Well the random order of cards in reality, I think there are two of each card in the deck, at least with the swirly card motion it's definitely more than 6 cards. I think if you wanted a system that offered more control it would have to come with sacrifice and the best way I can think of doing that would be by being able to combine 2 cards to gain the effect of a new card.

So if we saw the cards as Water-Fire-Ice-Wind-Earth-Lightning and in that respect Ewer-Balance-Spear-Bole-Spire-Arrow or

MP refresh-Increase dmg dealt-Reduce action recast-Reduce dmg taken-TP refresh-increase att speed then you would be able to do the following.

You don't like Bole, so you draw and spread your first card, say it's Spire, then you draw bole, since you have spire on spread and bole as your second the effect you would gain would be the one behind bole so spear in this case.

Basically the rule would be you gain a new card that isn't the spread card, so you will never have a situation where you are holding a card, and the combine of the two cards would just be the held card.

Basically this

Spire+Bole=Spear * the special case
Spire+Spear=Bole
Spire+Ewer=Balance
Spire+Balance=Spear
Spire+Arrow=Ewer
Spire+Spire=Arrow

Then the other special cases would be

Arrow+Spire=Bole
Bole+Spear=Balance
Spear+Balance=Ewer
Balance+Ewer=Arrow
Ewer+Arrow=Spire

That's my take on it though, I feel the above system would better serve to manipulate the cards rather than just making it a counting cards game.