I haven't proven it mathematically, but I suspect that there is no best opening, assuming that all players are equally knowledgable. It's a random game, at that point. After that point, play may become strategic, but it's mostly a game of memory (especially with 3+ players) and perhaps of bluffing - a little too simple, perhaps, for actual play.

I believe that it could be made better with one or more variants, though:

Scoring Variant: Totals The value of your score is the total of the cards in the pile, not the number of rounds won. This means that it's more-important that you win rounds with high cards in them. So losing to a King when you played a Queen is really painful, but it's not so bad if you'd played a Three. Further variants could, for example, rank all court cards (Jack, Queen, King) as Tens for scoring purposes (and faster score calculation at the end).

Scoring Variant: Totals (Aces Trump) As above, but Aces only score one point, but are counted as "beating" a King. This means that Aces are a great card to play to hedge your bets, because it'll beat anything (except another Ace) and in the event of a tie it doesn't put too many points in the "pot" to be stolen by another player.

Scoring/Ranking Variant: Low Wins As either of the Scoring Variants above, but the lowest card wins the round, not the highest. This is subtly different than the Scoring Variant, because the cards which are most likely to win you the round are the ones that gain you the least points.