# * 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