Thank you for your thoughtful response! I agree that looking into further heuristics would be interesting, and more realistically represent strategies that players can relate to. If you refer to my other comment, I did some exploration into the final distributions of scores. However, that is just the beginning of what we could dive into deeper.

I came across some Othello articles when reading up on the Alpha-Beta Search algorithm that me and Brad will implement this semester that accounts for some of the ideas you mentioned. This includes what they call a “piece differential” (maximizing your own pieces and lessening your opponent’s) and disc positioning (frontier versus interior, corners/edges/buffers), which would affect your choices and mobility later on. If we create a scoring system for spots on the board with these criteria to do the minimaxing, maybe we can update you on conclusions about their effectiveness.

Link to the source (section two mentions their “evaluation function” that rates how good a move is):

https://ai.stanford.edu/~chuongdo/papers/demosthenes.pdf

Very nice set of posts (although I'll need more time to go through Brad's Part B)!

In the discussion of "fairness" you mention the the number of tied games was surprisingly large. I also found the number of ties in my analysis of the Mancala game surprisingly large. I think we both draw that conclusion because we're both used to playing the game to win rather than exploring all possible games.

I downloaded the notebook and did a little exploration. The number of terminal game states (outs in the PathCount function) is quite large: 1988. Or more than 20% of the vertices in the canonical game graph of 9617 vertices. Only 567 of these terminal game states completely fill the game board, and the least filled game board has eight empty squares.

Have you explored other characteristics of the game, such as the distribution of the final scores, or the distribution of the number of flipped pieces, or the distribution of score reversals?

The number of pieces of each color for a given game state defines a point in the first quadrant of the Euclidean plane, so a game could be plotted as the scores along a path from the root vertex to some terminal vertex. The same technique could also be used to visualize the distribution of final game scores with Histogram3D.

I'm glad to see that you would like to examine different game rules. That was very enlightening for the Mancala game.

The operation of the PathCount function is a bit obscure. Perhaps a small worked example would help readers follow the logic.

I also found the plot of the frequencies of the path counts confusing. The association pcData has an element 4 -> 126, what does the 4 represent (there are 126 4s in the output of PathCount)?

I'm sure there are a great many papers published on this game and the larger version Othello. Do you know if there are any unanswered questions in these papers that might be attacked with multiway analysis?

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