Thank your for the detailed, well thought out comment and for the feedback. This is exactly what I'm looking for as I move forward with this game.
I am looking for ways to minimize the "luck" factor and add more strategy to the game and converting the mind games that typically happens on a face-to-face interaction to a virtual ones comes with some challenges. I have been thinking a lot about this and your idea about using avatars to simulate human "tells" is one that would be fun to experiment with.
Also, the "risk-reward" throw 3 rocks against paper idea you mentioned is one I have been considering to add something like light, medium, and heavy attacks that cannot be easily broken with a simple "block." Think of it like breaking down defenses with powerful attacks making your opponent vulnerable to your next 2 or 3 attacks for example.
First thing on my list is to add a way to fight back so that you can react to a lost and not have to try again later. I think that will help to put things more into perspective and help me to know which rules of the games and/or mechanics need improving/revising to really nail that sense of progression and satisfaction a player might be seeking for as you so well put it.
Thank you for playing! :)