You know of course that if this game has an enigmatic form, THEN the same game, with the exception of announcing any players play(how many points every player played) at the end of the turn, will create a totally different game that its enigmatic nature will be much higher and it will be based more on luck.
Now by knowing how much points every player has in any move, some mathematics can be applied to ensure in some cases "perfect play".

The "" at the perfect play have to be put, since there is no perfect play when randomness comes to play....This game is not a perfect-information-game, so there is no perfect play in general.