I think I can divide the players thinking into three categs

1) Supervised Artificial PI (SAPI): the designer designs what the player should think to go through the game. Quests, adventure games, part of RPG''s (the story, the quests) use this PI a lot. In a RTS type 1 PI would be learning what the buildings do, what the building/fighting rules are, etc. This leads to the player reverse engineering the game design rather than going through the mental process he was supposed to. (i.e. if you find a crate you ask yourself "why did the designer put it here", and start searching using for the crate like climbing). PI1 appears when the designer hides game information from the player; it''s his job to find them out; after he does find them out, going through the game again is trivial.
examples :

2) Unsupervised Game PI (UGPI): this is where the strategy games come in. After the player learns SAPI game rules quite fast (they are not classified, reading tutorials on these rules isn''t cheating), he starts combining these rules in different strategies. Though with some games you can go on for ages doing this and still coming up with new strategies, after awhile it gets boring, as you have tried them all, and found the few strategies wich are working best. After that point, you just keep going using those.
examples : all the games you mentioned are UGPI high powered; VGA Planets (fascinating game; try reading the strategy guides first, coz the game isnt really user friendly), Lemmings, TIM


3) Out of game PI (OOGPI) : it appears when the thought process''s target is not the game itself, but the person at the other end of the multiplayer network. I wont go into defining this one cause it''s not really done in a lot of games. However bits of OOGPI do from time to time rise to the surface. An trivial example of OOGPI was me making a joke in a msn zone hearts game (also has a chat window). All multiplayer games have some form of chat implemented and that is a window to OOGPI (especially in RPG''s). The problem with these is you cant really make a strong connection betwen the game and the OOGPI. Jokes & similar stuff require huge intelligence, beyond the wildest AI dreams, but they don''t have a continous direct effect on the game. Maybe in an RPG you form an alliance with some chaps, but after that is all RPG monster bashing again. Likewise in an RTS. Notice that these alliances are more of a direct consequence of UGPI (the game requires them to achieve some goals), so jokes remain, well, jokes.

My vision is a game where you have to talk alot, lie and find out if you''ve been lied to, threat people into submission or making other people friends, a game of intrigues and secret alliances. This kind of game will be very soon made possible by real-time audio&video images.
examples:
Learning from your spies that a neighbor you just signed an neutrality treaty with is mobilizing his army is UGPI, but telling him that one who would stab another in the back is a big fat rat is OOGPI.
A guy used the following "Terror tactics" in Total Annihilation : he packed a large number of very cheap bots, teamed them with an radar erase (wipes you off the enemie''s minimap), moved them close to the enemy lines, into the enemy radar range, made the bots move towards the enemy and turned off the anti radar. After few seconds, he turned his radar on again and retreated to safety. What the enemy was seeing on his radar was a huge battle group (many dots, cant tell if they are heavy tanks or peewees) allout attacking him out of nowhere. Dont know if this worked, but this is game connected OOGPI at it''s best.


I think that OOGPI has by far the greatest potential in the industry (after all, we all get tired of bragging about headshots or level 5000 characters whith 7941421634 zillions XP to our fellow gamers). Talking about how you''ve fooled some dwarves (player characters) into believing you have real magic powers, or how king playerX is just a corrupt politician and with him the hole of Azeroth will fall in orcish hands would really make gamers able to brag to people who never played the game (_Out Of Game_ PI), making both them and the non-gamers feel better (better inclined to buy the game that is).


What I want from you is fun examples of OOGPI that did happen or you''d like to happen. Perhaps a pattern would come out...