troydaniels: It's not that simple. There are a lot more cases to consider. For instance:

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

If shooting on a2 reveals a 1, it can be determined that d4 must be a zero.

AbigailII: It's not that difficult to determine which ones must be zero.  If you shoot in square S1 and get zero, then you need to check

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".

troydaniels: It will be tricky to programmatically determine which squares have to be 0; it's easy to come up with examples, but it'll be hard to find all possibilities.

Here's a table with expected scores, assuming you guess, and subsequent guesses are only done if they give a positive score.

    +-------+-------+-------+-------+-------+-------+-------+-------+
    |   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 |
+---+-------+-------+-------+-------+-------+-------+-------+-------+

'+0.00' means there's a small positive expected score, '-0.00' means there's a small negative expected score.

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.

Another possibility to make game more atractive is to prohibit shooting on field what is connected to two or more 0.

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)

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.

AbigailII: 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. Only now if they do decide to take a chance and guess (and guesses wrong), it would be to my advantage to try to guess also. But also lets say there are 3 possible places a frog could be (33% chance) - I may also decide to guess - at worse (if my opponent did not guess at all), at worse I would end up -1 point (guess wrong twice, then correct third time) - but also keep those points away from my opponent.

As for the other ideas (my quick opinions)

1. 49 just seems like way too many. 25..... now that might be interesting. It will leave less 0 spaces on the board - but also might "block" part of the board in which players would have to take "wild" guesses behind a "row" of frogs. (then again 49 might work - I would have to see what a board would look like)

2. I think that would end up with players on turn 1 taking a shot which only reviels 1 space - that way on turn 2 they could guess correctly. Would help speed up the game, but my quick thoughts is not make it much better.

3. To me shooting the frogs instead of guesses seems like more of a different game - that is possible a different variant other then a solution to help Frog Legs.

4. I think it would end up like #2 - that is players would try to only make shots that give information to just 1 space (that way they can use that information next). A solution which may not make the current game any better.

And yes, and idea should be thought out very well - tested outside of the site if possible before anyone tried to convince Fencer to change something. (which is why I would LOVE to hear from anyone with ideas or suggestions or comments about other ideas.)

Overall - I would like to see something small changed which will (1) not change the game too much and (2) make it so it is worth to take more wild guesses. when there less then 100% chance of guessing correctly.

coan.net: Having the game balanced doesn't necessarely make it fun. Flipping a coin is balanced game as well, but not really fun to play.

I think the "problem" with Frog Legs is that your move reveals information that can immediately be used by your opponent. This, in combination with low density of frogs (only 9 out of 169 squares contain a frog, which means that no matter how the frogs are placed, over half of the squares show a 0) makes for a dull game. The dullness lies in the 60 or 70 moves that are played before the game becomes interesting - no more "waiting moves" can be played.

I don't know if the flaw can be fixed - and I suggest to Fencer he won't make any chances to the game unless it was properly play tested.

Not knowing where one has guessed changes the situation where there's a 50% chance of finding a frog: it will then become advantageous to guess. However, this makes it even better to shoot on squares knowing it will reveal a 0, as revealing a 1 (or an even higher number) becomes worse than it's now.

Here are some ideas that may work (although only play testing will reveal whether it actually does)

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)

coan.net: I think the MSN rules set for Minesweeper fit best here. No guessing anymore, Just shooting.

lukulus: I'm guessing you are talking about Frog Legs. One of the things I liked about Frog Finder was that I was able to sit down with a friend in real life and test that game many times on paper before it was brought here. So I was able to get many of the rules, points and such pined down - and I think that shows in the finished game stats of it being a very balanced game [red 8731 (50.03 %) vs. blue 8694 (49.81 %)] After over 17,000 games, about 40 games difference between the 2 players.

Anyway, for Frog Legs it was harder to test in real life - since we would had needed to have a person just play the "computer" while 2 others did the guessing.... so it was not tested as much as the original.

One of the main goals of Frog Legs was to introduce more guessing - getting more to take chances, and making more guessing. Of course I see this goal failing mostly because a person who does guess and gets it wrong - their opponent then has a much better chance of guessing correctly.

If anyone has suggestions, I'm happy to read them. As for your suggestions, I think #1 would go to far. #2 wouldn't be that bad - but I don't think that would help in getting people to guess more often.

My idea: To hide where you guess at from your opponent. This way if there is a 50/50 chance of where the frog is, and you guess - your opponent can see you guessed - but WILL NOT KNOW WHERE. So that will leave your opponent with either (1) going on with their game like normal and leave you to guess correctly next turn, or (2) take a 50/50 guess themselves to try to find the frog before you.

So what do you (anyone) think of this idea?

This game is so booooring. What is your opinion about this changes:
1. You will shoot until you will discover number 1 or higher, or kill the frog, or you will guess.
2. If you guess successfuly, you can continue or you can pass your turn.

I think this changes could improve this game a lot.

I agree with AbigailII. Perhaps it would make more interesting games if shooting and guessing was not exclusive, but rather that player could guess after his own shooting (even multiple guesses should be possible).

After playing hundreds of moves (but only actually finishing a few games), here's my first evaluation of Frog Legs.

Play wise, it's quite boring. There's no real strategy, except from avoiding playing bad moves. If both players don't play any obvious bad moves, the game boils down to filling up allmost all the squares, delaying having to reveal essential information until there's no other move. And then it becomes a game of luck, with the frog(s) to reveal only having two or three squares. Games will last 70 to 80 moves, which, I think, will rank them along the longest games found here on BK.

As for strategy, I use the following guidelines:

• 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).

Of course, the current score can influence things. If there are only N frogs to be found, and your are ahead more then 5 * N, by all means, narrow down where the frogs are as soon as possible - it's ok if your opponent guesses the remaining frogs.

Here's an example of where you shouldn't shoot:

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

Don't shoot at b2. It's already known that a1, a3, c2 and c1 do not contain frogs; c3 is the only unknown neighbour of b2. So, if b2 reveals a 1, there will be a frog at c3 with 100% probability. Unless your opponent is making a very stupid mistake, you will lose 5 points.

Jaak: Sure but it's not an easy task to change the model of already existing game, i.e. change the board size etc.

My first move in 2 price tournament games with white: Frog Finder (Jaak vs. DamnCat) and Frog Finder (Jaak vs. Holyman)
You see that I shooted the same square in both games, allocation of my frogs is differen in those games.
However it is a good game, if it is possible to delete tournament games and begin the same game anew? Or to have some safe squares - 4 corners or 5 (9) central squares!

AbigailII:  Interestingly, if you know there are two frogs in four squares, you shouldn't guess.  However, if you know there are two frogs in five squares, you should guess. 

In both cases, you'll guess right often enough that you'll score more points for the right guesses than you'll lose for the wrong guesses.  However, with four squares, if you guess wrong, your opponent can guess with a 2/3 chance of being right, which is good enough that the points he gets from guessing right outweighs the points you might get from guessing right.  With five squares, you still leave your opponent with enough options that guessing is a bad idea, so you just get the payoff from your initial guess.

For those interested in both Frog Finder & Frog Legs - I have to prize tournaments starting soon:

Feb 5 - my 5 year anniversary on the site - coan.net 5 YEARS on BK Frog Finder

Feb 29 - Not often we can start tournaments on this date - coan.net new game Frog Legs PRIZE

Should be fun - come and join!

Fencer:

coan.net: Since I have already tested it on more than 50 games (locally, not here), I declare this issue not to be.

Fencer: OK - So then hopefully the bug has been fixed then!

coan.net: It's important when the invitation was created, and it was most likely before applying a fix.

WellyWales: I would think (and this is a total guess) - but I would think that the game would not be "created" until someone picked up the game - which gave it the game number 3022152

... which the last game mentioned in the bug tracker was 3021714

So I would guess your game was made after the last bug was "fixed" - but maybe it does have something to do with it sitting in the waiting room... but would not think so. (again, just guessing)

coan.net: Would games started or set up before the fix need to be deleted ?? I set the game up in the waiting room, when it was first announced

WellyWales: Which would mean that Fencer has not fixed the bug completely yet.

coan.net: The move was made at 19.03 GMT i.e. 38 minutes ago

AbigailII: Hum... and the game below looks like it was started after Fencer's latest fix (if I'm reading the time of everything correctly).

coan.net: That has been reported and said to be fixed some hours ago: http://brainking.com/en/ReadBug?bgi=1457.

WellyWales: I would not think so - hurry and put that in the Bug Tracker so Fencer can find it and fix it.

note: I would think that since Fencer has it set up for the first middle square to be zero when the game starts, he did not remember to make the random frogs not to be put in the spaces next to the zero. (would be my guess on the bug)

Is this correct ?? a zero next to a frog Frog legs (WellyWales vs. TheCrazyPuppy)

coan.net: It's a very great game to play though. Basiccally, of course, it's just minesweeper, although you have to score by shooting mines.

Futhermore, there are some other rules:
The board is 18x18 and has 51 mines (i think!)
if a player shoots a mine, he'll score, and may play again. (This could cause a problem in BK. But there should be a solution. Just pass the game directly back to the player after every move he scores a hit, like Dice Poker Style. If he didn't score a hit, the move is directly passed to the opponent.)
If a player shoots a zero, ALL squares adjadent to that zero will also open, if there are any zeros among them repeat for each one the process. So shooting zeros is very bad, for you opponent has lots of mines to score.


Conclusion, as, especially I read Abigaill's post, we should add more mines (frogs, sorry) and remove guessing. Just shooting.!

coan.net: I did some calculating what the best action would be if there's a square showing a 1, and it has N neighbours that may have the frog (frog is still hidden). That is, there are N squares around the 1 that are not showing a number, and from the rest of the field, it cannot be determined whether they have a frog or not.

Obviously, if N == 1, you should guess the square, it will contain the frog with 100% certainty, and you will score 5. If N == 2, guessing one of the squares would be wrong. If you guess right, you score 5, but if you guess wrong, not only do you score -3, your opponent will score 5, so your expected result from guessing is -1.5. For N == 3, guessing is also wrong, but your expected score is less bad as in the N == 2 situation. If N == 3, you have a 1 in 3 chance of guessing right, so the expected score is 5 * (1/3) - 3 * (2/3) == -0.33. Note that after guessing wrong, you leave a situation where there are 2 squares that may contain a frog, and it's in your opponents best interest to leave it like that. In fact, for N >= 3, the expected score from guessing is 5 / N - 3 * (N - 1) / N == (8 - 3N) / N.

This will be a very defensive game.

And what we really need is a marker on the field indicating which squares have been unsuccesfully guessed.

joshi tm: Well if it ends up not working with the current point system, then of course I'm sure we can get Fencer to change that if needed..... but we won't know that for sure until we see a few hundred games played.

Nope, never played on MSN network - about the only place I've played minesweeper is the version that comes with windows.

Maybe you can subtract points from the penalty.

By the way do you know of the MSN network game Minesweeper? That one is lots faster to play (and had more mines making everyone crazy)

AbigailII: Yea, it will be interesting to see how much cat/mouse type of play - that is would it be better to just make a dummy shot that you know will show a 0, or take a guess when you have a 33% chance (or 50% chance) - since a wrong guess will only cost you 3 points.

It will be interesting to see if a "safe" game or an aggressive guessing game will work the best.

coan.net: Unfortunally, it also means that it's an advantage to shoot squares where you will already know how it will reveal 0 (like shooting in the corner if your opponent shot (diagonally) one step away from the corner revealing a 0). Such a shot reveals no information at all.

YEA - A new Frog Finder Variant - Frog Legs.

It is played the same way Frog Finder is.

The difference: Instead of each player having 5 frogs, there are 9 frogs that BOTH players are looking for. So your opponent will see your shots - will use the information you got in their next move (and you will use theirs).

So you have to be careful to not give your opponent too much information - and at the same time, don't be afraid to take more guesses since if you wait to figure out 100% where the frog is, your opponent will just swoop in and take it away from you!

HAVE FUN!

coan.net: Interesting. Two more points: if you go first, and you decide to shoot, you don't have a 'safe' shot, there's always the chance to hit something. Making your first action a guess doesn't give your opponent a field he can shoot knowing there's no frog there.

But here's another thing. Say starting with a guess would be a good thing. Then, wouldn't it be good for the player going second to start with a guess as well? But if both players start with a guess, followed by a shot on their guess, what about their third moves? Shouldn't that be a guess too?

coan.net: Personally, I don't hit a frog on my first shot very often. (Rarely, in fact). So, I wouldn't think it was worth it to start off 3 points behind. I suppose if there were more frogs on the board, it might be more worth it, but with the current configuration, I don't think it would help often enough to bother.

I was playing a few games recently, and I noticed someone who is each of our games would make a guess the very first move, then after losing 3 points for bad guess - would take their first shot there.

At first I thought maybe they did not know what they were doing - then after thinking about it (and noticing they have a higher rating then me so they must be doing something right), I started to think if this was a good strategy.

Of course if you have very first shot and shot a frog, all of a sudden you are 10 points behind (since you lose 5, and your opponent gains 5) - this way, they are only down 3 points to start.

Taking a look at about 25 of my past games, the closest score I could find was 5 points - with a few at 8 points, and most more then 10 points separate the 2 sides.

So obviously 3 points lose at the start would not do much damage - but I was wondering what others thought? The risk of hitting a frog on the first shot is slim: 5/139th chance. So what do others think of this strategy?

I still would appreciate if Coan submits the Co-Op variant of Frog Finder to Fencer...

:)

Here is the other interesting game, now that it is complete:

Frog Finder (grillyx vs. coan.net)

B2 is actually a 5 box! (If I had an extra move before losing, I would have taken it to show the "5", but had to guess quickly before losing)

5 box - 4 of my own, and 1 of my opponents hidden in there - making it really hard to find without giving up my own!

Now to find a "6 box"

Here is a game which has 4 of my opponents frogs in an area which I got a "4" box:

Frog Finder (kleineme vs. coan.net)

(and even though I found those early and thought I had a good chance of winning, I still lost.)

I have another interesting game, but it is still ongoing so I will post about that after it is complete.

WellyWales: yes, I hate it !!!
But, I won two of three (or four, not sure) games in which this happened ... it IS possible to win it

coan.net: I have already twice (!) seen a 4. But those were tree of my opponent + 2 of mine.

coan.net: I know, but don't you just hate it when you hit one on the first move. you feel like throwing the towel in

coan.net: I personally have never seen a "4". The highest # I have seen is a "3"

I agree that the random set up is much better.

WellyWales: Actually Frog Finder is the most balanced game on the site!

After over 11,000 games:

red 5938 (50.0 %)
blue 5921 (49.85 %)

To have a 17 game win/lose difference after so many games - WOW.

Maybe the first move by each opponent in frogs should be hidden, this way the second person does not have the advantage of shooting next to the first persons move .....

I've been thinking for awhile about if it would be a good or bad thing to set up your own frogs. (ignoring the fact that there has to be a check in place to make sure frogs aren't setup on same spot)

After thinking about it for awhile, I don't think it would be good for the game.

Why do I think that? Well if I could setup my own frogs, I would probable mostly set them up close to each other - that is for example, put 4 frogs in one of the corners - making it impossible to even see the 4th frog hidden in the corner - leaving someone to either guess blindly - or wait until he checks all other squares on the board.

It could also become more predictable. For example, if I know another player always sets up their battleboat boards - I can learn things like how they normally setup boards. Do they never have any touching each other. Do they never have any touching the side. Do they ... etc.. etc... So if a person always set's up their own frogs, it would also become predictable.

So even though occasionally the random computer will set up my frogs in a "bad" way, after thinking about it - I think it is still best to have the computer randomly place the frogs rather then try to let the users do it themselves.

QUESTION OF THE DAY: Have you seen a setup which would put 4 frogs touching 1 square? (that is to possible see a "4" on a square)? (or a 5 for that matter, even though that would be VERY rare.)