Widest Path

PageType: Path     Keywords: Opening

This page is in need of attention.
Reason: Missing widest path for last 4 years

This is a simple abstract concept that applies to database search, and gives one answer to the question: what do 'they' play? It is particularly interesting for whole-board (fuseki) patterns, which tend to fluctuate according to fashion.

In its pure form, you look at the most popular B1 play, then the most popular W2 given that B1, and so on. This process comes to an end as soon as continuations from the position reached have become unique.[1] Picturing the game records as a unified tree branching from its root, one follows the widest branch at each point. Putting it yet another way, one takes the most probable replies.

Note that this doesn't necessarily reach the most common position to be found in the database, at a given depth. Logically speaking an option followed 50% of the time might next split ten ways each getting 5%, while the option followed 20% of the time might next split three ways getting 10%, 6% and 4% of attention. If it does reach the most popular position there is perhaps something going on: for example one can speculate that certain plays are adopted because they have a constraining effect on the opponent. This effect is to be seen in Kobayashi Koichi's research, to give one salient example.

In a less pure form one can take into account transpositions: allow different orders for getting to the same position to count together. This is potentially a nuisance to express, but in practice interchange of B1 and B3, or of W2 and W4, must account for a high proportion of all opening transposition in the normal case where the first four plays occupy different corners. There are for example two ways to set up a Chinese formation: the 4-4 point is usually played first (because it is flexible and commits one less), ahead of the 4-3 point, but there are many games reversing that order.

Examples of widest path analyses can be found on the statistical analysis path.

Charles Matthews

[1] Impress your friends by using the scholarly term hapax legomenon for this concept, the down-to-earth phrase being each game goes its own way.

Widest paths collection

Widest Path last edited by bugcat on October 30, 2021 - 19:04
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