Re: [pbmserv] Five in a row.... with a twist

["Roland Johansson" <roland.johansson@mbox2.swipnet.se>]

aha, you meant this, hartwell...   :)

well, I don't think the board can change that much,
there are only 4 pieces that turn, probably
4x4x4x4 = 256 positions

First move can be 9 different if I understood it right
(not counting same symmetry),
second move a lot more though....

rolle



-----  below is from hartwell ------

36 moves
first move:
(empty board) 36 holes left, 2 ways to turn the quadrant.(clockwise or
anti-clockwise)

secong move:
35 holes left, 2 ways to turn the quadrant.

so if the game goes 36 moves you've got 36! * 2^36
36! is a big number 3.72 * 10^41
2^36 = 68,719,476,736

multiplied together, that's 2.56 * 10^52  if you could do a billion
(10^9) positions a second, then it would only take you
810048507056489158666383530485910000 years to go through all the
positions.  You'll want to move that computer off-world because the sun
will go nova before we're done.

BUT, the game can be won on the 10th move IF everything goes perfectly.
(and we're looking for a perfect game)  perhaps we only need to look out
to 20 or 25 or 30 moves.

so only looking at N moves gives you Y possible boards:
N       Y
10     3.7 billion
15     4.28 * 10^16
20     2.55 * 10^24
25     5.20 * 10^32 probably the limit of "do-able" by brute force
although it's still 1.65 * 10^16 years to look at a billion per second)

30     2.85 * 10^41
35     3.55 * 10^50
36     2.56 * 10^52

enough maths

the thing that made connect 4 so easy to solve was that ther's only 6
moves.  (5 moves? i dunno)  you drop the checkers in from the top

also, along the way, some symetries will develop, 10 different moves
leave you at the same position.



Roland Johansson wrote:

> well the rules are easy
>
> start with an empty board and then you add a marble
> and then turn anyone of the quadrants 90° in any direction
>
> it's probably rather easy, there are only 36 moves to do,
> shouldn't be that hard to solve although the changing board
> might complicate it...
>
> they ask for 350 SEK for it in one of the shops,
> that's close to $40, they can keep dreaming...  :)
>
> Rolle
>
>
> ----- Original Message ----- From: "David J Bush" <twixt@cstone.net>
> To: <pbmserv-users@gamerz.net>
> Sent: Friday, December 17, 2004 3:57 PM
> Subject: Re: [pbmserv] Five in a row.... with a twist
>
>
> > | A Swedish publisher is just launching a new game called Pentago
> > | (http://www.pentago.se/) the page is still only in Swedish. The
> > game is
> > | a simple five in a row but with a little diffrent concept as the board
> > | moves...
> > |
> > | Now to why I am actually writing all this is to see if anybody can see
> > | if this game have the same disadvantage as a standard game of five
> > in a
> > | row? In five in a row the first player has quite an advantage compared
> > | to the second player. It is evem proven that with a perfect game the
> > | first player can always win but what do you think about this version?
> >
> > Like you said, only in Swedish. When I click on the English flag I get
> > "under construction." So how can I answer your question? I don't know
> > what the opening protocol is. I see the java moving board display, but
> > that leaves lots of unanswered questions. Even with the rotating
> > quadrants, it looks like such a simple game compared to Gomoku or
> > Renju, that a computer program could probably completely solve it.
> > So, perhaps game balance is not the main issue; it doesn't seem very
> > interesting in the first place.
> >
> > David Bush (chmeee)
> >
> >
> > To unsubscribe, send a message to esquire@gamerz.net with
> > unsubscribe pbmserv-users@gamerz.net
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>
>
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