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!