Dvonn surprised me as being one of those games that is inscrutable the first time you play it, but makes some basic sense after several plays.
During the first part of the game you are jockeying to put your pieces down in positions to control the red pieces. That means: place pieces that can directly jump onto the red pieces. Place pieces that can jump onto your opponents pieces that can do the same. Place pieces that, after one jump can jump on the red pieces. Etc... The more control you establish, the better.
During the second half, you have to keep control over different areas of the board. A single move by your opponent can do several things: prevent you from moving a piece that could have landed on his; capture a piece you needed for control; and threaten a new area with the resulting piece. This is a lot to absorb, and the number of potential moves at any time except the very end is large, usually more than chess.
This is a good thing. I think with repeated plays, one can get much better at the game. In fact, my first few plays I felt that the whole game was almost random. If I had given up then, I would have missed a whole depth of understanding. This patches in with the discussion I am having with Jeremy Avery on Gamefest.
Anyway, I won once, and then Saarya won once. As we played, the moves became more deliberate, and the zones of control began to glow in our heads, like the patterns in the newspaper in the movie "A Beautiful Mind", or like a game of Go to an experienced player.
Sometimes you can gain something special if you persevere.