I am currently implementing Dots-and-Boxes on BoardGameArena.

No ETA yet, but I just could complete a test game without server errors, so it should not take overlong to be at least in Alpha and having it testable (a notice will follow…).

Question: Which board sizes do you feel important to support?

Right now I am tentatively supporting 5x5, 5x7 and 7x7 box sizes (I am speaking here of 5 boxes x 5 boxes and sim., not of 5 dots x 5 dots).

I would like to support only sizes with an odd number of boxes (to rule out any possibility of draw) and this would exclude any board size where one of the two dimensions is even (4x4 and so on).

Adding more sizes after the fact seems not complex, so we could also grow by steps.

Comments and suggestions are welcome. Thanks!

Hey!
That's good news, thanks!
I guess 5x5 is currently the best size but personally, I'd like to play on a 5x7 board as well and see how complex that would be :P
7x7 doesn't look that fun since I find it incomprehensible and I can't really come up with the right move

That's awesome and makes me very happy, thank you so much.

5x5 is the most important size and I think it's mostly sufficient for human play. It's very complex and I'm still learning new things about the early stages of the game. I think that on bigger sizes there would be a very long phase at the beginning that will feel extremely arbitrary. Even on 5x5 it's only the current best of the best who understand the first 5 moves or so.

That being said it's also true that 5x5 is a solved size that is confirmed to be a first player win and that some people without a doubt will want to move to a bigger size. I think 5x7 is a great addition that is sufficiently big to fullfill all human needs. 7x7 will feel extremely random for a huge chunk of the beginning.

I think the pie rule could work very well for Dots and Boxes: The first player gets to play up to 5 or so lines and then the second player can choose between switching colors and playing the next move.

Thanks for all the comments!

If neither Lazy-Bear not -syLph-, with all their experience, seem particularly interested in 7x7 I can easily drop it; thinking again, it might even be counterproductive, at least for a while, attracting beginners and confusing them utterly! (there has to be a reason if, here on LG, 5x5 games are 10 times all the other sizes together!)

Nobody is proposing smaller sizes, like for instance 3x5 or even 3x3; they would not be a challenge (not even interesting!) for the experienced player of course, but might be a 'soft' entry for beginner? Also taking into account that BGA might expose the game to a wider audience?

@-syLph-: I cannot grasp what the pie rule would mean in the DnB case. The game is totally 'isotrope' (there is a more specific term, but I forgot it!) with regard to the players, at least until some boxes have been claimed (which is unlikely to happen in the game opening), so it seems to me that exchanging the colours makes no difference and would simply mean a purely visual difference in the box colours once boxes begin to be claimed by either player later in the game. Am I missing something?

Thanks again!

I'm not sure if there is any board size that's particularly good at teaching new players the basics. For new players this game feels essentially completely random. Knowledge of two certain things is what turns it from a game that feels completely random to a strategic game.

The first is the “all but 2”-trick and the second is the chain-rule

Let me try to explain both of those using two positions on the 3x3 board:

This (left) is a position with 1 chain that has 14 lines played. Because of that it's the turn of player 1 who can play anywhere into the long chain (middle). And then player 2 takes all boxes of that chain (right).

In this position on the other hand there is two chains and only 13 lines played in total (1st position).

Then its the turn of player 2 and they can play into either of the two chains, but will likely pick the shorter one (2nd position).

Player 1 can now take that box at the bottom (3rd position) and its their move again.

Now this is where the magic happens: Instead of taking two more boxes player 1 instead plays at the top. This is the “all but 2”-trick. (4th position)

Player 2 now gets two boxes but is forced to play into the chain of length 6. (5th position)

And player 1 takes the remaining 6 boxes, thereby winning the game. (6th position)

So there is two things to take away from that. Firstly, there is that “all but 2”-trick that let's you gift two boxes to your opponent in exchange for forcing them to play into the next chain. This basically means that once your opponent has played into one chain you can get all except two boxes of every remaining chain. The very last chain you can even take completely.

Then secondly, the thing that ultimately decides the winner is the amount of chains at the end. The top picture has that position with one chain and that causes player 2 to get all of the boxes, whereas the bottom picture starts with a position that has two chains and as a result of that it's player 1 who wins. That's what the chain rule is about: One player wants an even amount of chains, while the other wants an odd number of chains.

Once you know the chain-rule the game turns from a game where you just play moves randomly into one where you try to form a specific amount of chains and then it's about dividing the board into a desirable amount of areas and do certain types of shaping.

Anyway, back to board sizes.

I think if there is a board size that does a better job at teaching chain-rule and “all but 2”-trick than 5x5, then that would be a better board size for beginners than 5x5.

First there is 3x3. This board is actually so small that it's quite difficult to squeeze any number of chains other than 1 onto the board. So the vast majority of the time I would expect new players to just build one chain with completely random moves and then the second player just wins by taking that resulting chain at the end without understanding why they actually won. I also just generally don't like the idea of giving two competing minds a board where one player just wins 6-3 with optimal play from both sides. So I'm not a fan of 3x3.

3x5 on the other hand I think may be good. This one I would consider an actual game. My guess would be that with optimal play it's a 7-8 victory for player 2, but it's not trivial and I'm not sure I'm even correct. For new players I think this is actually quite a big size already and I would assume that most of the time in a game between new players it would result in 2 chains, which, contrary to my own assessment of who should win, would result in a player 1 victory, and also does provide an opportunity for the “all but 2”-trick to be used. In order for someone to master playing this size as player 2 they would have to learn important concepts like sacrificing in order to win with the chain rule.

I think overall 3x5 does make for a good size for beginners, I don't know if it's better than to just let people play on 5x5 from the get-go though.

I think much more valuable than just providing a beginner friendly size would be to actually provide some kind of tutorial that explains the “all but 2”-trick and chain rule. I think while people may discover the “all but 2”-trick on their own it's going to be very difficult for people to discover the chain-rule. In my opinion these 2 things should be explained to people somewhere on the site.

As for the pie rule:

With optimal play the first player wins 13-12 on 5x5 and I would say player 1 actually has quite a relevant advantage. If I played a bunch of games with myself then depending on the time settings I'd assume that about 70% of the games would be won by the first player in a turn-based scenario and like 55% in real-time or something like that. I would never resign immediately because I have to play second, but I would say it's a quite relevant advantage to go first, especially in turn-based play.

The pie rule would allow the construction of early positions that are much more favorable for player 2 than the empty board. I'm pretty sure you can construct a position that wins for player 2 with 5 lines, I'm not sure about 3. But yeah, the idea would be to get rid of the first player advantage.

Maybe I shouldn't have said switch colors and instead said something like “choose which player makes the next move”. It's not about the colors, it's about the move order.

Thanks for your suggestions, -syLph-.

Tutorial: agreed. However, the first step is to provide the game itself. Then it will be possible to provide links to existing resources, maybe the 'classic' by Ilan Vardi (if still available somewhere) and other which can be suggested: BGA game pages have a link area. I am not good in writing tutorial (assuming I know enough of the game, which is very dubious!), but perhaps someone else can step in (hint, hint…).

'Pie' rule: sorry but I still do not understand. Even “choosing which player makes the next move” seems to me off point. The player who has to make this choice in practice has to decide between playing or not (passing) and it can hardly be an advantage to pass, so the choice will almost always be to go on without any change. This mostly depends from the fact that the drawn strokes do not belong to a player (like Hex stones do, for example) but are simply 'there'.

Sizes: after this discussion, I am speculating of starting with 3x5, 5x5, 5x7. Then, as I said, adding more sizes, if deemed suitable, will not be a big deal.

Because of the chain rule the players have different goals. On all of the board sizes where both dimensions are odd (which includes all of 3x5, 5x5, 5x7) player 1 wants an even number of chains, while player 2 wants an odd number. The pie rule would let you pick whether you want to aim for an even or an odd number of chains.

On the 5x5 board player 1 wins with optimal play and that's because 2 chains is the most natural amount of chains to form on this size. The board is too big for player 2 to just aim for 1 chain, but it's also not big enough to easily squeeze in 3 chains.

So passing in order to become the person who needs 2 chains, makes a lot of sense.

But placing up to 5 lines at the beginning gives you a lot of options to construct a position where it's much easier to aim for 1 or 3 chains.

This for example could be a construction that makes it easier to aim for one chain:

Whereas the following could be a construction that makes it easier to aim for 3 chains:

These are very different positions and I could come up with many more 5-move-constructions that are very different from these 2. Speaking as someone who is very good at 5x5, I think that there is a bit of a redundancy problem, in that many games are very similar to each other. But I think with the pie rule people could come up with an almost endless amount of interesting early-stage positions that are all fairly different from each other and I think that makes it both fair and very rich in variety.

Ok, I am convinced. I'll try to implement it.

In the BGA framework, it is important to foresee since the beginning all the choices / variabilities the players may / must / will have, as adding more of them after the fact often breaks already running games (and/or compromise the replays of older games) and players are not fond of this! So:

1) I gather that the player to whom to give this choice may change with different sizes. In sizes with an odd number of boxes (both dimensions odd) it has to be player 2 (choice given at an even move count), while for sizes with an even number of boxes (at least one of the dimensions even) it will be player 1 in need of a bonus (none of them exist now, but they may be added in the future). Correct?

2) Is it reasonable to fix the moment of the choice to one particular move for all the odd sizes and to one for all the even sizes, or it is better to have a different choice point for each size? (the specific point(s) may be adjusted later)

3) May make sense to allow for a range of moves: for example, in 5x5 player 2 may skip his move only once (of course) between move 3 and 7? (again, the specific numbers may be easily adjusted in Alpha or Beta or even in production, the important point is to have the 'code slots' for them ready).

4) In general it is better to limit the game setup choices to the really indispensable ones, so I would prefer not to have this kind of pie rule as a game option at start-up (pie rule yes / no; like the selection among the sizes is) and have it available to the relevant player in any case. But if this may result hard to understand to not very expert players (as it has been for me), it is possible to have it as an option. Ideas?

A part for this pie rule, the game is completely and correctly running and I could ask it to be moved in Alpha testing, but it is better to take another 2 - 4 days and implement the pie rule before proceeding. I may speculate to have it on Alpha somewhen next week.

Thanks for all the thought given to this and for the contributions!!

I think the best implementation would be one where in turn 1 player 1 gets to play 1, 2, 3, 4 or 5 moves all at once and then in player 2's first turn they make the decision to either swap or just play the next move. This would work for any size.

What you seem to have in mind is to just let the first turns play out normally but then provide the swap choice to one of the players. This would be a bit difficult to do correctly. You would have to give the choice to swap to the player who loses with optimal play. In 5x5 that is player 2, in 3x5 it is player 1, in 5x7 it is unknown. On any map that is a draw with optimal play, it wouldn't matter who gets the choice (arguably, with a draw you may also not need the pie rule in the first place).

I actually think 5x5 may be the only size for now where the pie rule would be a major improvement. In theory one player has an advantage on 5x7 too, since it can't be a draw, but the board size is completely undiscovered as of yet. The pie rule also makes sense on 3x5, but if that's supposed to be the beginner friendly map then I think it makes sense to not add it there, in order to avoid potential confusion about it. For 5x5 I would make the pie rule mandatory, especially in rated and tournament games.

Forgot to mention in my previous post: I'd be happy and honored to help wherever I can (for example with the tutorial).

I thought to have understood, but I am no longer sure!

“What you seem to have in mind is to just let the first turns play out normally but then provide the swap choice to one of the players.”

Yes, I do and I have a basically working code for this already. If I understand correctly, what you propose is a play flow like this:

1. Player 1 plays a certain number of moves in a row;
2. player 2 may choose whether to skip his turn or play one 'standard' move;
3. after this, players alternate as usual (from player 1 again).

Correct? I have two kinds of doubts about this:

1) Isn't allowing player 1 to play several moves in a row going to give him an even greater advantage?

2) This seems to me quite a big change from the kind of DnB implemented everywhere else: if not a different game, at least a distinct variety of it. It also seems to me such a variant may be hard to understand (and even more to master) for a sizeable portions of players and resulting unappealing to less-than-top-grade players.

So, my idea at the moment is to implement 4 variants of sizes/rules:

• 3 boxes x 5 boxes, “standard” rules

• 5 boxes x 5 boxes, “standard” rules

• 5 boxes x 5 boxes, with this pie rule

• 5 boxes x 7 boxes, “standard” rules

  Now, back to the pie rules details:

Is the number of moves allowed to player 1 in the first turn fixed (say 5) or he may choose how many moves to play from a minimum (say 1) to a maximum (say 5)?

Once this detail is cleared I can adjust the current code and move to Alpha; numbers can be tuned later, but it is better to fix the mechanics as soon as possible.

Last but no least, thanks for you offer to help with the documentation!

If I understand correctly, what you propose is a play flow like this:

Player 1 plays a certain number of moves in a row;

player 2 may choose whether to skip his turn or play one 'standard' move;

after this, players alternate as usual (from player 1 again).

Correct?

Yes, you got it! “Skip his turn” may not be the best way to phrase it though. Player 1 could take a box in his first turn. That taken box could have either of the 2 colors depending on how player 1 takes that box with his first turn. Lets say player 1 chooses to do 5 moves in his first turn, if the third move completes a box that box will be red, if the fourth move completes the box instead then that box will be blue. Player 2 could pick which of the two players he wants to be.

By the way, the same kind of pie rule is used on littlegolem in Gomoku-Pro: https://littlegolem.net/jsp/game/game.jsp?gid=2159009&nmove=1

1) Isn't allowing player 1 to play several moves in a row going to give him an even greater advantage?

In theory player 2 would be winning and have the advantage since they get to choose which side to play. But I do think there is something appealing to being the one to design the initial position, I'd certainly enjoy it. Overall though I think it's fair. One player gets to design the first position, but in exchange the other player gets to pick who plays which side.

2) This seems to me quite a big change from the kind of DnB implemented everywhere else: if not a different game, at least a distinct variety of it. It also seems to me such a variant may be hard to understand (and even more to master) for a sizeable portions of players and resulting unappealing to less-than-top-grade players.

It would mostly be appealing to competetive players who have really figured the 5x5 game out and want to have a game as fair as possible. I'm not sure how confusing it would be to less experienced players. There is a very wide range of people who have fully understood the chain rule, but are nowhere close to being a top player; I think these players would understand what effect the turn-skip has and wouldn't get confused by it. But those who have only just begun to grasp the chain rule may get confused by the turn skip.

So, my idea at the moment is to implement 4 variants of sizes/rules: 3 boxes x 5 boxes, “standard” rules; 5 boxes x 5 boxes, “standard” rules; 5 boxes x 5 boxes, with this pie rule; 5 boxes x 7 boxes, “standard” rules

I think that's perfect.

Is the number of moves allowed to player 1 in the first turn fixed (say 5) or he may choose how many moves to play from a minimum (say 1) to a maximum (say 5)?

I would let player 1 play any number of moves from 1 to 5. I think that gives the players the most freedom to choose what kind of game they want to play. It kind of gives them a slider on how impactful they want the pie rule to be. If player 1 plays only 1 or 2 moves, the game would be fairly close to the game without pie rule, with 4 or 5 moves it would be pretty different, and with 3 moves it's in the middle.

“if the third move completes a box that box will be red, if the fourth move completes the box instead then that box will be blue”

Oops, I said this. Of course there is no way to complete a box within 3 turns, my bad. It could be done in the 4th turn which would make the box blue or it could be done in the fifth turn which would make the box red (if default colors are red for player 1 and blue for player 2).

Oh, well, things are getting more and more complex…

1. Why the box which player 1 might complete may be of a different colour depending on when it is done? The usual rule is that the colour of a box depends on who claims it, not on when it is claimed.
2. Who is getting the extra move that claiming a box gives?
3. If a box is claimed on the first initial run and it is of the player 2 colour, why should player 2 give it up? This seems more an anti-pie rule… ;)
4. If no box is claimed in the first run, which would be the “pie slices” for player 2 to choose between?

Things are getting complex, unexplored and likely to require an extensive testing (and maybe fine tuning).

I am starting to believe that it is perhaps cleaner and quicker to separate the project into two, releasing now a “standard” version with the well-known rules and later another version, perhaps even as a different game (“Dots, boxes and pies”? ;) ) with the improvements you suggest.

It's actually not that complex.

Let's look at it like this: the game has 2 colors, let's say red for the player who goes first, and blue for the player who goes second.

Now let's imagine 2 kids, Bob and Emma, deciding to play the game. First they decide to play a standard game without the pie rule. Bob wants to go first so he becomes red and Emma becomes blue. Their color is set from the start to the end of the game.

Next they decide to play a game with the pie rule. Bob goes first again and decides to play all 5 moves that the pie rule lets him play, for these 5 moves he plays for both colors:

Move 1: For this move he is red and he plays reds move

Move 2: For this move he is blue and he plays blues move

Move 3: For this move he is red and he plays reds move

Move 4: For this move he is blue and he draws a line that completes a box, this box will be blue, because move 4 is the move of the blue player. Because a box was taken move 4 is still ongoing. He draws another line and finishes blues move.

Move 5: For this move he is red and he plays reds move. This concludes Bobs turn 1.

Now Emma gets to pick which color, red or blue, she wants to play. She wants to have the box so she takes blue. Bob is now red and Emma is now blue for the rest of the game.

Move 6 begins and as always move 6 is blues turn. Emma plays move 6, Bob plays move 7 etc., they alternate for the rest of the game.

If a box is claimed on the first initial run and it is of the player 2 colour, why should player 2 give it up? This seems more an anti-pie rule… ;)

Player 2 should definitely always pick the color who owns the box. Taking a box with the first 5 moves would not be smart.

If no box is claimed in the first run, which would be the “pie slices” for player 2 to choose between?

You pick between red who needs an even number of chains, or blue who needs an odd number of chains. To make this decision you need to look at the position constructed by player 1 and form an opinion on whether it is easier to aim for an even or odd number of chains.

I am starting to believe that it is perhaps cleaner and quicker to separate the project into two, releasing now a “standard” version with the well-known rules and later another version, perhaps even as a different game (“Dots, boxes and pies”? ;) ) with the improvements you suggest.

I wouldn't seperate them into 2 different games or projects, I think it really is still the same game. But I think it's fine to go ahead and only release the standard version of the game for now. No need to rush this pie rule thing imo, I think it's wise to take some further time to think things through and perhaps get some more opinions on it, to form a clear vision of what it is you are implementing, why it is that you are implementing it that way and to gain confidence that it is the best way to implement it.

Let me see if I got it. The following is an attempt to formalise things, in order to explicit all assumptions, NOT intended as an explanation of the rule to learning peoples!

First assumption: let us separate the concept of acting player (the player who is actually doing things), of acting colour (the player colour which is assumed to do things) and of wearing a colour (which colour a player is at any moment). The start of a game under the pie rule may be described with a pseudo-code like this:

acting_colour = RED
acting_player = player1

/* setup state begins */
/* the acting player draws a box side under the acting colour: */
acting_player.draws_boxside(acting_colour)
flip(acting_colour)            /* but DON'T flip acting player! */
for (4 times)                  /* at most for other 4 times */
    if (acting_player.leave_setup() ) /* if player 1 chooses to leave setup... */
        goto PIE                      /* ...go to pie rule; otherwise: */
    acting_player.draws_boxside(acting_colour)
    flip(acting_colour)        /* but DON'T flip acting player! */
    /* differently from standard playing, completing a box does not */
    /* keep the same acting colour for another move */

/* setup state is over; pie rule begins */
PIE:
player2.wears(choose_colour()) /* player 2 chooses which colour he wants to wear */
player1.wears(unchosen_colour) /* player 1 wears the 'other' colour */
acting_player <= acting_colour /* the acting player is the one wearing the active colour */

/* pie rule is over; 'standard' game playing goes on from here, */
/* where each player always acts under the colour he is wearing */

Hoping this is making any sense to anybody, this is what an attempt at defining what is going on. Do you think I got it correctly?

That looks mostly correct to me. The only thing I had differently in mind is the part with taking a box

You wrote this:

/* differently from standard playing, completing a box does not */
/* keep the same acting colour for another move */

I was thinking within the for-loop ```
acting_player.draws_boxside(acting_colour)

so something like this:

    for (4 times)                 

        if (acting_player.leave_setup() ) 

            goto PIE                      

        box_completed = acting_player.draws_boxside(acting_colour) /* returns true if the boxside completed a box, false if it didn't */

        while(box_completed)

            box_completed = acting_player.draws_boxside(acting_colour)

        flip(acting_colour) 

this would be keeping the acting color until a line is drawn that doesn't complete a box, it would also not advance the for-loop to the next iteration if a box is completed

oh my god, what is this formatting. it does not look the way the preview looked

I note that the pseudo-code doesn't quite match.

Most importantly, if a box is completed, the acting_colour should not change.

Less importantly, if a box is completed, the acting player gets to make an additional move (i.e. as many as 6 total).

“I was thinking within the for-loop actingplayer.drawsboxside(actingcolour) is executed until a line is drawn that doesn't complete a box”

something like this is what it was supposed to say, the last part was swallowed by formatting.

Thanks for the comments. So, in the (actually rare) event a box is completed during the setup state, the mechanism should be the same as during the standard game play. I got the impression it was not, whence my sample pseudo-code; I'll adjust it.

@William Fraser: well, the pseudo-code does match; the loop

while(box_completed)
    box_completed = acting_player.draws_boxside(acting_colour)

is repeated as long as the drawing completes a box (ok, with the current parameters it can't happen more that once in the setup, but it makes sense to have a loop, in case the parameters are modified), changing neither the acting player nor the acting colour (flipped in the following statement after the while completes); it also gives more side(s) to draw as the outer for loop does not tick while the inner while loop goes on.

So, I think to have all the needed info to arrive at an implementation. I also think there be a way in the BGA framework to publish a standard version without the pie rule while having an option with the pie rule debuggable and testable in the dev/test area; this would make simpler to go by steps.

The Alpha version of my DnB implementation on BGA is practically ready, including the pie rule as described above. I expect it to be accessible to alpha testers early next week.

I am not familiar yet with these bureaucratic aspects, but I assume (presume?) to be able as author to invite as testers, for this game only, specific BGA users who do not qualify as testers in general (pre-requisites are rather stringent). So, if anyone is interested, please let me know.

I would be interested in testing it on BGA. My username over there is Bressette

Hi There I Think None.
I'm looking for something new Idea for the dots & Boxes Game My idea is to develop this game in 2v2 For the first time, I made this Suggestion to Plato team (for Plato App) Aslo
Two player have to Make The Chain even Number And Two Players Should Make chains To Odd number
Whats You Think About This?

@Eykca: as soon as it will be on line, I'll try to have you on board!

@Amir_EES: interesting suggestion. If I understand correctly, you think about 2 teams (each of 2 player laying cooperatively), right? In this case, I do not think it necessary to rephrase the victory condition: the team which collect the more boxes wins (then this indirectly leads to the parity of the number of box chains…). Still this would be rather different than the current implementation: I would prefer to have it as solidly implemented as possible before adding new options… but I'll keep it in mind, thanks!

Any updates on the project?

@Eykca: “Any updates on the project?”

Yes and no. The project has been pushed to Alpha (and it already has some bug reports from testers) but, for technical reasons, before pushing it, the staff person in charge has to clone it into a different project and right now I have no access to it (I cannot see nor do anything). I expect this to be fixed soonish, but I have no ETA, as the stuff seems to be managed on a “when possible” basis…

At last, technicalities are over and I have full access to the BGA Alpha version of Dots-and-Boxes I developed.

It implements 3 sizes (3x5, 5x5, 5x7) and, on 5x5, also the pie rule as devised above by syLph.

If somebody has a BGA account and would like to give it a try, just let me know the account name and I can invite as tester (for Dots-and-Boxes only) anyone who does not qualify globally as a tester/reviewer.

In chess, there is a term zugzwang (pronounced tsoogsvangh) which refers to a position where the obligation to move confers a disadvantage. syLph, if I understand you correctly, a single line added to the board is not nearly enough to produce such a position. The idea for the first player is to add enough lines to produce a position where it is not clear whether it is zugzwang or not, and it might be reasonable for the second player to pass or not to pass. Did I get that right?

Essentially correct. After any single move, the position is always, in fact, zugzwang. As a result, with any TWO lines on the board, the position is known to be a win for player 1 – i.e. not zugzwang. (Not saying that any mere human knows how to win all of these positions, but with no pie rule, player 1 has a strong advantage.)

(Wrote this before I saw The_Shark reply, bit redundant now lel)

I think you got the idea right, David.

If I wanna be really nitpicky I would say (with my limited understanding of chess which may very well be wrong) that being in a position of zugzwang in which all moves make your position worse doesn't necessarily mean that you are losing. I think you could have a chess position in which you are winning even though all of your move-options worsen your position. Allowing the construction of such a position would not be the goal of this pie rule, what I'm looking for are positions in which the decision to pass or not to pass truly makes the difference between winning and losing. But I believe this was also your understanding of it.

5x5 dots and boxes has been strongly solved by William Fraser and he has revealed that player 1 only has winning moves in their first turn. Accordingly player 2 only has losing moves with the next turn. So yes, you do need at the very least 3 lines to construct a position in which player 2 needs to even consider whether they wanna pass or not. I think it's reasonable to speculate that even with 3 lines a position that loses for player 1 can't be constructed (aside from positions in which the third line sacrifices a box), as the answer to this question hasn't been revealed by William Fraser as far as I know. It is trivial to construct a losing position with 5 lines.

I know I am late but the topic was interesting.
I love the idea of introducing dnb to a new community and attracting new audience and I think introducing the chain rule in the tutorial
(in a clear and simple way) is so important if we want to hook new players to the game.

About the whole pie rule thing, it definitely sounds exciting for a game between 2 experts. But I don't think implementing it in a site where everyone is new to the game is a very good idea.

I think the phase of exploring the chain rule and how it works in an actual game is one of the most interesting phases of the game, so adding a rule that's suited for people with so much experience will just complicate the process for them.

As for the size of the board I honestly don't think any board other than 5x5 would give the same rich and beautiful experience to a new player.

This is just my opinion and I can be very wrong.