* NKT

The Game of "15"

  • Game I found in some old Martin Gardner book

  • Rules:

    • Start with tiles labeled 1-9 in the center

    • Players take turns choosing a tile from the pile

    • Any time a player holds 3 tiles whose total is 15, they win

  • Perfect information, alternating, terminating, zero-sum: check

  • (There's a fantastic trick to playing this game)

Solving "15"

  • Build a negamax search http://github.com/pdx-cs-ai/nkt

  • Can cheaply calculate value of any position in practice

  • Or can calculate the value of all possible positions and record them

    • (How many possible positions are there?)

"NKT": Generalizing "15"

  • We will generalize to "NKT": N tiles, exactly K tiles in a win, winning total is T

  • Next natural size is N=15, K=4, T=28, so we'll call this game "28"

  • Calculating the exact value of the starting position is going to take a long time

Last modified: Sunday, 18 October 2020, 10:54 PM