Pattern Search Tree
It is interesting that both Tempo and I are dealing with the same question these days: How many different tactic patterns exist? Our estimates differ a lot, from my initial idea of over a thousand pin patterns to his idea of pin as a single pattern. This could be viewed as a source of dispute, but it is not. I even go beyond Tempo and postulate that pins are only a fraction of one and the same super-pattern.
Before I explain this let me tell you how I found out. I was jogging this morning with my old doggie, I have to jog very, very slowly so that she can follow me (years before it used to be the other way round). I just was contemplating what it could mean to count patterns, and if there is any method that would allow a reasonable count. And then it flashed to my brain. Pattern search is a kind of tree search, and the number of patterns you get depends on the level of ramification.
Thus, Tempo is right to count one single pattern of the pin, and I am right to count 144 different pin patterns. We just count on different levels.
- The first level of ramification is the dichotomy of «tactical» vs. «non-tactical» positions.
- The second level is the super-pattern or pattern category, such as «inline-patterns» (pins, skewers, forks of B, R and Q on a single file, rank or diagonal)
- The third level is the pattern itself, for instance the «pin»
- The fourth level is the most important feature of the pin. If a queen is pinned against the king, this feature will be the «pinnee value», if the pin helps a mate, it will be the «pin degree» (absolute pin required)
- At this level, additional features or details will not be helpful. Instead, the patterns of achieving will emerge: How do I get this pin ready? What pieces should be pushed or pulled to what squares by what means?
Instead of doing more pattern counting my next posts will deal with building a pattern search tree. The idea behind this project is the way we detect simple, well-known patterns in noisy and confusing environments of positions we see the very first time. The first thing we see is two targets, such as the King and an unprotected piece on the same line. The «inline-alert» lamp flashes up. Then we find an attacking piece that can go in front of the target of lesser value (pin), of the target of higher value (skewer) or between them (fork).
My idea is that we can detect patterns faster if we have a clear concept of what exactly we search and how these things are correlated. My future performance at CTS will show me if I am right.
(Just for the record: Yesterday I did about 200 CTS problems with about 90% success rate at an average rating of 1450.)