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To: K-list
Recieved: 2002/10/11 11:47
Subject: [K-list] minesweeper as a brain-balancer?
From: Stephen Kowalchuk


On 2002/10/11 11:47, Stephen Kowalchuk posted thus to the K-list:

Now here's something you don't see everyday...

When I get left-brain-taxed and I can't think logically anymore, I like to give
my right-brain a little fun and play minesweeper. You know...that Windows game
where you have a matrix of boxes and within each box is either a "mine" or a
number telling you the number of mines in the squares immediately surrounding
it.

I realized recenetly I was using both brains to win at Minesweeper. At the
expert level, it was practically the only way one could win. Read on if you are
interested...

I start the game by clicking on a box at random, which either gives me a number,
a mine, or an open space. If I get an open space, any adjacent open spaces are
likewise disclosed. The player can right-click on a suspected mine to flag it,
making it easier to recognize where they are. The game is won when all spaces
except the mines are uncovered.

So on the surface, the game is a left-brain exercise in deductive reasoning.
Pick a random starting point and deduce where the mines are. Build on guesses
and previously-uncovered spaces and with any luck one can win at the lower
levels.

The beginner level sets 10 mines in 64 spaces, giving an average of 6.4 random
guesses before one would expect to hit a mine. The intermediate level sets 40
mines in 256 spaces, still giving an average of 6.4 guesses before hitting a
mine. The expert level, however, sets 99 mines in 480 spaces, giving an average
of 4.8 quesses before hitting a mine. As you can imagine, since there is the
possibility of more spaces being uncovered if you hit an open space, there is
some bias to the equation. Hit an open space, and any open space attached to it
automatically opens, reducing the total number of spaces available on the next
"random" guess and raising the probability that a mine will be hit.

I have been doing the expert level for a couple years, trying to master how to
guess the right way, logic the right way, etc. It always seemed that several
times during any game, I would be at a space where no more logic was useful and
I had to guess again, with increasingly-difficult odds of success. Wins were
few and far between.

During these moments of guessing, especially late in the game, the focus is
usually on finding the last few mines so we can wrap up the game as quickly as
possible. And without a doubt, at these moments of guessing, even if there is
only one mine anywhere near my selected square, by god I'd land smack on it and
the game would end. Time after frustrating time.

It became maddening enough that I didn't play for a while, because I'd never
win. The closer I got, the worse the tendency existed.

One day, as if by accident, I managed to blow through the expert level in about
6 minutes. Clueless and doubting my good fortune, I tried again, and won again,
albeit at a much slower time.

What changed???

In retrospect I found that my orientation to the game was completely flipped.
Instead of looking to find mines and eliminate them, I was looking for
white-space with my right-brain. Then, when I had enough data to "clean up the
details", my left-brain went to town and puzzled out which spaces were really
numbers and which were mines.

Interesting...

Steve
--
--------- Stephen Kowalchuk
spkATnospamkowalchuk.org

Who can face the knowledge that the truth is not the truth?
Obselete...Absolute... -- Neil Peart
------------------------


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