The design goal of Senket is to have the simplest rules and the deepest gameplay possible. Based on the numbers alone it seems that Senket is far more complex than almost any other board game. For example, on a 31×31 board, the log10 of the state space (all possible board positions, legal or not) appears to be at least 500, compared to 171 for Go and 50 for Chess. The log10 of the game tree is at least 2450, compared to 360 for Go and 123 for Chess. The numbers for Go and Chess are from the wikipedia article on game complexity.
It remains to be determined whether the complexity class of Senket is in PSPACE (similar to Othello, Hex, or Connect6) or EXPTIME (similar to Chess, Go, or Checkers), but PSPACE seems possible. Strictly speaking this would mean that Senket is in this respect less complex than Chess or Go, but consider that Nine Men’s Morris is in EXPTIME, but has been solved because of its small state space.
Looking solely at the number of possible board configurations doesn’t accurately reflect the depth of a game. Another indicator is the depth possible in a local situation. One measure of this is the sequence of moves required to resolve the situation, and the breadth of the tree of move sequences the situation can lead to reasonably.
Based on experience, it would seem that local Senket gameplay is at least equivalent to Checkers. Certainly, sequences of five to ten moves are common, and it seems vision beyond that level is possible and beneficial. Simultaneous cost-benefit analysis of multiple positions is required. Until experts have played Senket for some time, the true depth and complexity of the game will remain unknown.
My next post will be a problem designed to illustrate local depth.