# * Puzzle Solving

## Solving Shut The Box

What does it mean to solve a probabilistic game?

Suppose we had a table that told us the

*expected value*of every possible positionThen "perfect" play would mean always choosing the move that minimized EV (STB is upside-down)

How many entries does such a table have? 2^9 = 512

Build the table using

*dynamic programming*EV of a shut box is 0

EV of a box with one digit open is computable from EV of all successor states

Same for 2…9 digit boxes

## Let's Solve STB!

http://github.com/pdx-cs-ai/stb

EV of starting position is about 14762

Maybe want to maximize shut boxes? Minimize EV(log(

*s*))?Could calculate a fancier table useful for competitive play

## Search In Sliding Tile Puzzles

See the course notes on Sliding Tile Puzzles

http://github.com/pdx-cs-ai/slider

Can solve 8-puzzle (3×3) instances reasonably quickly

15-puzzle (4×4) is pretty hopeless