1st or second player adv?

Hey.

Do you think the 1st or 2nd player has the advantage in D&B? Also, do you think it depends on the board size?

On 3x3 i'm pretty sure second player has the advantage. Also on 5x5 I feel it is easier to play 2nd. 3 is a good number of chains :) What do you think? Are there any known results?

Off course it depends on the board size.

1x1 is a 2nd player win.

1x2 is a tie.

1x3 is (I guess someone has calculated that).

As for who has the advantage at 5x5, no idea.

Well, we have yet to find a board where first player has the advantage.

Does it matter if we limit ourselves to quadratic boards?

Thnikkaman: you should read Winning Ways -- this contains some small board analysis. Here are some results for a square board.

The 1x1 game is a 1-0 win for player 2.

The 2x2 game is a 3-1 win for player 1 with best play. Because of this, to maximise fun, you should decree that in a 2x2 game if it ends 2-2 then player two is the winner: "two twos is a win for two", as Conway puts it in Winning Ways.

3x3 is a win for the second player and again this is in Winning Ways. The winning strategy is in Winning Ways in fact. Here's something that I think is not in Winning Ways though: with best play the second player wins 6-3, so again you can make it more fun on a 3x3 board by saying that the first player wins if he gets 4 boxes (equivalently, consider the game as having two extra boxes, both awarded to player 1 at the start).

4x4 is a tie with best play, but player 2 has to work very hard. This is not in Winning Ways, and was proved by computer -- but some humans can play 4x4 essentially perfectly. There are various openings in which player 2's first couple of moves are basically forced, so if P2 doesn't know their openings and they're playing someone who does, they're dead.

5x5: this is still an open question, although in a few years' time the answer will probably be known. My firm belief is that 5x5 is a 13-12 win to player 1 with best play. Time and again one sees championships decided because one lucky player got to be player 1 against the other strong players.

Hope this helps!

wccanard, can you fill missing proven results? Perhaps you can put this in your wetpaint site.

<br/><font face="courier"><br/><br/>     1     2     3     4     5<br/>  +-----+-----+-----+-----+-----+<br/>  |     |     |     |     |     |<br/>1 | -1  |  0  |     |     |     |<br/>  |     |     |     |     |     |<br/>  +-----+-----+-----+-----+-----+<br/>  |     |     |     |     |     |<br/>2 |     | +2  |     |     |     |<br/>  |     |     |     |     |     |<br/>  +-----+-----+-----+-----+-----+<br/>  |     |     |     |     |     |<br/>3 |     |     | -3  |     |     |<br/>  |     |     |     |     |     |<br/>  +-----+-----+-----+-----+-----+<br/>  |     |     |     |     |     |<br/>4 |     |     |     |  0  |     |<br/>  |     |     |     |     |     |<br/>  +-----+-----+-----+-----+-----+<br/>  |     |     |     |     |     |<br/>5 |     |     |     |     |     |<br/>  |     |     |     |     |     |<br/>  +-----+-----+-----+-----+-----+
<br/></font>
<br/>

Anything in the top 4x4 square can easily be answered by computer (given time). I don't have time to do the calculations myself though -- I have a proper job now, and have to get the kids up in 4 minutes :-) I only answered the question because the dots and boxes forum is usually so quiet and Thnikkaman seemed to be asking interesting questions where I felt my contribution might be of some interest.

Well for bovious reason the matrix would be symmetric.

1x3 should be possible to figure out too without too much of a headache :)

2x3 >=0 clearly

hmm, not so clearly...

Modulo any slips...(and I could have made slips; I used some computer-analysis but then had to do some translating into human-readable answers)

3x4 is a tie with best play; P1 has to play one of the three lines which together divide the board into two 3x2's, or else he loses 7-5.

3x3 is 6-3 to P2 regardless of P1's opening move.

3x2 is 4-2 to P2 regardless of P1's opening move. Boards this small are not hard to analyse by hand. P2 either makes 1 chain and wins because he's won the chain battle, or there are 0 chains and P2 wins because he wins the short chain battle anyway. There's no room for 2 chains.

3x1 is 2-1 to P2 for much the same reason.

4x2 is 5-3 to P1: P1 makes a chain (or at least makes sure there aren't 2 chains).

4x1 is a tie: P1 must divide the board into two 2x1's or else he's dead, because P2 wins with a chain and almost always wins with 0 chains.

5x1 is 3-2 to P2 wherever P1 moves.

I agree that 5x5 is probably a first player win. The Shark usually knows that it is ahead before it makes is second move.

While on the other hand, it is often behind even when it has made 5-6 moves if it goes second.

That is very impressive :)

Yoyoyoyo, chickenlord here ;DDD

This is a VERY interesting topic and I guess the best player here should definitely say a thing or two <(^_^)>. Both sides have their very own advantages and ways to approach the victory, let me explain how the LORD owns XD.

The strongest weapon of second player is playing symmetry. Like in this game (http://www.littlegolem.net/jsp/game/game.jsp?gid=1649329&nmove=8) my poor victim stands no chance XD. The good thing about this is I can bash my opponents without thinking :P. ABSOLUTE REQUIREMENT though for symmetry to work perfectly is a chain through the middle which might appear like quite the burden BUT UNFORTUNATELY there is no way for the first player to prevent that chain without sacrificing a box TOO BAD HAHAHA. XD And does not rly help much, see http://www.littlegolem.net/jsp/game/game.jsp?gid=1649909&nmove=9. Anyhow this is a truly devastating technique to use not to mention the psychological impact on my opponent SURPRISE ANGER DESPAIR! XD

Another KILLER TECHNIQUE for second player is to spam new regions everywhere on the board. If done correctly your opponent will not be able to catch up AT ALL!!! Here is a awesome example (http://www.trmph.com/dnb/board#5,h7e8d9d5c4g4) where the first player uses the third and fifth move to prevent a seperate corner but right after another region is created and it looks SUPER DIFFICULT XD. Y U SO EVIL CHICKENLORD ᕙ(⇀‸↼‶)ᕗ

Also if both me and my opponent do not play the game for some reason it's superior being second as my opponent will time out first! Nicely demonstrated here: http://www.littlegolem.net/jsp/game/game.jsp?gid=1652115. B-)

So far so boss! Time to investigate the BLOODY RED COLOURED FIRST PLAYER ლ(ಠ_ಠლ)ლ(ಠ_ಠლ)ლ(ಠ_ಠლ) As first player it's YOU to decide the course of the game. Occupy the IMPORTANT centre before your opponent does and KILL HIM: http://www.littlegolem.net/jsp/game/game.jsp?gid=1647107&nmove=1

As for SUPER SKILLS I only recommend my self designed SUPER SHAPE the CHICKENWING. As depicted here (http://s22.postimg.org/ireanl7q9/chickenwing.png) it is a corner move with an effect similar to spreading wings like a real CHICKENLORD HAHA. Spreading it's wing into the corner threats to connect to the bottom for making it hard to build a third chain but is at the same time so far into the corner that a second one is still possible!!! (⌐■_■)