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Just moving this Cheversi discussion from the Requests Board to here, so if you would like to read the preceding posts, thats where they are ;)
AbigailII/Perfect information: Say White has three equally good moves A, B, and C and Black has the Moves X, A',B' and C'. X garanties a draw, A', B' and C' win against A, B and C respectively, but lose against the other two. So Black should play X, but he might choose to play a mediocre move and get lucky and win. In case of simultaneous placing of pieces, a player cant know the outcome of a game anymore by solely doing enough calculation, so luck comes into play, hence there's no perfect information anymore.
AbigailII/Swap rule: Of course in your example a swap rule wouldnt help. That's because in that game there are no positions that are drawish. But thats not the case in Cheversi. If after any of White's possible first moves, Black is able to construct a drawish position with his first move, then adding the swap rule after move 1 would cure the imbalance problem.
Ok, agreed, if White plays Qa1 in his first move, there probably wont be any drawish positions anymore after Blacks first move, no matter what he plays, so the restriction for White's first move might still be necessary.
dresali: I grant you that if there is a drawish move for black that a swap rule could "work" (although that would be a very different game, one that is decided on the first move). But it's not at all clear to me that, for any first move of white, there is such a move for black. Not that I really like games where blacks first move has to be a bad one.
As for your perfect information example, I'm a bit confused about your meaning of 'good' and 'mediocre'. Since all moves of white (A, B, C) can be beaten (A', B', C') and alternatively lead to a draw (X), I wouldn't qualify them as "good" moves. Although I guess that if white doesn't have any moves available that win, all moves are equally "good".
I still claim such a game would be a game of perfect information (nothing is hidden or determined by a dice roll). But I'm fine with you seeing it differently.
AbigailII: Things are not determined by a dice roll, but by luck. Consider a game of rock paper scissors, nothing is hidden there either, a single game of it is still completely luck dependant.
And A,B and C are 'good', since if Black decides to play A',B' or C', White will win 66% of the time, so it would be irrational for Black to not choose X, so with everyone playing rationally, the game would end in a draw.
Concerning the swap rule, I see that its probably not as perfect as I first thought, since White can play really bad which leaves Black no 'bad enough' moves, so restrictions would still be necessary. And all that bad play really isnt so nice at all, thats true ;) Which still leaves this great game at a way too imbalanced state.