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Hex

Hex. Combinatorial Search in Game Strategy by Brandon Risberg. Menlo School. May 2006. Background. Where I got the idea: I first got the idea for “Hex” when we played it during an Algebra 2 class period with Mr. Squilante.

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Hex

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  1. Hex Combinatorial Search in Game Strategy by Brandon Risberg Menlo School May 2006

  2. Background • Where I got the idea: • I first got the idea for “Hex” when we played it during an Algebra 2 class period with Mr. Squilante. • I got the idea to make an artificial intelligence for the game when I went to see the “Mastering the Game” exhibit about computer chess at the Computer History Museum.

  3. Introduction • “Hex” is a board game defined by the mathematician Piet Hein • It is a two player game played on a diagonal board.

  4. Rules • Both players trade off claiming “hexes” on the game board. • The goal is to create a chain of hexes from your side to your other side.

  5. Java Game Programming • Used nested “Swing” components and graphics. • Imported image files created in Photoshop. • Used multiple threads to handle animation. • Implemented a recursive method to detect a winning chain. • Added help files and windows for ease of use. • Created an opening splash dialog.

  6. A.I. Algorithms • Mini-Max • Generate a move tree. • Evaluate each position in tree. • Select best move at each level: • Minimize score on opponent move. • Maximize score on own move.

  7. Example Search Tree

  8. A.I. Algorithms (con’t) • Alpha – Beta pruning • Pruning branches of the search tree that will yield less favorable results. • Improves search speed; does not improve quality of moves. • Heuristics or “Rules of Thumb” • Guidelines that will help constrain the search.

  9. Examples of Heuristics • In real life: • Menlo registrar must assign students to class sections. • This is a complex search problem. • Heuristic: make the critical assignments first. • Senior English sections (workshops) cannot be interchanged, so begin with these. • Freshman English classes are interchangeable so do these last.

  10. Examples of Heuristics • In board games: • In chess, keeping your pieces in the center will usually be a stronger position. • “A knight on the rim is dim” • In Hex, a longer chain of connected hexes will usually be a stronger position. • This logic is typically built into the static evaluator.

  11. Care to try a game?

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