Entropy Evaluation method for Bulls and Cows game

AI midterm presentation

Transcript

1. Bulls and Cows solutions Hongyi Shen wilbeibi@gmail.com
2. ‣ key property: symmetric ‣ how to make next guess ‣ entropy evaluation ! ‣ five guess algorithm
3. target: guess: 0123 0364 1A1B 0213 4075 9138 5421 0123 0364 … … 1A1B 0A2B 0A1B 0A1B 4A0B 1A1B ?A?B ‣ key property: symmetric
4. Guess the one that would eliminate the most possibilities. ‣ Entropy evaluation map each guess to a possible group, choose the group with maximum entropy ‣ Five-guess algorithm use minimax tech to score each guess, choose the one might eliminate the most possibilities ‣ How to make next guess
5. 3 digits, 0~5 ‣ Entropy evaluation
6. Rounds Complexity Entropy 5.31 O(m^2). Five-guess < 5.31 O(n^2). Random guess 5.63 O(1). ‣ Performance VJGQTGVKECNNKOKV
7. Reference:! ! The Computer As Master Mind by Donald E. Knuth! ! Mastermind as test-bed for search algorithms by J.H. O'Geran etc.! ! Strategies for playing MOO, or “Bulls and Cows” by John Francis Thanks