I would like to know what are some quantitative criteria to characterize chaotic or volatile positions, and if there are engines or other programs that implement such criteria. One application I have in mind is extracting such positions from games for the purpose of calculation training. For example, finding positions in which one move leads to chaos on the board. Another would be to implement engine settings where the engine prefers to go into chaotic lines.
I thought of some characterizations.
- Let us say we analyze the game tree to k plies to evaluate a given position P, and arrive at an evaluation eval(P,k). Now we look at the subtree in which all nodes have an evaluation close to eval(P,k). If this subtree is large, then the position would be difficult for humans to analyze. A drawback of this definition is that such a criterion may also include many quiet positions.
- Volatility: if the sequence eval(P,k), k = 0,1,2,... shows a lot of fluctuation, then it means the position is quite volatile.
- Both sides on attack, e.g., multiple pieces on both sides attacked, both kings vulnerable, etc.
The second criterion is certainly interesting, but would also like to also incorporate something like 1 and 3. What are some other quantitative criteria?