• Never guess unless the chance the square contains a frog exceeds 50%.


• If you can shoot a square that is only surrounded by squares of which it's known whether they contain a frog or not, shoot it.


• Never shoot a square that has only one unknown neighbour (an unknown neighbour is a square of which it's unknown wether it contains a frog or not) - you'll give your opponent 5 points if the square reveals a 1. (See below).


• Avoid shooting squares that have an odd number of unknown neighbours; if the number reveals the same number as the number of unknown neighbours, your opponent can guess one more frog than you do. (This is a generalisation of the previous point).

   +---+---+---+
 3 |   |   |   |
   +---+---+---+
 2 | 0 |   |   |
   +---+---+---+
 1 |   | 0 |   |
   +---+---+---+
     a   b   c

1. Increase the density of the frogs. There will be less no-information revealing moves possible if there are 25 or 49 frogs. It will not lengthen the game, as currently, between good players, most of the board will be shot anyway.


2. Give players two moves per turn. Then, in his/her second move, the player can use the information gained in the first move.


3. No guessing - just shoot the frogs (change them into bunnies). First to shoot 5 frogs wins the game.


4. If you shoot a square revealing a non-zero number, you get an extra turn (or a free guess)

1. Your opponent guesses right. Probability: 0.5. Score: -5.


2. Your opponent guesses wrong, you guess right. Probability: 0.25. Score: 3 + 5 = 8.


3. Your opponent first guesses wrong. You guess wrong. Your opponent finds the frog. Probability: 0.25. Score: 3 - 3 - 5 = -5.

    +-------+-------+-------+-------+-------+-------+-------+-------+
    |   1   |   2   |   3   |   4   |   5   |   6   |   7   |   8   |
+---+-------+-------+-------+-------+-------+-------+-------+-------+
| 1 | +5.00 | -1.50 | -0.33 | -1.00 | -1.40 | -1.67 | -1.86 | -2.00 |
+---+-------+-------+-------+-------+-------+-------+-------+-------+
| 2 |       |  0.00 | +2.33 | -0.17 | +0.20 | -0.47 | -0.71 | -1.00 |
+---+-------+-------+-------+-------+-------+-------+-------+-------+
| 3 |       |       | +5.00 | -0.00 | +1.80 |  0.00 | +0.43 | -0.27 |
+---+-------+-------+-------+-------+-------+-------+-------+-------+
| 4 |       |       |       |  0.00 | +3.40 |  0.00 | +1.57 |  0.00 |
+---+-------+-------+-------+-------+-------+-------+-------+-------+
| 5 |       |       |       |       | +5.00 | -0.00 | +2.71 | +0.00 |
+---+-------+-------+-------+-------+-------+-------+-------+-------+
| 6 |       |       |       |       |       |  0.00 | +3.86 | +0.00 |
+---+-------+-------+-------+-------+-------+-------+-------+-------+
| 7 |       |       |       |       |       |       | +5.00 | -0.00 |
+---+-------+-------+-------+-------+-------+-------+-------+-------+
| 8 |       |       |       |       |       |       |       |  0.00 |
+---+-------+-------+-------+-------+-------+-------+-------+-------+

for each unlabled square S2 next to S1

  mustBeZero  = false

  for each labeled square S3 next to S2

     if S3 is labeled with 0

       mustBeZero = true;

     endif

  endfor
  if (mustBeZero)
     label(S2, "0")
  endif

endfor

This would cause the "barren plains" where there are no frogs at all to be quickly filled in.  It also means that if there's a 1 two squares away that's next to a known frog, that won't fill in the square, which might be reasonable, since you might not want to do too much thinking for the players.  If you wanted to also fill in those squares, replace "if S3 is labeled with 0" with "if S3 is labeled with the number of known frogs in neighboring squares".

  +---+---+---+---+---+
6 |   |   | 0 |   |   |   
  +---+---+---+---+---+
5 | 0 |   |   |   |   |
  +---+---+---+---+---+
4 |   | 1 |   |   | 0 |   
  +---+---+---+---+---+
3 |   | 1 |   | 1 |   |   
  +---+---+---+---+---+
2 |   |   |   |   |   |   
  +---+---+---+---+---+
1 |   | 0 |   |   |   |
  +---+---+---+---+---+

  +---+---+---+---+---+
6 |   |   | 0 |   |   |   
  +---+---+---+---+---+
5 | 0 |   |   |   |   |
  +---+---+---+---+---+
4 |   | 1 | ? |   | 0 |   
  +---+---+---+---+---+
3 |   | 1 | ? | 1 |   |   
  +---+---+---+---+---+
2 | 0 |   |   |   |   |   
  +---+---+---+---+---+
1 |   | 0 |   |   |   |
  +---+---+---+---+---+

See? The frog can be anywhere on the ?-squares.

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

  +---+---+---+---+---+
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

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