Analyzing the Game Mechanics of GoPop!™: How the most likely path to win is not always the best one.


We have analyzed the game mechanics of GoPop!™ Roundo by FoxMind. For the simpler variant independent of the previous move, the full game tree can be stored in 12 gigabytes and generated in about 15mins. However, just evaluating local probabilities at each step performs very badly against random play and multiple random self-plays until known outcome, two reasonable baseline benchmarks. Evaluating the game tree by self-play to the end - excluding those moves which later lead to a lost game and weighting by local move probability to win - vastly improves performance but still loses against random play in 1.32% of games. There seems to be a slight first-move advantage as random play wins 1.5% of first-move but only 1.14% of second-move games. We show that a perfect mastering of this game is only possible if the opponents moves are known in advance, which makes obtaining good mental model of the opponents' strategy a primary objective. This makes it a far more collaborative game than e.g. chess where good moves are not as dependent on the opponents strategy, but somewhat similar to Go where player's strategies are known to have far more effect. As such it might be an interesting game to build opponent models from a small number of plays to improve performance towards perfect play. This however enables the opportunity to deliberately choose moves to confuse the opponent as to one's own strategy, which also could be used by the system itself. It would also be interesting to have the system play against expert human players, which you can do right now on this page.

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