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Sten Sture
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SF, CA don't call it frisco... Striker!!
Mar 1999 time: 21:12
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Okay, some of you all might be aware that the AI can be... challenged, shall we say, when trying to efficiently manage a city. I was digging into an OCC2 save to check out some stuff for my good pal from Colorado, the Honorable Mr. Clark, and I found a beauty of an AI city. Let's see if you can top this: (I am sure everyone can - the AI is limitlessly befuddled)
Rheims: Democratic French provincial city.
The French are running a 1T/5S/4L tax structure (because Lyon is in disorder from having 5 naval vessels out chasing an Aztec explorer on the south pole, but that is another story.)
Size: 8 with 5 happy and 3 content (WLTPD!!!)
Improvements: Temple & Marketplace. (perhaps an Aquaduct would be helpfull??)
Shield production: 8 with 3 fortified (nonvet) riflemen & a fighter in town, and an explorer & engineer out and about. That makes for a net of 2 shields.
City radius: 9 double irrigated squares - (6 plains and a desert included,) half have roads, and a fish special is being worked. Alas, the gold mountain is unworked. (I might recommend a supermarket if you are going to double irrigate plains)
Building: Cure for Cancer. 76 more turns to completion.

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Genghis Al
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of the Russian horde
Dec 1999 time: 05:12
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Using the auto settler that's a no no.
Alex v4.6
------------------
See you in court.
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KhanMan
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Fort Worth, Texas, USA
Jan 1970 time: 05:12
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Well, if you try a few games of the Nomads Challenge (either the original version, or ColdWizard's version), you'll see an interesting trick: the ai hates seeing beseigers in the squares around it's city. Even if these units are vet legions, fortified, on hills, it will most of the time, attack, down to it's last unit, leaving you free to waltz in.
What's more, if it refuses, one attack (whether it succeeds or fails), will almost always provoke a suicide-counter-attack.
Used this strategy to capture top two Roman cities (Rome and Veii), as well as the entire British empire, in a Nomads game.
Hows that for stupid?
-KhanMan the LLSS
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geofelt
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Neptune Beach,Florida,USA
Jan 1970 time: 00:12
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I once laid siege to an AI city with a republic government. I covered every shield producing square with a unit, depriving the city with the ability to support it's garrison, save one. One sieger was a vet alpine in a fort on a mountain. The ai surprised me, and bribed this unit. The real surprise was that supporting this new unit caused the only defender to disband, allowing me to walk in to an undefended city!
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Best dum ai thing I saw was I was playing a game on an earth map and I got hold of the middle east. Turned out this civ in Africa started a war and kept sending units up through Egypt. I positioned a couple of catapults at the point where the attackers turn ended (the neck out of Egypt leading to Israel). Turn after turn they sent units to that point and my catapults destroyed. Those 2 catapults must have destroyed 30 or more units. The ai never varied its attack.
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jpk
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Minneapolis
Feb 1999 time: 05:12
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One time I had a city on the peninsula of the AI's home continent. The AI lost diplomat after diplomat as it tried to us a land route to get to my city. A half dozen squares from my city the AI had a coastal city. Since I wasn't patrolling the ocean, that city could have built a boat, put a diplomat on that boat, sailed up to my city, and done what ever it wanted to do.
The AI's motto: If at first you don't succeed, try, try again.
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SCG
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of less than all that I see
Jun 2000 time: 00:12
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Actually, Hasdrubal, that doesn't sound that bad. Both of those wonders are civ-wide, so as long as it is built, all cities get the effect. And it prevents others from having use of that wonder.
As for bone-head AI, I just can reiterate the attack stratagies everone else has been bringing up. I had a city on a peninsula of a large continent completely owned by the Zulu's. I put a fortress on a chokepoint, and put a couple vet musketeers in it, with a catapult and a horsie of some sort, and every turn it came under attack with every catapult, chariot, elephant and other unit they had. There was a narrow channel between their continent and mine and plenty of coastal cities for both of us, but the attack never varied. my attack units took out the catapults and such, while everything else beat itself senseless against the fortress 
Although I do have to give the designers a small bit of credit with the AI. In Civ I, the AI rated islands of 4 land squares or less as worthless. They wouldn't even look at them. So i would build cities on them never even consider building a defender. First time i tried that in Civ II, I lost my city 
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The Mad Monk
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of Ice Cream
Mar 2000 time: 23:12
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The funniest event I've seen to date was in a TOT fantasy game; I'll introduce it by saying there is a unit called a 'Sorcerer', a fairly high-powered unit that has a move of six and acts as a fighter (so attacking after three squares becomes a suicide run). I was in republic, and at war with the Infidels, who were in fanaticism.
I had just captured a coastal Infidel city; It was lightly defended after capture, but I wasn't worried because the nearest Infidel city was the magic three squares away, and the AI dosen't deliberately kamakazie...
So imagine my surprise when a sorcerer comes right at me, makes a turn, and finishes its sixth move in an apparently empty square just outside my city radius. Then a second. Then a third... Six sorcerers paraded past my city this way!
I "knew" from past exploration that the square was empty, but something was clearly up. I checked my city, noticed I still had the ship my force came in on, and a skald (dip). I put the skald in the ship and sent it to the "empty" square, and found a size four city. I decided to bribe--and the price was right.
In addition to the six sorcerers, I found an additional five, several units of cavalry, a couple elephants, two settlers, and another skald. Since I was in republic, I knew most of them would be lost the next turn, so I sent most of the sorcerers on Kamakzie runs against everything within five ssquares. The Infidels lost another fifteen units that way...
I was in hysterics the whole time... 
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