Arun - regardless of the method of picking, the best idea, or rather the only sensible one would be to play 2 games for each of the AIs (in case you will get participants of course) - each game with "opposite" picks. To make that happen you would pick only 3 not overlapping picks, and as it's without fog, you would not need to remember the other picks, nor would you need to start many games in order to get both players win "first pick"..
I'm not sure if i made myself clear enough - instead of picking 123456, and counting on luck, knowing one player gets 145 and the other 236, you would pick 123 for one player, and 456 for the other, and then play a rematch when first picks 456 and the latter picks 123 to find out how do the algorhythms cope with different positions.. (this will allow draws as a resuld of a duel, but you may easily create a point system like in football leagues or sth..
again - i would like to but i have not much time.. on the other hand - aahh what the heck, ok :P - just create a game with me when you get at least two participants because i find this idea really interesting :)
btw - it would be also funny to compare the player-created AIs to the built-in AI, but that would be biased a lot based on picks.. :/