You gentlemen do not understand what I wrote.
First of all, there is no need to use phrases like 'cute formulas', or 'what this guy [please use my handle, not 'this guy'] is trying to prove'. I wasn't proving anything, I was making a distinction, I was describing something. If you don't understand what the other fellow is saying, please ask for a clarification and not assume that he's trying to "prove" something.
The only reason I provided some numbers and
acknowleged what seems to be a correction of my understanding is so that readers could understand that I was illustrating that 32 pieces on 64 squares obeying a small ruleset can generate some very large numbers, indeed.
Secondly, if I'm understanding what
I read correctly, you folks don't get the point. Is anyone here going to seriously argue that AACW is a more difficult game than top-flight Chess, Go, or Bridge? If you are of that persuasion, then go to USCF, get a membership and start playing. Heck, just log onto Caissa and start playing some games. Or buy Chessmaster and set it to an 1800 rating and see how you do. As someone once said, it's amazing how much hot water even a Grandmaster can get into in ten moves.
Then go look up Steintiz vs. von Bardeleben (Hastings, 1895): this (link below) is the Wiki for Wilhelm Steinitz and it has a depiction of the game just before his 22nd move as White. Work your way through the permutations of the combination and keep in mind that he demonstrated a 10 move mate to the audience which would have been forced
after the resignation on Black's 25th move.
http://en.wikipedia.org/wiki/Wilhelm_Steinitz (the game is on the right sidebar about halfway down)
There is no commercial game that approaches, even
approaches, the intellectual endeavor of something like seeing from a dozen moves ahead what Steinitz saw and executing it
while every important piece was 'en prise' AND forcing every move by the opponent while one slip meant an instant back-rank mate.
That's the point I'm making. Large rulesets, e. g., AACW, do not tell you anything about the complexity of the game. OTOH, even though the intellectual complexity of a commercial computer game is not in the same league as Chess, for example, it is probably more difficult to program, because of the size of the ruleset (more SQA to run) and the fact that you have extraneous factors involved (modelling of a universe or behavior, commercial considerations, audience expectations, etc.).
Open ended NxN games are solvable and lend themselves to sophisticated, but relatively straightforward techniques for implementing them in a program. The straight poop is that the best chess players are programs. In ten years they'll be beating the Anands of the world with depressing regularity.
AACW is
not an 'OE NxN' game, by definition (neither is Bridge).
That's all I'm saying; although AACW, HOI2, Railroad Tycoon, Pirates!, and a host of others are much simpler games (as a
game, i. e., in order to play it well; very, very well for sustained periods in your life), interestingly enough, they're probably harder to program succesfully than Chess & its cousins.
Which is my way of saying that the North's AI is not 'broken.'
FURTHERMORE:
Just 'cuz something is an OE NxN game does not mean it's complex. Tic-tac-Toe is simple. Bridge, when played at the highest levels, is quite exacting, as difficult as Chess at times, and is not OE NxN. It's ruleset is somewhat small, maybe smaller than Chess's.
If I were rated in Chess and did my studying, I'd probably be around 1900 - short of an Expert. I played in some strong company at one point; my very good friend was around 2400, and his buddies were all at least 2100. I beat a 2200 player once - straight up. I play Bridge casually and can appreciate what really good players can do.
And I stink at Checkers.
And none of this was meant to denigrate the finest strategic ACW game on the market. It's just not as hard as Chess, that's all.