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.
Also, I tend to play with score piles face up so that you don't have to remember every card played. But there's no reason you can't make it a memory game.
Great! These ideas all change the game dramatically. While I'm personally not a fan of the Totals style, I think your Low Wins Total is an excellent idea. I'm definitely going to try it out! You are correct that their is no best opening- and mathematically this is difficult to prove because of the phrase "assuming that all players are equally knowledgable." The game depends on Yomi- being able to predict the move of your opponent. At a very simple level, it seems like you'd want to play your highest card first then work your way down- but all I have to do to win against that is recognize what you're doing, throw my 2 to your King/Queen (I lose something to your Ace/King when you throw it), then throw my highest card every round, and I will always beat your "strategy" Similarly, if you start playing by any strategy which allows me to anticipate your moves, I will be able to win. Reliable prediction means you're screwed in this game, and that's why I think it's a great place to start thinking about strategy. Because it is completely and unabashedly a game which acts as a very thin interface between two minds. If you know that I already blew my Ace on a 7, then you have the advantage of being able to beat any of my card, but you still need to be able to guess when I'm going to throw high, or trick me into playing lower cards out early to give you an advantage in the later game. I'll be posting some variants of my own that I think you'll be happier with and move into the realm of incomplete information. Thanks for playing this!