2009-05-05
Richard Malaschitz ★
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2009-05-05
Macbi
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Cool, thanks.
Will these be incorporated into tournaments?
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2009-05-05
wccanard
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4x4 is solved (i.e. 4x4 boxes). It’s an 8-8 tie with best play, although player 2 has to work hard to ensure the tie. Richard: does it bother you that you have implemented a solved game?
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2009-05-05
ypercube
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Yes, they are already available for User Tournaments.
I’ve made a 6x6 rated tournament. It starts at May 12th.
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2009-05-05
flipster
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Nice! Is 5x6, 5x7, 6x7 etc possible as well?
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2009-05-05
ypercube
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No. For the moment, I see only 4x4, 5x5, 6x6 and 7x7.
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2009-05-05
Macbi
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And symmetry makes odd by even games less fun for player two.
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2009-05-05
kpato
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in my thinking, there is no sense
to play dots in 5x6 5x7 .etc...
i mean..
how combinations we can find??
3-infinite.
its better to play in a few of tables (in my opinion)
just 5x5 6x6 7x7 its fine :)
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2009-05-05
kpato
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2009-05-05
flipster
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6x6 has the possibility of a tie and 7x7 is probably all about nim, but they’re worth a try I guess!
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2009-05-05
Macbi
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I believe wccanard has quite a bit of experience at 7x7.
I think large boards could be fun though, not having to think about “close” games would take out a lot of the stress.
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2009-05-06
wccanard
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I’ve played some 7x7 games before at Richard’s PBEM site. I played them like nim but I don’t know if that was the right thing to do: I didn’t play many games and my opponents weren’t in general that strong.
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2009-05-06
aldiris
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I’ll stay with 5x5 for now. I dislike 4x4 and 6x6 because of the possibility of a tie and 7x7 seems too large, it’ll take out some of the subtilities (is that a word? FF thinks it’s not :P) of the game. I like the stress Macbi talks about :P
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2009-05-06
aldiris
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btw: even though I won’t play the other variants, I still think it’s nice Richard added them! What next, hex-DnB? :P
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2009-05-06
MarleysGhost ★
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2009-05-06
MarleysGhost ★
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Oops. @aldiris: subtleties
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2009-05-06
aldiris
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2009-05-06
wccanard
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I’ll make a passing remark that when I’m telling my nerdy mathematical friends about dots and boxes, I’m always very careful to say “...and I've become quite good, over the last 2 years, at 5x5 dots and boxes”. I never claim to be good at the game in general. I have played 4x4 at yahoo games and there are plenty of people there who are much better than me. gej, for example, knows a lot about 4x4, and his teacher was a guy with the userid of wc (no relation to me!). There are also other players, who don’t play here because “it's too boring” (i.e. they want games to be over in minutes rather than weeks), but who regularly beat me at 4x4. Part of this is because I’m 40 years old now and am less sharp than I used to be, so can’t play face-to-face so well, but part of this is inexperience on my part: these people know 4x4 opening theory well (opening theory exists because the game has been completely solved) and I don’t know it at all. It’s possible for P2 to lose the game on move 1 if he/she doesn’t know what they’re doing, on a 4x4 board.
I agree with aldiris that 6x6 seems a bit ridiculous; you can tie and it takes longer than 5x5, which are two negative points. 5x5 is still not computer-solved and is in my mind the “best” size to play on. It will be solved one day though (perhaps within 5 years) and then perhaps 7x7 or maybe 7x5 will be the place to be.
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2009-05-06
Roel
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So, there is a lot try. 4x4 and 6x6 having the risk of ties is not that bad. An odd number of boxes implicits an unbalanced game.
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2009-05-06
michael
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I used to play DnB with wc on yahoo too. 4x4 almost always ends in a tie between 2 strong players. Playing that game on a turn based site will only result in even more tied games.
I’ve played quite a few 7x7’s on facebook, and they are ok. Never tried 6x6, but my guess is there won’t be that many ties there.
On yahoo I used to play alot of 11x11 games too, but that would take too long on a turn based site. Those were fun too though.
-michael
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2009-05-06
wccanard
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@michael: did you ever play a 7x7 game when the winner of the chain battle didn’t win the game?
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2009-05-06
flipster
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I think preemptively opening chains is gonna be a big part of this game
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2009-05-06
wccanard
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I see that user tournaments are piling up! If anyone wants to play 4x4 or 6x6, go and register for a user tournament!
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2009-05-06
michael
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@Wc a couple, not more than a handful though. But that’s probably because I haven’t played many 7x7’s against strong competition. But I’m sure you can imagine games with 5 or 6 quads and loops..always close calls.
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2009-05-07
wccanard
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Sure I can imagine these things, but in some sense “quads are commonplace” in high-level games of dots and boxes: a “natural” state for the board to be in is two chains and a quad, and P2 pressing for a 3rd chain so P1 has to sacrifice a box or two and then the game is going to be close. On a 7x7 board I wonder what the “natural” state for the board is. I feel that as P2 on a 5x5 board I can almost always force a quad; P1 hardly ever gets 4 chains and there’s space enough for 3, just not enough time to make 3 because a quad forms instead: P2 “forces P1 to make it”. I don’t know what the dynamics on a 7x7 board will be though.
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2012-02-11
Marius Halsor ★
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I have still no clue whatsoever about what the “natural” state of a 7x7 board will be, but this game was really fun and close. Look at this position: http://www.littlegolem.net/jsp/game/game.jsp?gid=1402891&nmove=58. Lots of quads and small chains. In fact, I think I had to give away control to win here (I did, anyway), which I think was quite interresting.
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2012-02-12
antony
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7x7 is weird indeed, the first 30 moves or so look completely random to me. But yes, you get to see stuff that rarely appears in 5x5 games: earmuffs, 8-chains, etc. There is at least one of my games where I’m about to start computing a huge endgame with a dozen of short chains and cycles.
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2012-02-13
Hettsea
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I used to play with gej in 4x4 yahoo dots and boxes. Fun times, but the game is solved and a bit too easy to calculate.
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2012-02-15
Christian K ★
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cool thread and cool games Marius :)
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2012-02-15
Carroll ★
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In the game you point to Marius, shouldn’t the outcome have been 25-24 for you as you are 1 point down on move 58 and with the same following order of opening the chains :
3 3 3 Q (5 Q Q) 6 8, in reverse order the value should be :
2 1 2 1 3 2 6 10 8 with the theorem 5+5=6 so 6+8=10.
So you should have gained 2... Did Nagy expect you to open wrong chain in move 62 when he played the domino move in the 3-chain?
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2012-02-16
FatPhil
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I wrote this ‘long chain battle’ analyser a long time ago, and RoRoRo’s been using it blindly ever since. I’d forgotten it understands earmuffs, I’m glad I don’t have to add that as a feature now, as I don’t understand the code at all any more!
$ ./lcb.pl c ‘C3 C3 C3 L4 C5-L4-L4 C6 C8’
C3 C3 C3 C5-L4-L4 C6 C8 L4 : C3=-2 all
Anyway, -2 says that if you’ve got those things untarnished in front of you, you should open the C3, the opponent will take all boxes, and it will cost you 2. So agreement with Carroll’s 2. (I then manually plucked the chains off one by one as it made its recommendations, and they pretty much all agree with the above except at the very end where it says:
$ ./lcb.pl -c -v ‘L4 C6 C8’
Opening C6 leaves [C8,L4]=-4 (control=-6 all=-2) so action=dx :>
Opening L4 leaves [C6,C8]=-10 (control=-6 all=6) so action=ddx =-|
C6 C8 L4 : C6=-6 dx
(here the two methods of control are dx = double-cross, ddx = double-double-cross, all means you take all and give up control) I don’t know if the above disagrees with Carroll’s analysis, as it seems Carrol wants to open the ‘Q’ (= ‘L4’), or do I misunderstand things.
It’s nice to have hairy examples to test RoRoRo’s endgame against. He keeps a “book” of known endings, and I notice that he has encountered earmuffs several times in the past.
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2012-02-16
Carroll ★
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@FatPhil your pearl script seems to have a problem when quads and chains are mixed:
for example [C8,L4] should be played with the quad first [L4,C8]=-4, then the value for opening C6 before [L4,C8] results in a domino move in C6 with result -6, or is it what you call "control=-6) ?
When there are no more 3-chains, a theorem states you should always open smallest loop before chains, with strict order for one loop L and one chain C as [L,C]=8-L-C whereas [C,L]=4-L-C.
In case of one loop L and two chains C and D, the Loop can either be played first or second : [L,C,D]=[L,C+D-4]=8-L-C-D [C,L,D]=[C,L+D-8]=12-L-C-D
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2012-02-16
Carroll ★
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Hum typo in last sentence :
In case of one loop L and two chains C and D, the Loop can either be played first or second : [L,C,D]=[L,C+D-4]=12-L-C-D [C,L,D]=[C,L+D-8]=12-L-C-D ; for example here L=4, C=6, D=8 value is 12-4-6-8=-6
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2012-02-16
Marius Halsor ★
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Yeah, I think the outcome should really have been 25-24 for me. Nagy probably made a mistake somewhere, but I think the interresting position was at move 58, where the endgame starts. It’s easy to prove that I have a win at that point, but it’s not really that easy to determine HOW to win. Also, winning with only one point, and having to give away control in order to do so, fascinated me. :-)
Not sure I understand earmuffs either, but isn’t that the equivalent of a 3-chain ending in a quad? It would seems so to me.
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2012-02-16
Carroll ★
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Yes for earmuffs, the way I see it is that you can not play one of the ears first:
say it is [C,L1,L2] where L are the ears, if you play in this order the value is 8-L1-L2 for the ears and so 12-C-L1-L2 for the earmuff.
If you play ear L1 first you basically transform it into a Chain+L2 where the chain has length C+L1: [C+L1,L2]=4-C-L1-L2 which is 8 less than playing the central chain first.
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2012-02-16
FatPhil
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@Carroll, it looks like we, and the script, agree. The ‘=-|’ smiley at the end of the ‘Opening L4’ line means “this is the same as the previous best”, and sure enough, if your opponent keeps control with a double-double-cross, he’ll end up 6 ahead. (Hence the “control=-6”). So it doesn’t matter which of the two are opened. I could modify the script so that it prefers to open loops than chains if they’re both equal, but I don’t see the need to do that if in reality they are both equal.
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2012-07-25
halladba ★
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@wccanard, and now 5x5 is solved! A paper about this result has just been presented at the AAAI conference on Artificial Intelligence. I cannot see a pdf version the article available online yet, but one can probably get one by emailing one of the authors.
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2012-07-25
FairyTail
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Even though it is quiet a big accomplishment to solve 5x5(boxes, aka, 6x6 dots), I absolutely hate the idea of its pdf going public.
Now the games will be predetermined with just the 1st 5-10 moves and any novice player will be able to play as good as those playing it for 5 years of experience or so. I hope that solving D&B stops at 5x5 (assuming it has been solved), otherwise, i would have to resort to playing larger sized board just to keep it fun to play I also used to play (and sometimes do play) at yahoo dots on 5x5 dots which always ended with a tie against a good player. Ever since it has been solved which lead to a tie in every game, i got bored of playing the same moves and started 10x10 dots. If the same is going to happen to 6x6 dots, i guess that will be the end of dots for me and maybe for couple other players who feel the same as well.
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2012-07-25
sghsal
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Yeah, I agree. But as far as I understood they only have a weak solution meaning a proof that either of the two players does have a winning strategy. Apparently these guys solved 4x5 as well, just google it. The pdf itself does not contain any information about the strategy and the moves.
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2012-07-25
FairyTail
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oh ok! if its just that which player has the winning strategy, then thats alright. i personally thought it was giving away the game as in 4x4 boxes (it had all possible moves for a tie outcome) that was a misunderstanding from my side :)
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2012-07-25
sghsal
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No no, I am not sure, just my personal believe! . I hope I am right though...
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2012-07-26
halladba ★
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If I understood correctly, they’re computing not only who’s winning but also the score différence in the optimal case. I haven’t read the pdf, but I would be surprised if it included any specific useful information on the principal variation. As for 4x5, if I remember correctly, I was told that at the very beginning, all moves were optimal. Things start getting interesting a bit after. If the pdf doesn’t leak signicant information on the best strategy, I really do hope that it goes public, and I don’t think it can hurt the game community. Additionally, I wish the optimal strategies and the proof trees were avaible upon request for the sake of potential independant (scientific) verification, but not given away to any random cheater.
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