The proposed methodology for comparing chess openings is then used to compare each of the test openings with the baseline opening. The ten opening sequences selected for this study are shown in Table 1. The rarity data shown in the table refer to the frequency of the baseline relative to the test opening according to the opening database used for this purpose3 Meyer-Kahlen, Opening Database, The nine test openings shown were selected to include a large rarity range and they are listed in the table from the most frequently played to the least.
The first four test openings listed may be considered to be commonly used. The next two are not very common, and the last three are rarely played. The test openings selected are expected to represent a wide spectrum of possibilities in the Queen's pawn game. The dual engine design DED described in a previous paper Munshi, Comparing Chess Openings, is used to compare each test opening with the baseline using chess engine experiments. Each experiment consists of games played between two chess engines. The engines selected are Houdini3Pro and Houdini4Pro Houdart, , generally regarded as the leaders in this kind of chess software Wikipedia, All engine parameters are set to their default values.
In each experiment, each of the two engines plays games as white and games as black. Every game of each experiment begins with the six half moves being evaluated. These move sequences are shown in Table 1. Engine calculations begin with the fourth move by white. The engine moves may cause transpositions of the opening into different opening designations than that by which it is identified in this paper and these transpositions are noted in the Appendix.
The selection of the baseline is therefore somewhat arbitrary since any of the first three openings listed could have been used as the mainline.
They should be taken only in a very approximate sense. The search depth is fixed and set to 21 half moves for both engines, a level at which the engines are expected to play at the grandmaster level or better Ferreira, The very high level of play is evident in the relatively low percentage of decisive games and a low estimated value of IMP. Also, a comparison of the playing strength of the two engines6 under the controlled experimental conditions of this study shows no evidence of a significant difference in playing strength DIFF.
These statistics are indicative of a very high level of play in which the effect of the opening is unlikely to be overcome by move imperfections IMP or by the difference in playing strength DIFF. The relevant data recorded for each experiment are shown below. The opening variability is a count of the number of unique moves made by the engines from the fourth to the tenth move.
It serves as a measure of the number of variations computed by the engines during the opening phase of the game Munshi, Comparing Chess Openings, White the number of games won by white 2. Black the number of games won by black 3. OV the opening variability 4. Transpositions whether the engine moves changed the opening designation 3. We then use the data to classify each test opening into one of three categories: Category A: Successful innovation. The probability vector has been changed in favor of the innovator.
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Category C: Benign innovation. The probability vector is either unchanged or it was changed in a neutral direction. Category F: Failed innovation. The probability vector has been changed in favor of the opponent. The test is carried out in stages. First we test to see if the Euclidean distance between the baseline opening result and the test opening result in the population from which our sample was taken is greater than zero.
It is assumed that any opening sequence that differs from the mainline is an innovation. If the probability of observing a sample distance as large or larger8 than the one being tested i. In these cases we can immediately classify the test opening into Category C as a benign innovation because we have no evidence that the probability vector has been changed by the test opening.
If the direction is well within the first or third quadrant, it is possible that the change is in a neutral direction and therefore we can classify the opening as Category C, benign innovation.
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This finding implies that the effect of the opening was only a change in the probability of decisive games with p w and pb changing proportionately with neither color gaining an advantage due to the opening innovation. If the direction is in the second or fourth quadrant, then the relative values of pw and pb have changed and one color has gained an advantage over another.
In this case we can classify the opening as either Category A or Category F according to whether the change favors the innovator or the opponent. The possibilities are shown in Table 2. As in the previous papers we use a Monte Carlo numerical technique to create a simulated sampling distribution from which we derive a measure of variance that we use in our hypothesis test for distance Munshi, A Method for Comparing Chess Openings, Wikipedia, For each opening, we compute the squared Euclidean distance of each simulated game from the mean9.
Thus we have one thousand squared distances for each opening. When comparing two openings we have two thousand squared distances from their respective means.
These squared distances are used to estimate what may be termed the "within treatment" variance of distance This probability serves as the basis of our hypothesis test. The reference to the magnitude of the distance as being "large or larger" refers to its absolute value. The essential data are the number of games won by white White , the number of games won by black Black , and the opening variability OV.
The OV data serve as a measure of the number of different variations played by the engines in the "opening phase12" of the game after the first three moves specified and fixed for each experiment are exhausted.
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These variations often cause the ECO designation13 to change. All such transpositions are listed in the Appendix along with references to high profile grandmaster games14 for each ECO designation played by the engines. We can now use the sample data15 to compute the Euclidean distance of each test opening from the baseline opening. The distance may be visualized in Cartesian coordinates where the x-axis represents the number of white wins and the y-axis represents the number of black wins in any given simple random sample of games.
Each point in this x-y space represents a sample in our study. In the population of all possible games each point in this space represents a unique chess game and its probability vector. The data in Table 3 are shown in this format in Figure 1. So what we are interested in is the distance and direction of each of the test openings from the Queen's Indian.
Complete Defense to Queen Pawn Openings
Chess opening statistics can been viewed on the display to the right of the board. To search the chess database, either enter your criteria into the quick search box or use the advanced search by clicking on the advanced search label. To see the chess games in the database for the current position, click on the "Games for Position" tab. By default, the database only shows chess games where both players were rated over , you can change the database subset using the database selector at the top of the page. There is also a non-searchable HTML only game list , but most users will want to use the main game database page.
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