Re: [computer-go] Search = Bad!

[Don Dailey <drd@xxxxxxx>]

>  OK, I vaguely remember seeing this idea once before in the past, but it 
>  doesn't help you play the game mathematically (i.e. choose the next move 
>  using a mathematical formula).  I don't see it anyway.

I didn't present it for that reason and I'm not the one that claimed
it could be played by formula.  But this might be a first step towards
creating a formula if it's even possible, so I presented it as a
curiosity.

What is interesting about this way of looking at tic-tac-toe tells us
something about how we approach problem solving.  How would you write
a tic-tac-toe program?  I suspect if we were given the rules in this
form below, we would write a signficantly different program.  We might
still use a search, but instead of checking an array visually
(scanning the rows, columns and diagonals) our program might be
focused on which combinations of numbers we need to get 15.

Which makes me wonder if there is a reasonable alternate way to
represent the game of Go?

Incidently, I'm no math whiz, but isn't a computer program basically a
mathematical representation of something?  And isn't a computer
function pretty much a mathematical function?  Isn't a recursive
function a finite series?

- Don






   Don Dailey wrote:

   > Tic-Tac-Toe can be reformulated to seem more mathmatical.   It goes like
   > this:
   > 
   >    Given a set of numbers, 1 - 9,  each player alternately chooses 1 number
   >    from the set and adds it to his own collection of numbers.   It is forbidden 
   >    to choose a number that has already been selected.    The first player
   >    who can take any 3 of his numbers and make 15 wins.  
   > 
   >    This game, as it turns out,  is the equivalent of tic-tac-toe.  I'm not
   >    sure how to solve it by formula,  but in this form it seems more possible.
   > 
   > The trick is that you lay out the 9 numbers as a kind of magic square like so:
   > 
   >     8  1  6
   >     3  5  7
   >     4  9  2
   > 
   > And getting any 3 of your numbers to add up is the same as putting X
   > or O on a row, column or diagonal.
   > 
   > Since a magic square can be layed out in many configurations, it is
   > like you are playing a "pure" form of tic-tac-toe, the reflections,
   > rotations, symetries are automatically handled and you are not
   > concerned with the visual aspect of the game.

   OK, I vaguely remember seeing this idea once before in the past, but it 
   doesn't help you play the game mathematically (i.e. choose the next move 
   using a mathematical formula).  I don't see it anyway.

   Somebody apparently made the remark that Tic-Tac-Toe can be played using 
   a mathematical formula.  I'm missing a post or something because it's 
   not apparent who made this assertion.  Anyone know?

   Some may find this link interesting: 
   http://www.klab.caltech.edu/~ma/tictactoe.html

   Matt
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