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 Frog Finder

Frog Finder & variants (Frog Legs)


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11. februar 2008, 18:45:06
AbigailII 
Emne: Re: change the rules please
coan.net: in the idea of hiding where your opponent guesses, I'm trying to see how you would think revealing a 1 (or higher) would become worse than it is now. If I shot and reveal a 1, my opponent will still have the same chance of guessing where the frog is as they did before.

Yes, but your opponent goes first, giving him the edge. Take for instance the simplest example, you reveal a 1, with only two possible places for the frog. Assumming both players now guess until the frog has been found, there are three possibilities:

  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.


So, your expected score after revealing a 1 with two unknown squares surrounding it: 0.5 * -5 + 0.25 * 8 + 0.25 * -5 = -3.

Things looks less grim if there are 3 unknown squares, but if both players guess until the frog is revealed, the player guessing first (the opponent of the player revealing the 1) has an expected gain in score of 0.44 (if I did my math correctly).

There's no real solution here, even if you play with the rewards/penalties. If, when a 1 (or a different number) is revealed guessing gives an expected positive score, the opponent of the revealer has an edge. Then it doesn't pay to make a move that may reveal a non-zero number. If guessing gives a expected negative score, we have the same situation as we currently have. And if the expected score is 0, it's just a blind luck.

11. februar 2008, 19:23:37
coan.net 
Emne: Re: change the rules please
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)

14. februar 2008, 04:27:39
troydaniels 
Emne: Re: change the rules please
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.

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