User avatar
Pocus
Posts: 25433
Joined: Wed Oct 19, 2005 7:37 am
Location: Lyon (France)

Fri Aug 14, 2009 8:39 am

Putting more efforts on a theater (in offensive or defensive) can easily be done with the AI commands exposed to modders. Again, the WIA community did an impressive job with them.
Image


Hofstadter's Law: "It always takes longer than you expect, even when you take into account Hofstadter's law."

User avatar
Nikel
Posts: 2574
Joined: Sun Apr 20, 2008 8:38 pm

Fri Aug 14, 2009 9:37 am

I do not want to add fuel, the contrary :)

Barksdale, the problem IMHO is in the way you said it.

You could be even constructive, posting a savegame where the AI did something that evidently is wrong, perhaps you already did it, sorry

But for you, the AI is no match and find that you enjoy a lot more vs a human opponent, and that is fine of course :) Surely you will enjoy even more if your opponent has the same level (I mean knowledge of the game) than you, because sure there are better and worse human players, try Manstein :D




But the way you said it perhaps hurts other players (AI players) and of course the AI developer.

User avatar
Franciscus
Posts: 4571
Joined: Fri Apr 20, 2007 8:31 pm
Location: Portugal

Fri Aug 14, 2009 10:32 am

Well, then, why not declare a truce and together rejoice on the fact that we found a game that both pleases pbem and AI players? :coeurs:
(we just must refrain from joining hands because of the flu...:neener :)

User avatar
Nikel
Posts: 2574
Joined: Sun Apr 20, 2008 8:38 pm

Fri Aug 14, 2009 11:42 am

Franciscus wrote:Well, then, why not declare a truce and together rejoice on the fact that we found a game that both pleases pbem and AI players? :coeurs:
(we just must refrain from joining hands because of the flu...:neener :)



Not to talk about kisses :D ;)

User avatar
slimey.rock
Major
Posts: 211
Joined: Thu Dec 11, 2008 9:11 pm
Location: Arkansas

Fri Aug 14, 2009 11:47 am

Franciscus wrote:<snip>

(we just must refrain from joining hands because of the flu...:neener :)


Yes, we would quickly spread an intercontinental pandemic :cthulhu:
Image

User avatar
MrT
Colonel
Posts: 334
Joined: Wed Jun 10, 2009 5:38 pm
Location: Zürich, Switzerland

Fri Aug 14, 2009 11:51 am

I had the flu already... were can i get a "i survied swine-flu'' t-shirt?

This also means i can kiss everyone.

woot. :coeurs:

User avatar
arsan
Posts: 6244
Joined: Tue Nov 28, 2006 6:35 pm
Location: Madrid, Spain

Fri Aug 14, 2009 12:07 pm

MrT wrote:This also means i can kiss everyone.


Not me, thanks! :neener: :D
Now, if you were Miss T... ;)

User avatar
slimey.rock
Major
Posts: 211
Joined: Thu Dec 11, 2008 9:11 pm
Location: Arkansas

Fri Aug 14, 2009 1:17 pm

MrT wrote:I had the flu already... were can i get a "i survied swine-flu'' t-shirt?

This also means i can kiss everyone.

woot. :coeurs:


I would buy that tee shirt :mdr:
Image

User avatar
jack54
Brigadier General
Posts: 491
Joined: Fri Jan 18, 2008 12:08 am
Location: East Tennessee USA

Sat Aug 15, 2009 12:18 am

gekkoguy82 wrote:I for one enjoy playing the ai, because obviously I can do it whenever I want, and all things considered I really think athena puts up a pretty dang good fight, at least for me. I haven't had an occasion where I've steamrolled her in the first couple years. But maybe that's just me being boneheaded, which is not nearly as stressful when I'm just playing her :) Then I'm the only one who knows what a dumb thing I did, and she'll always come back no matter how much I stink at it! :love:


perfectly said, I totally agree . Athena doesn't even mind all the times I've started over...lol .nothing against pbem but for the most part I hate to wait...

User avatar
bigus
General
Posts: 599
Joined: Wed Oct 24, 2007 11:43 pm

Sat Aug 15, 2009 6:46 am

Pocus wrote:Putting more efforts on a theater (in offensive or defensive) can easily be done with the AI commands exposed to modders. Again, the WIA community did an impressive job with them.


Exactly!
I've used the local interest commands because of the limited scope of my scenarios. The theatre commands have not even been touched yet.(as far as I know)
I think the potential is there to have a decent Campaign scenario if the will to use these commands are there.

@Barksdale and Arsan: It's hard to see two vets go at it over something so trivial as game preference. The game was meant to be played in both modes.
I consider the AI to be highly dynamic and enjoy playing against it. However there is no substitute for playing against a human opponent and there never will be. It's as simple as that.

User avatar
Redeemer
Major
Posts: 228
Joined: Mon Dec 15, 2008 10:27 pm
Location: Eastern US

Sat Aug 15, 2009 11:09 pm

tagwyn wrote:HOI3 for me! :p apy:


It is a little broke atm. Tried it, but I will wait for a few patches.
[SIGPIC][/SIGPIC]

Omnius
Lieutenant Colonel
Posts: 290
Joined: Tue Jul 03, 2007 2:15 pm
Location: Salinas, CA

Turn the AI Off!

Thu Aug 27, 2009 4:21 pm

Let's not forget that AI stands for Artificial Ignorance when it comes to computer opponents, well in the case of AACW it's Athena's Ignorance. The best feature of AGEOD games besides WEGO is the easy ability to turn the AI off. I gave up on playing AI's except early on and now just turn off the AI. I grew up playing old Avalon Hill and then SPI board wargames and played them mostly solitaire. Now I've gone back to my roots and play computer wargames without the AI. Yeah it's a little more work playing both sides but you can have lots of fun setting up cool big battles you can't get playing an AI.

The one big failing of AI's is the industry-wide fallacy that busy AI's are good AI's. All busy AI's are are annoying as they just don't do smart things like forming up Corps in AACW or resting units when they've become exhausted. In the demo I've noticed how the Union AI runs around huge armies in the dead of winter and the cohesion of those armies is horrible.

There is the button for allowing the AI more time to think that helps very slightly. Actually it reminds me of the old George Carlin joke about television, there's a knob for brightness but no matter how much I turn it it never makes the tv any smarter.

There's a limit to what can be done with an AI while we have PC's sitting on our desks. Maybe someday someone like IBM might make a truly supreme AI the way they did with Big Blue for chess. Until we're all having Cray supercomputers on our desks and an IBM doing a massive AI project we just have to grin and bear it with inferior AI's. The solution is for more companies to follow AGEOD's lead in allowing players to turn off the AI and play solitaire like in the good old days of board wargames. :thumbsup:

User avatar
arsan
Posts: 6244
Joined: Tue Nov 28, 2006 6:35 pm
Location: Madrid, Spain

Thu Aug 27, 2009 4:51 pm

Omnius wrote: The solution is for more companies to follow AGEOD's lead in allowing players to turn off the AI and play solitaire like in the good old days of board wargames. :thumbsup:


To each his own... i'm glad the "good old days" are over and computers can give us a decent AI rival for us to play with. Even a not so bright AI can give me more surprises than myslef ;)

By the way, before bashing AGEOD AI and putting down the time and efforts put on the AI by developers and betas you woudl do good to first try the "real" game, to know what you are talking about ;)
Since the last demo was made, months (even years??) have passed and there has been dozens of patches and improvements added to the game, including quite a lot of Ai tweaks :cool:
Regards

User avatar
gchristie
Brigadier General
Posts: 482
Joined: Wed Jan 23, 2008 5:31 pm
Location: On the way to the forum

solitaire

Thu Aug 27, 2009 4:57 pm

Ah, the days of playing Avalon Hill's Third Rieche solitaire (cause my pal got whipped early and refused to play any more.)

As to AACW, I'll take helpings of either. AI cause it fits my irregular ability to play, PBEM when I've got the time to devote. Both work great for me! Never considered playing it solitaire, but one thing's for sure, you're guaranteed a victory ;)

This got posted elswhere in the forum, but seemed appropriate here. Geri's Game
"Now, back to Rome for a quick wedding - and some slow executions!"- Miles Gloriosus

User avatar
Generalisimo
Posts: 4176
Joined: Wed Jun 07, 2006 10:03 pm
Location: Buenos Aires, Argentina
Contact: ICQ WLM

Thu Aug 27, 2009 5:11 pm

Omnius wrote:Let's not forget that AI stands for Artificial Ignorance when it comes to computer opponents, well in the case of AACW it's Athena's Ignorance. The best feature of AGEOD games besides WEGO is the easy ability to turn the AI off. I gave up on playing AI's except early on and now just turn off the AI. I grew up playing old Avalon Hill and then SPI board wargames and played them mostly solitaire. Now I've gone back to my roots and play computer wargames without the AI. Yeah it's a little more work playing both sides but you can have lots of fun setting up cool big battles you can't get playing an AI.

The one big failing of AI's is the industry-wide fallacy that busy AI's are good AI's. All busy AI's are are annoying as they just don't do smart things like forming up Corps in AACW or resting units when they've become exhausted. In the demo I've noticed how the Union AI runs around huge armies in the dead of winter and the cohesion of those armies is horrible.

There is the button for allowing the AI more time to think that helps very slightly. Actually it reminds me of the old George Carlin joke about television, there's a knob for brightness but no matter how much I turn it it never makes the tv any smarter.

There's a limit to what can be done with an AI while we have PC's sitting on our desks. Maybe someday someone like IBM might make a truly supreme AI the way they did with Big Blue for chess. Until we're all having Cray supercomputers on our desks and an IBM doing a massive AI project we just have to grin and bear it with inferior AI's. The solution is for more companies to follow AGEOD's lead in allowing players to turn off the AI and play solitaire like in the good old days of board wargames. :thumbsup:

Sorry, but I really think you have no clue of how an AI works and how much time and effort is needed to make a complex AI like the one needed for such an enormous game like AACW.

Really, comparing AACW with Chess :bonk: ... do I need to go into details about the HUGE difference in rules and variables that you need to manage? ;)

But if you are happy by turning the AI off and you have fun while doing that, it is great for you! :thumbsup:
Like arsan said, I will really encourage you to try the full (patched) game... the demo is just that, an old demo (2 years old) of a game before release. ;)
Also, if you find the AI "dumb", you can always look for a PBEM enemy to test your expertise... ;)
"History is the version of past events that people have decided to agree upon."
Napoleon Bonaparte


BOA-AAR: ¡Abajo el imperialismo Británico! (en español)

AGEOD Facebook Fanpage - news & screenshots about the upcoming games!

dragoon47
Private
Posts: 39
Joined: Tue Oct 14, 2008 4:51 am

Fri Aug 28, 2009 4:11 am

I've only turned off the AI for Hotseat campaigns :thumbsup.

How many of you actually play hotseat campaigns here?

enf91
AGEod Veteran
Posts: 724
Joined: Sat Dec 06, 2008 6:25 pm

Fri Aug 28, 2009 4:16 am

I sometimes play scenarios or the 1862 theater mini-campaigns against myself. Campaigns are too long.

Schattensand
Lieutenant
Posts: 118
Joined: Tue Jul 21, 2009 6:28 pm

Fri Aug 28, 2009 8:57 pm

Play 62 scenario

as rebel you will have a pretty hard time.

Ai will not help you buildung replacements

You start with 10% inflation already, the yanks none

unlike 61 WS is the biggest problem, not enough to build up railroad, ships arty. You have to say the rookies: sorry no arms, no uniforms, no guns
- go back home until we call you again -

At all fronts Athena is well organized and superior in numbers.

They advance step by step. Main Front in the middle, strong corps on both sides, You attack one corps -sound of the guns- and 120000 yanks are upon you.

Grant in the Tennessies advances with cavallery on the flanks, so piff-poff
again, no chance to trap them with no chance to retreat, what is anyway the only chance to eliminate a whole army, oki mayor river fording battles are an other, but that happens very rarely.

In the west your generals are crap.

Foote has a big riverine force and is willing to use it, they take No 10 and Memphis there is hardly anything you can do against it. Of course your own riverine force is nearly not existing at all.

You may have a decisive victory in the Georgia theather, if you send Jackson to Goldsboro, the Georgia force as well and attack at the 3 round - works only if the yanks there dont move.

Athena is not that bad in this scenario and will give you a hard time.

63 or 64 I have not even tried, will be for sure harder.

User avatar
bigus
General
Posts: 599
Joined: Wed Oct 24, 2007 11:43 pm

Sat Aug 29, 2009 5:32 am

Here's strong advice for playing the AI.

Check the "Activation" button in options and set it to "if checked, land forces with non activated commander can't move at all".

User avatar
GraniteStater
AGEod Guard of Honor
Posts: 1778
Joined: Thu Oct 09, 2008 5:16 am
Location: Annapolis, MD - What?

Sat Aug 29, 2009 5:37 am

Now compare such a complicated game to chess, which is relatively simple:

This is not directed at the poster.

No, it's the opposite. AACW is child's play compared to Chess, Go, or Bridge, and I mean that literally. The rulesets of the three above are much shorter than almost any computer game out there, but that is not a measurement of simplicity. Checkers is now solved, but not until recently and it took a quintillion some odd branched search tree to do it.

Consider this fact (it is a fact): the number of possible chess positions is larger than the number of electrons in the universe.

That's not 'atoms', boys and girls, that's 'electrons'. Now, in reality, the two numbers are largely indistinguishable (because of the overwhelming preponderance of hydrogen), but still...

Chess , Go, and Bridge are short rulesets and very complicated games. This means that actually, they're not hard to program; they're very difficult to program well enough to give Masters & Grandmasters a significant challenge. It took Deep Blue to give Kasparov a hard time.

AACW is a much simpler game that is harder to program because it has such a large ruleset. Any modelling of reality tends to show this. Chess, Go and Bridge are their own realities and model nothing. A game that models something not only needs to have a coherent and consistent ruleset but also needs to emulate conditions defined outside of the ruleset.


Thus, the difficulties in the programming. Bear in mind that it's also a commercial product and needs to please a market. Much harder than hooking up a CRAY and brute-forcing your way through a World Champion's repertoire.

Although the game is simple, really, compared to Chess, Go, or Bridge.
[color="#AFEEEE"]"Liberty and Union, now and forever, one and inseparable!"[/color]
-Daniel Webster

[color="#FFA07A"]"C'mon, boys, we got the damn Yankees on the run!"[/color]
-General Joseph Wheeler, US Army, serving at Santiago in 1898

RULES
(A) When in doubt, agree with Ace.
(B) Pull my reins up sharply when needed, for I am a spirited thoroughbred and forget to turn at the post sometimes.


Image

User avatar
MrT
Colonel
Posts: 334
Joined: Wed Jun 10, 2009 5:38 pm
Location: Zürich, Switzerland

Sat Aug 29, 2009 6:49 am

Now I remember why I never joined the chess club! ;)

gekkoguy82
Major
Posts: 205
Joined: Fri Aug 17, 2007 4:58 pm
Location: Nashville, TN

Sat Aug 29, 2009 2:52 pm

Interesting post GraniteStater, most interesting. And informative! :thumbsup:

User avatar
Gray_Lensman
Posts: 497
Joined: Mon Jun 18, 2007 4:04 am
Location: Who is John Galt?

Sat Aug 29, 2009 7:16 pm

deleted

mjw
Lieutenant
Posts: 132
Joined: Sun Nov 04, 2007 4:58 pm

Sat Aug 29, 2009 8:02 pm

Gray_Lensman wrote:I can follow most of your logic, but unless you can come up with an actual source for this part of your statement I'm afraid I'm gonna have to leave my skeptic hat quite firmly in place, especially since they haven't even determined how much matter yet exists in the universe. (re:dark matter for example)

Granted there are a lot of move combinations in chess, but does anyone really believe that "Man" can invent anything with more combinations than all the "electrons" in the universe? :bonk: :mdr:


Ok, I'm no physicist so I checked wikipedia (I know... but we are ballparking here ;) ), the estimated number of possible chess positions is 10 to the 43rd. the estimated number of atoms is 10 to the 80th...significantly larger. Now, most atoms (over 99%) are hydrogen so although there are more electrons, thats a good ball park figure for electrons as well. Maybe a couple of more powers.

BUT, I think the point has been made that chess is an ungodly complex game that requires immense computing power. Each turn there are over 130 possible moves. of course, I suck at it but its no wonder why people have been playing it for thousands of years.

Personally, i think the AACW AI is quiet good for a complex game like this. For some reason, it does not like to form corps and divisions on my rig but it still puts up a good fight.

User avatar
Nikel
Posts: 2574
Joined: Sun Apr 20, 2008 8:38 pm

Sat Aug 29, 2009 10:14 pm

It was Arthur Eddington who "estimated" the number of electrons in the universe.

http://en.wikipedia.org/wiki/Arthur_Eddington


But according to an astro-physicists biographies book I could find, his last years were not very scientific

[ATTACH]9036[/ATTACH]



Eddington number so is 1.57×10^79.

http://en.wikipedia.org/wiki/Eddington_number


There are some more modern calculations, in the observable universe and with some assumptions ;) , interestingly the result is not far from Eddington number :D

http://en.wikipedia.org/wiki/Observable_universe#Matter_content
Attachments
Eddington.jpg

enf91
AGEod Veteran
Posts: 724
Joined: Sat Dec 06, 2008 6:25 pm

Sat Aug 29, 2009 11:06 pm

Wow. This thread has gotten way off topic. Interestingly, it still connects.

richfed
Posts: 902
Joined: Tue Nov 21, 2006 9:50 pm
Location: Marion, North Carolina, USA
Contact: Website

Sat Aug 29, 2009 11:57 pm

In an effort to get it back on track ... while I would not go so far as to say the Union AI is "broken," I have noticed - in 1.14b - that they relinquish Washington, DC in favor of a new capitol WAAAAAY too easily. In two starts of that version so far, they moved to NYC both times in mid-62. I was not even in an adjacent region. ????
[color="DarkRed"][SIZE="2"][font="Book Antiqua"]"We've caught them napping!"[/font][/size][/color]

User avatar
Generalisimo
Posts: 4176
Joined: Wed Jun 07, 2006 10:03 pm
Location: Buenos Aires, Argentina
Contact: ICQ WLM

Sun Aug 30, 2009 12:04 am

GraniteStater wrote:Now compare such a complicated game to chess, which is relatively simple:

This is not directed at the poster.

No, it's the opposite. AACW is child's play compared to Chess, Go, or Bridge, and I mean that literally. The rulesets of the three above are much shorter than almost any computer game out there, but that is not a measurement of simplicity. Checkers is now solved, but not until recently and it took a quintillion some odd branched search tree to do it.

Consider this fact (it is a fact): the number of possible chess positions is larger than the number of electrons in the universe.

That's not 'atoms', boys and girls, that's 'electrons'. Now, in reality, the two numbers are largely indistinguishable (because of the overwhelming preponderance of hydrogen), but still...

Chess , Go, and Bridge are short rulesets and very complicated games. This means that actually, they're not hard to program; they're very difficult to program well enough to give Masters & Grandmasters a significant challenge. It took Deep Blue to give Kasparov a hard time.

AACW is a much simpler game that is harder to program because it has such a large ruleset. Any modelling of reality tends to show this. Chess, Go and Bridge are their own realities and model nothing. A game that models something not only needs to have a coherent and consistent ruleset but also needs to emulate conditions defined outside of the ruleset.


Thus, the difficulties in the programming. Bear in mind that it's also a commercial product and needs to please a market. Much harder than hooking up a CRAY and brute-forcing your way through a World Champion's repertoire.

Although the game is simple, really, compared to Chess, Go, or Bridge.

You fail to see the "simplicity" in the rules of chess... that's why it is the first choice for any serious AI programmer... even I did an AI for that.
That's NOT the case of AACW... the rulebook is FAAAAAR more bigger in AACW, and that adds a LOT of complexity to just take ONE small decision. ;)

And for example, it is IMPOSIBLE to use in AACW the brute force approach that Deep Blue used to beat Kasparov... there is not way to code that.
How can you create the entire decision tree for a specific AACW game?... it is IMPOSIBLE. ;)

This is more or less why you will never see an AI in a game as clever as the player... it is just imposible, there is not enough "computing" power to do that. ;)
"History is the version of past events that people have decided to agree upon."
Napoleon Bonaparte




BOA-AAR: ¡Abajo el imperialismo Británico! (en español)



AGEOD Facebook Fanpage - news & screenshots about the upcoming games!

User avatar
mikee64
Brigadier General
Posts: 413
Joined: Thu Jan 25, 2007 12:13 am
Location: Virginia
Contact: Website

Sun Aug 30, 2009 1:03 am

GraniteStater wrote:Consider this fact (it is a fact): the number of possible chess positions is larger than the number of electrons in the universe.


"That's a bold statement."
Vincent, Pulp Fiction

User avatar
GraniteStater
AGEod Guard of Honor
Posts: 1778
Joined: Thu Oct 09, 2008 5:16 am
Location: Annapolis, MD - What?

Sun Aug 30, 2009 9:23 am

OK, lemme try to address all this:

* I stated that as a fact, because I sincerely beleive it is. I read that statement years ago in a serious discussion and can't remember the book. I beleive it is a true statement.

**********************************
ADDENDUM: Go here: http://www.geocities.com/explorer127pl/szachy.html

from which (his English is good but a trifle inexact in a coupla spots):

"Yes! We have quantity of possible chess games: 10^134 .
And second question: what's quantity of possible positions on chessboard?"

and to the latter he gets 10^40. Obviously, he's making a distinction here, but it's a trifle unclear as to what that is.

AND

at http://www.mathematik.uni-bielefeld.de/~sillke/SEQUENCES/series014

"The following game position estimates are well-known:

Chess: 10^43
The estimate 64!/(32!*8!^2*2!^6) ~= 10^43 is given by Shannon in his
seminal paper "Programming a Computer for Playing Chess", Phil. Mag.
41 (1950) 256-275 (also in D. Levy's "Computer Chess Compendium").
As most everyone knows, we are far from solving the game of chess."

AND

from Wiki (see 'Shannon Number'):

...Shannon also estimated the number of possible positions, "of the general order of , or roughly 10^43". This includes some illegal positions (e.g., pawns on the first rank, both kings in check) and excludes legal positions following captures and promotions. Taking these into account, Victor Allis calculated an upper bound of 5×10^52 for the number of positions, and estimated the true number to be about 10^50.[3]

Allis also estimated the game-tree complexity to be at least 10^123, "based on an average branching factor of 35 and an average game length of 80". As a comparison, the number of atoms in the observable Universe, to which it is often compared, is estimated to be between 4×10^79 and 10^81....

My apologies, I stand corrected.

BUT

see: http://mathworld.wolfram.com/Chess.html

where (10^10)^50 is an estimate (of the number of games) and we learn that Shannon restricted the positions to games of 40 moves or fewer.

***********************************


* Let's keep it simple: starting position. There are 400 possible outcomes (i. e., positions) after White & Black have made one move (20x20; 16 pawn moves and 4 Knight moves). Now let's go down to everything swapped and just two Kings left. If my White King is at a1, then Black's can be on one of 60 squares, thus 60 positions just for a1. Now move it to b1, and there are 58 legal positions for the lone Black King, etc. Do that for all permutations of White, now swap and enumerate the Black viewpoint and delete all instances of repetition. That's an example of what I mean.

* Don't forget promotions at the eighth rank - different position.

The fellow a coupla posts up - you're very confusing; you seem to take issue with my statements, then seem to agree with everything. It's really clear - Chess, Checkers, Go, and Bridge have small rulesets but are very complicated games (i. e., they are very 'subtle'). Checkers is a dead game now, it's been solved, i. e., there is only one set of moves that results in a win every time. There is a solution for Chess and for Go and I think this is where I ran into my statement, I was doing some work in Game Theory, or Operations Research, if you're European. Bridge, I dunno, because it is not an "open-ended n by n" game.

At any rate, no computer game that I know of is as complex as CCG&B. Most computer games have large rulesets and very often model something that is extraneous to the game itself. Harder to program than CCG&B, but, as a game, vastly more simple.

To illustrate, I can put my Chessmaster program on ELO 2000 & I have to think, 'cuz that's about my strength (I'm an amateur, but a very good friend of mine is often the state champ in NH and I've beaten 2200 rated players; a very rare occurrence, I assure you). And that's nothing. If I put the program on even 2200, I'd never win, not in my lifetime, perhaps, unless I started studying again.

Larry Evans, a Grandmaster in both Chess and Go, thought the latter was the harder game. Bridge, if played correctly at the highest levels, is just as difficult as Chess, depending on the hand; over many hands, yes, difficult.

To wind up: there is a theorem (so it's true; theorems are true) that states that any n by n open ended game has one strategy that is a clear-cut win for one side or the other. N by n means a finite number of strategies on both side; open ended means that both sides have perfect information as to the game's universe, or information. Chess and Go fit this definition; Bridge does not.

Chess and Go have solutions. It is possible to argue that any given Bridge hand has a solution.

AACW has no solution because there are randoms introduced and the info is imperfect. AACW and its ilk are vastly simpler than CCG&B, much easier to play at a high level of skill.

CLARIFICATION

Tic-tac-Toe's "win" is a tie. IOW, a human's "win" results only with imperfect play. Thus, it's better to say 'solution' for the theorem. The real point is that there is a unique "winning" strategy (which could be a tie) in OENxN games, i. e., there is a solution. This is what is called an existence theorem. The identification (solution) of the unique strategy is another consideration.
[color="#AFEEEE"]"Liberty and Union, now and forever, one and inseparable!"[/color]

-Daniel Webster



[color="#FFA07A"]"C'mon, boys, we got the damn Yankees on the run!"[/color]

-General Joseph Wheeler, US Army, serving at Santiago in 1898



RULES

(A) When in doubt, agree with Ace.

(B) Pull my reins up sharply when needed, for I am a spirited thoroughbred and forget to turn at the post sometimes.





Image

Return to “AGEod's American Civil War”

Who is online

Users browsing this forum: No registered users and 8 guests