King Fish

1. King Fish Brian Wojcik Nikita Kiriy Juan Pablo Sarmiento

2. Challenges: very large branching factor limited hardware tricky heuristics Approach Make a decent static player - wins against known opponents Use machine learning to optimize mechanics/learn from opponents             *                       * *                     * * *                   * 1 * *         * * * * * 2 * * 2 * * * * * * * * * * * 2 * * * *   * * * 1 * 2 1 * * * *     * * 2 * 2 * * * * *       * * 2 1 * * * * *       * * * 1 2 * * * * *     * * * * 2 1 * * * * *   * * * 1 1 * 1 * * * * * * * * * * * 1 * * * * * *         * * 2 *                   * * *                     * *                       * Overview"It was the best of times, it was the 𝛽 of times"

3. The AI Progress • Stage 1: beat a random player with heuristic moves. • Implemented and optimized. • Bonus: able to beat eigenbot frequently • Stage 2: adaptive AI/learning. • Implemented and optimized.  Using: • Alpha/Beta search • Parametrized utility function • Random restart hill climbing • K-nearest neighbor with pre-loaded tournament logs Optimizations • 16 byte board hash

4. Game Stages Run-Through Opening: •     Not Interacting: Use A-Star •     Saves time/computations Interacting: •     When at a certain distance from opponents pieces, switch to Alpha-Beta •     Smart Hashing to minimize memory usage. •     Depth 5 in AB search easily achievable with good move ordering. •     Static Evaluation function to evaluate non-terminal nodes. Closing: •     Consider Special Marbles in AB search. •     Depth 7 in AB search after special marbles (depth 4 before).

5. Static Evaluation Function Alpha-Beta Search cant search to terminal depths. Better Static Eval Function = Better Bot Break down Function into Components: • Vertical Dist • Horizontal Dist • Straggler Utility • Chain Utility Different Scale & Different Importance Parameterize Weights for each component  Find a Good Weight Set.

6.             1                       * 1                     * 1 *                   * * 1 1         * * * * * * * * * * * * * * * * * * * * * * * * *   * * * * * 1 * * * * *     * * * * 1 * * * * *       * * * * * 1 * * *       * * * 2 2 * 2 * * *     * * * * 2 * 2 * * * *   * * * * * * * 2 * * * * * * * 2 * 2 * * * * * * *         2 * * 1          2 1 *                     * *                       *                        1                       1 1                     1 1 *                   1 1 * 1         * * * * * * * * * * * * * * * * * * * * * * * * *   * * * * * * * * * * *     * * * * * * * * * *       * * * * * * * * *       * * * * * 1 * * * *     * * * * * 1 * * * * *   * * * * * * * * * * * * * * * * * * * * * * * * *         2 2 2 2                   2 2 2                     2 2                       2            Example: Straggler Utility Same Bot: Player 1 not considering straggler utility, Player 2 is.

7. Multi-Run • Parameterize Static Evaluation function allows 2 bots with different eval functions to run against each other easily. • Hill-climbing search to find best static evaluation function. Multi-Run Game Server • Own version of GameServer • Runs multiple bot vs bot games, altering evaluation variables each time. • Random Hill climb to find best overall evaluation function.

8. Learning • Game parser and classification of moves • Used database of recorded games to determine which were "safe" moves and which were "losing" moves. • "Losing" moves were usually those that sent our pieces to the corners of the board. • Used k-nearest neighbors to classify losing moves. • Evaluated accuracy using cross-validation. • Ignore losing moves when performing AB search.

9. Statistics • Random player: played 50 times • 100% win rate • Greedy player: played 50 times • 100% win rate • Eigen player: ~ 50% win rate • Tournament: 5th place or better •  Uploaded much better bot for final tournament. • Awaiting Results

10. All Hail King Fish The Fish King Of AI