Hi Craig,

On Wed, Mar 27, 2013 at 4:03 PM, Craig Weinberg <whatsons...@gmail.com>wrote:

> From the Quora
> http://www.quora.com/Board-Games/What-are-some-fun-games-to-play-on-an-8x8-Checkerboard-besides-chess-checkers
>
> This is interesting because I think it shows the weakness of the
> one-dimensional view of intelligence as computation. Whether a program can
> be designed to win or not is beside the point,


That's not really fair, is it?


> as it is the difference between this game and chess which hints at the
> differences between bottom-up mechanism and top-down intentionality


I see what you're saying but I disagree. It just highlights the weak points
of tree-search approaches like min-max. What I gather from what happens
when one plays Arimaa (or Go): due to combinatorial explosion, players
(even human) play quite far away from the perfect game(s). The way we deal
with combinatorial explosion is by mapping the game into something more
abstract. Our brain seems to be quite good at generating such mappings. We
do it with chess too, I'm sure. Notice that, when two humans play Arimaa,
both can count on each other's inabilities to play close to the perfect
game. As with games with incomplete information, like Poker, part of it is
modelling the opponent. Perhaps not surprisingly, artificial neural
networks are quite good at producing useful mappings of this sort, and on
predicting behaviours with incomplete information. Great progress has been
achieved lately with deep learning. All this fits bottom-up mechanism and
intelligence as computation. It doesn't prove anything because I can't
attach the code for an excellent Arimaa player but, on the other hand, if I
did I'm sure you'd come up with something else. :)

A lot of progress has been made in Poker, both in mapping the game to
something more abstract and modelling opponents:
http://poker.cs.ualberta.ca/

Cheers,
Telmo.

PS: The expression "brute force" annoys me a bit. It implies that
traditional chess algorithms blindly search the entire space. That's just
not true, they do clever tree-pruning and use heuristics. Still, they are
indeed defeated by combinatorial explosion.


> .
>
> In Arimaa, the rules invite personal preference as a spontaneous
> initiative from the start - thus it does not make the reductionist
> assumption of intelligence as a statistical extraction or 'best choice'.
> Game play here begins intuitively and strategy is more proprietary-private
> than generic-public. In addition the interaction of the pieces and
> inclusion of the four trap squares suggests a game geography which is
> rooted more in space-time sensibilities than in pure arithmetic like chess.
> I'm not sure which aspects are the most relevant in the difference between
> how a computer performs, but it seems likely to me that the difference is
> specifically *not* related to computing "power". To wit:
>
> "There are tens of thousands of possibilities in each turn in Arimaa. The
> 'brute force approach' to programming Arimaa fails miserably. Any human who
> has played a bit of Arimaa can beat a computer hands down."
>
> This to me suggests that Arimaa does a good job of sniffing out the
> general area where top-down consciousness differs fundamentally from bottom
> up simulated intelligence.
>
>
> --------------------------------------------------------------------------------------------------------------------------------------
>
> *Arimaa, the strategy game that confounds computers! *
> It can be played, not only on an 8x8 chess board, but with the same chess
> pieces as well!
> The pieces are :
>
>    1. 8 Rabbits (Pawns)
>    2. 1 Elephant (King)
>    3. 1 Camel (Queen)
>    4. 2 Horses (Rooks)
>    5. 2 Dogs (Bishops)
>    6. 2 Cats (Knights)
>
>
> It doesn't matter in what way you want the 2 horses/dogs/cats to be
> designated by the 2 bishops/knights/rooks.
>
> *What sets apart Arimaa from Chess?*
>
>    - There is no draw in Arimaa. Good news for elimination tournaments.
>    - In Arimaa, a player has 64,864,400 choices for the first turn. Thus
>    unlike chess, memorizing openings is not gonna help you.
>    - There are tens of thousands of possibilities in each turn in Arimaa.
>    The 'brute force approach' to programming Arimaa fails miserably. Any human
>    who has played a bit of Arimaa can beat a computer hands down.
>    - It places less emphasis on tactics.
>
>
> I believe Arimaa is *way* better than chess in terms of abstract
> strategical thinking. It needs a higher level of intuition and
> understanding, discourages memorization and is simple to learn and play. It
> took me some time to play good chess, but it took me a small fraction of
> that time to learn and play good Arimaa.
>
> The Arimaa community is offering $10,000 for anyone who can come up with a
> program able to beat a top-level human Arimaa player, by 2020 : The
> Arimaa Challenge <http://arimaa.com/arimaa/challenge/>
> This will help us to attain the next pinnacle in Artificial Intelligence
> Programming.
>
> *Rules :*
> In the starting, both players arrange the pieces in whatever way they
> fashion in their first two rows, something like this :
>
> The pieces can move only one square horizontally or vertically. In case of
> rabbits, you can only move upwards or sideways. You have four moves to play
> in each turn.
>
> In order of their power, the *pieces can either **'push'** or **'pull'**other 
> pieces of the opponent
> *. In addition to this, if a less powerful piece of yours is adjacent to
> a more powerful piece of the opponent's, then your piece will be *frozen,
> **unless your piece is adjacent to another one of your pieces.*
>
> The order of power is as follows :
> *Elephant > Camel > Horse > Dog > Cat > Rabbit*
> That is, your camel will be able to push or pull the opponent's
> horse/dog/cat/rabbit. You can freeze the horse/dog/cat/rabbit if it doesn't
> have any friendly piece adjacent to it.
> *Elephants are all-powerful* : they cannot be pushed, pulled or frozen.
>
> See those dark squares in the diagram above? They are *'Trap Squares'*.
> If any of your piece lands in here and if there is no adjacent friendly
> piece to it, your piece will be 'captured'.
>
> *So, How do you win? *
>
>    - Your goal is to get one of your rabbits to the last row(or home
>    rank). Whoever manages to do this first, wins.
>    - If you manage to capture all your opponent's rabbits, you win.
>    - If your opponent has no legal move, you win.
>
>
> Since one of the above situations is bound to occur, there is *no* *draw*in 
> Arimaa. This is unlike chess where there is an unusually high
> probability of a draw.
>
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