6-man chess and zugzwangs

With 6-man Chess essentially solved, the available 6-man Endgame Tables (EGTs) have been scanned for zugzwang positions where, unusually, having the move is a disadvantage. Review statistics together with some highlights and positions are provided here: the complete information is available on the ICGA website. An outcome of the review is the observation that the definition of zugzwang should be revisited, if only because the presence of en passant capture moves gives rise to three new, asymmetric types of zugzwang.

6-man chess solved

Eugene Nalimov has completed the computation of a set of endgame tables for 6-man chess, and independently, Marc Bourzutschky has completed tables for 3-3 chess and for 4-2 chess where Black is not just ‘KP’. The ICGA salutes both achievements and looks ahead.

Chess endgames: 6-man data and strategy

While Nalimov’s endgame tables for Western Chess are the most used today, their Depth-to-Mate metric is not the most efficient or effective in use. The authors have developed and used new programs to create tables to alternative metrics and recommend better strategies for endgame play.

Ken Thompson's 6-man Tables

Ken Thompson recently communicated some results mined from his set of 64 6-man endgame tables. These list some positions of interest, namely, mutual zugzwangs and those of maximum depth. The results have been analysed by the authors and found to be identical or compatible with the available or published findings of Karrer, Nalimov, Stiller and Wirth.

Space-efficient Indexing of Chess Endgame Tables

Chess endgame tables should provide efficiently the value and depth of any required position during play. The indexing of an endgame’s positions is crucial to meeting this objective. This paper updates Heinz’ previous review of approaches to indexing and describes the latest approach by the first and third authors. Heinz’ and Nalimov’s endgame tables (EGTs) encompass the en passant rule and have the most compact index schemes to date. Nalimov’s EGTs, to the Distance-to-Mate (DTM) metric, require only 30.6 × 10^9 elements in total for all the 3-to-5-man endgames and are individually more compact than previous tables. His new index scheme has proved itself while generating the tables and in the 1999 World Computer Chess Championship where many of the top programs used the new suite of EGTs.

Space-efficient indexing of endgame tables for chess

Chess endgame tables should provide efficiently the value and depth of any required position during play. The indexing of an endgame’s positions is crucial to meeting this objective. This paper updates Heinz’ previous review of approaches to indexing and describes the latest approach by the first and third authors. Heinz’ and Nalimov’s endgame tables (EGTs) encompass the en passant rule and have the most compact index schemes to date. Nalimov’s EGTs, to the Distance-to-Mate (DTM) metric, require only 30.6 × 109 elements in total for all the 3-to-5-man endgames and are individually more compact than previous tables. His new index scheme has proved itself while generating the tables and in the 1999 World Computer Chess Championship where many of the top programs used the new suite of EGTs.

3-5-man chess: Maximals and mzugs

This article reports the combined results of several initiatives in creating and surveying complete suites of endgame tables (EGTs) to the Depth to Mate (DTM) and Depth to Conversion (DTC) metrics. Data on percentage results, maximals and mutual zugzwangs, mzugs, has been filed and made available on the web, as have the DTM EGTs.

Excess open solar magnetic flux from satellite data: 1. Analysis of the third perihelion Ulysses pass

We use the third perihelion pass by the Ulysses spacecraft to illustrate and investigate the “flux excess” effect, whereby open solar flux estimates from spacecraft increase with increasing heliocentric distance. We analyze the potential effects of small-scale structure in the heliospheric field (giving fluctuations in the radial component on timescales smaller than 1 h) and kinematic time-of-flight effects of longitudinal structure in the solar wind flow. We show that the flux excess is explained by neither very small-scale structure (timescales < 1 h) nor by the kinematic “bunching effect” on spacecraft sampling. The observed flux excesses is, however, well explained by the kinematic effect of larger-scale (>1 day) solar wind speed variations on the frozen-in heliospheric field. We show that averaging over an interval T (that is long enough to eliminate structure originating in the heliosphere yet small enough to avoid cancelling opposite polarity radial field that originates from genuine sector structure in the coronal source field) is only an approximately valid way of allowing for these effects and does not adequately explain or account for differences between the streamer belt and the polar coronal holes.