AbigailII:  My proposal doesn't introduce any more chance than there already is.  It automatically fills in the ones that are obviously zero (with a precise definition of obvious) but not the ones that a more complication intuitive process would also reveal to be zero.

I'm in several games right now where part of the board looks like below.  The rest of the board consists of squares where, for either player, it gives the opponent an advantage if you guess or shoot in any square.  Consequently, we're going through and filling in this section of the board with solid zeros.  This is rather boring and time consuming and doesn't actually accomplish anything, since we're both making shots that we know will reveal a zero.  I'm trying to create a rule that bypasses this part of the game.  (It will probably be still be there with my rule, but much shorter.) 

  +---+---+---+---+---+
6 | 0 |   | 0 |   | 0 |   
  +---+---+---+---+---+
5 |   | 0 |   | 0 |   |
  +---+---+---+---+---+
4 | 0 |   | 0 |   | 0 |   
  +---+---+---+---+---+
3 |   | 0 |   | 0 |   |   
  +---+---+---+---+---+
2 | 0 |   | 0 |   | 0 |   
  +---+---+---+---+---+
1 |   | 0 |   | 0 |   |
  +---+---+---+---+---+
    a   b   c   d   e

By the way, I'm not neccesarily opposed to long games.  I play anti-backgammon, which can easily run into hundreds of moves.  But most of those moves require actual thought (and auto-pass is there to skip many of the ones that don't).  But under the current rules, Frog Legs usually leads to 50 or so moves where the only thought is to correctly figure out a square that won't matter (which is probably the same calculation you did in the last 10 moves).