be obtained in general. However, there are positions in which only after the mat 66 is to force trains. This collides with the practical aspects of uncommitted 50 - move rule, so that such positions final outcome in both sides best game in a chess game but a draw, although Matt would be unavoidable.

Meanwhile, the shortcomings of classical works by André Cheron, Yuri Averbakh, Max Euwe and Reuben Fine has been in recent endgame books (eg by John Nunn and the two principal works by Frank Lamprecht and Karsten Müller) corrected, clarified and completed.

During a practice match on board the endgame databases play (especially for this long rapid playoffs ) does not matter. On the one outside help is forbidden during the game. On the other hand, even the best players can not play exactly as in complicated positions. This can be observed for example in a queen ending " against queen and lady farmer" when testing the game of course with a final database. Reflection shortage and abolition of suspended games have led to deterioration in the final phase at chess games.

Can be used in correspondence chess endgame databases in game analysis, proof of the correctness of studies or More Zügern in chess composition and in chess programs.

Manufacturing process

On a large scale Ken Thompson created at Bell Laboratories with a computer program of chess endgame databases under advice of John Roycroft. However, there were earlier work on limited sub-regions by Ströhlein, Zagler and the Soviet Union. At that time, computers were still too expensive to be widely disseminated. It was not until after some time the opportunity came to pass Thompson's results on CD and use, they found attention in wider circles of chess players.

The algorithm for the creation was in 1912 by Ernst Zermelo published on a Congress of Mathematicians. Later he found himself as a special case in mathematical game theory again. The method is relatively easy to describe in 4 steps:

Step 1: Generate all possible positions with no more than n stones For all admissible positions with at most n blocks, an index is allocated to a file. This file was at Thompson ( n = 5) several gigabytes in size.

Step 2: Determine all winning positions for white

Eventually dropped out of the process, because in one step the newly formed set of positions remains empty and so no further non- empty sets can be generated. Then all positions are found, in which White wins. Go to Step 3

Step 3: Determine all winning positions for black These positions can be found by the same method as in step 2

Step 4: The remaining positions are drawn. The remaining positions can be obtained either from white or black. There are therefore draw positions.

The methods in use today by Nalimov includes some improvements of a technical nature The algorithm remains basically the same.

Theoretically, you can then analyze the entire chess game completely by extending the method to 32 stones. Practically, this is not possible because with every additional stone the number of positions and hence the computation time dramatically increases. Notwithstanding this, working with the help of powerful computers continue to corresponding analyzes. The end of 2002, all positions with a maximum of 5 characters were already recorded and analyzed positions with 6 figures are finished since August 2005. Since the spring of 2006 are the first results of positions with 7 stones (excluding farmers ) ago. 2012 reported the Moscow University that the databases are created completely with seven stones. Currently, the data is imported into a format that can be used by chess programs. It is estimated that the full 7- stones databases include about 100 terabytes.

Metrics

Endgame databases is available in several metrics. In the DTM metric (Depth to Mate, ie depth to Matt ) the distance is stored, which is required for the longest opponent's counterplay for Matt. However, the 50 - move rule is not considered. For this reason, databases with the metrics DTC (Depth to Conversion, ie depth to the change ) and DTZ (Depth to Zero, so depth to zero) were created. It then emerged the DTZ -50 - metric that takes into account the 50 - move rule. In DTC, the distance is stored, which is required by a particular position in a conversion or a flip case.

Practical benefits

The chess players are placed in the direct use of recent research on your own computer by size and number of files and thus the required disk space limits. However, there are special servers on the Internet, which can be determined by querying the results of a specific final position. Thompson gave his prospective results from the basic price of the CD, with a company these four CDs with positions to 5 stones and a maximum of farmers were commercially available. Thompson compressed its data with the Huffman method in order to get along at all for the query with a CD can. This decision proved to be a hindrance in the development and optimization of chess programs.

In a chess program with activated endgame database you notice in the final a significantly higher frequency of trains because the computer now expects less and has frequently look in his endgame database, similar to the previously calculated Search positions in its hash table.

50 - move rule

The sensible for practical chess games 50 - move rule more difficult, especially in endgames with pawns the computer calculation extreme. Either the program ignores the draw rule and goes straight to Matt, or it is drawn primarily the farmer, but this can lead to a much longer version, even in positions that are dull than 50 trains. The correct solution must all finals further subdivided with the exact positions Bauer as " king, queen and pawn on the 5th row against king and queen ." As soon as the pawn moves, the 50 - move rule is broken and the final takes on the number of moves from endgame with pawn on the 6th row, which must already be calculated, and so on. The number of positions thus gained will hardly differ from the direct Mattweg, so that the practical benefits for the much more complex process appears too low.

Example

For this particular example shows the endgame database that disregarding the 50 - move rule and mutual optimum playing white to 65 trains sets mandatory matt. There is a final, " rook and bishop against rook ." According to 50-move rule, this final is a draw at best black defense. This final type led to the FIDE, the 50 - move rule temporarily replaced by a 100 - move rule.

Grandmaster Edmar Mednis has the database solution presented and commented in detail the course. However, he refers to studies by Ken Thompson on the computer Belle in 1986. This is the 55th train is not the best black defense and ends after 59 trains with Matt.

Chess composition

Endgame databases can be used to check orthodox problems and studies. By refuting false assumptions may also be a large number of studies are incorrect. An example of this are studies in which it was assumed that two bishops for a knight could normally only remisieren. However, blind faith can lead to incorrect results to the database, such as when a Datenbankzug is indeed faster, but later opens into the solution of the author and do not always provide for the longest resistance, but the one in which White has only one possible winning move.

At the Congress of the Permanent Commission for Chess Composition with FIDE in 2007 Rhodes was determined that an endgame database does not anticipate chess compositions.

Examples

Links: The database shows that in addition Heuäckers solution 1.Lf6 Ke8 2.Lg2 Kd7 3.Le5 Sg4 4.Lh3 Ke6 5.Bf4 Kf5 6.Lc1 d3 7.Bd2 also 1.Lxd4 wins - a train that is not of Heuäcker was overlooked, but judged wrong then.

Right: The database confirms that only Gasparjans solution 1.Ka2! Th3 2.Kb2 Tg3 3.Kc2 Th3 4.Kd2 Tg3 5.Ke2 Th3 6.Kf2 wins.

Endgame databases for related games

Chess was completely dissolved on the boards 3x3 and 3x4. Checkers is still in the research, but the best practical game histories were dissolved in the variant Checkers. Other games see the article " Dissolved games".