AbigailII: OK, I see what you are saying now. Hum.... maybe there is a solution in changing around the points awarded (and lost for wrong guess)

AbigailII: One thing that would help is to have squares where the result must be a zero automatically be filled in with zeros. For example, if there are zeros at A2, B1, B3 and C2, it's impossible for B2 to be anything but a zero, since all adjoining squares are next to a zero square. This would eliminate (or greatly shorten) the phase of the game where both players shoot squares that they know will return zero, since any other move gives an advantage to your opponent.

Another improvement would be to increase the density of frogs, so that revealing a 2 is more likely. With the current scoring, guessing next to a 1 is always a bad idea unless there's only one possible location. But guessing next to a two has a variety of result. 2/2 and 2/3 are both good. 2/4 is bad, but 2/5 is actually good. (The 40% chance and 5/3 reward mean your guess has a net positive value, but it's likely enough that your opponent would guess wrong and then you would guess right, that at 2/4, it's a bad idea to guess.) If two's were fairly likely, guessing next to a spot with 3 or 5 unknown squares is much more attractive.

It might also work to give points for finding frogs in neighboring squares. For example, it you got the number of points shown in the square for shooting an empty square, that would provide an incentive to shoot in squares that neighbor unknown squares. If the values are balanced correctly, it should be possible to create a situation where it's advantageous for me to shoot a square that might reveal neighboring frogs and then for my opponent to guess where a frog is.