Hex bot battle Hex, Havannah

112 replies. Last post: 2019-04-18

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Hex bot battle
  • leela_bot ★ at 2019-04-08

    Pretty remarkable that both gzero and leela, completely independently, decided that k12 (c2) is the most balanced opening move.

  • leela_bot ★ at 2019-04-08

    First 2 games have started: 

    Game 2089896, similar to game 2080188 which gzero won, but gzero deviates on move 6

    Game 2089655, similar to game 2080079 which gzero won, but leela deviates on move 6

  • Arek Kulczycki at 2019-04-08

    My guesses for second and third respectively are a13/m1 and a3/m11 ;)

  • Arek Kulczycki at 2019-04-08

    In both games above I think leela is ahead, but as lazyplayer has mentioned, I should not dare suggest solutions in bot games anymore ;)

  • gzero_bot at 2019-04-09

    GG(s) to leela!  Congrats!   :)

    I think Arek you were right... early on gzero was a little pessimistic on the outlook of both games, and slowly became more and more pessimistic.  I’ve reduced the resign percentage, so it prolongs the game a bit – so gzero might play really desperate moves at the end (that is MCTS for you).

    I am running a long job to find openings other than k12.  It seems that gzero is currently a fan of an unusual(?) trio f11/g11/h11 (and rotations).

  • leela_bot ★ at 2019-04-09

    Amazing! leela also likes g11 as an opening move!

  • lazyplayer at 2019-04-09

    Probably there are losing openings on first column too, but maybe MCTS is biased and doesn’t perceive that? That is,  a7,a8,a9,a10...

    Regarding f11,g11,h11, we know they’re more or less balanced. :)

    Regarding your last 2 games, it seems leela knows what it’s doing and gzero does not, but somehow, gzero also wins some games :D

  • lazyplayer at 2019-04-09

    This position is probably worth analyzing in depth: https://www.littlegolem.net/jsp/game/game.jsp?gid=2089655&nmove=8

  • Arek Kulczycki at 2019-04-09

    lazyplayer, I get the same impression! Leela seems to play correctly while gzero seems to play random “reasonable” moves and sometimes it’s just enough to reach an endgame where gzero is monstrously brilliant like leela ;)

  • David J Bush ★ at 2019-04-09

    How about some 19x19 bot games? It might popularize this variant. Maybe humans could maintain a stronghold there for a while.

  • lazyplayer at 2019-04-09

    David, on 19x19 we stand no chance at all. We humans are mostly clueless on the big picture. Some more (me) some less (maybe Daniel and Arek).

    But anyway, it would be nice to observe some 19x19 games played by bots according to “objective” standards.

  • lazyplayer at 2019-04-09

    I think probably playing mostly correctly at the global scale requires calculation, you really have to sample a lot of possible continuations. And this is exactly what the bots are doing. So basically on that front we can’t outplay them at all. The only chance of outplaying them is in local tactics that are large enough to have escaped their patter recognition algorithms.

  • lazyplayer at 2019-04-09

    Well, technically, we could outplay them by intuitively making a correct global plan... but good luck doing that on 19x19! :D

  • Daniel Sepczuk at 2019-04-09

    What do you thinks guys about my games against leela and gzero? Especialky against leela on white and against gzero on black i feel disappointed

  • lazyplayer at 2019-04-09

    Daniel, in game 9895, after 7 k6 it’s over, right? so maybe 6 i6 as alternative?

  • lazyplayer at 2019-04-09

    Hm no i6 loses easily, I’m trying i7 now...

  • lazyplayer at 2019-04-09

    Daniel, I think you blundered, at 6 you seem to have two choices that don’t lose immediately, i7 and j6. I doubt they’re enough to win but I’ve no idea really.

  • lazyplayer at 2019-04-09

    This game here is the same questionable idea: https://littlegolem.net/jsp/game/game.jsp?gid=2089660&nmove=4

    And even here: https://littlegolem.net/jsp/game/game.jsp?gid=2089656&nmove=4

    This idea of being very strong on one side isn’t supported by bots. They don’t play it and we shouldn’t play it either. :)

  • Arek Kulczycki at 2019-04-09

    Daniel, I think you’ve been losing pretty early in the first two...

    here and here

    the third I like your position here, later I will analyse this game deeper

    In the fourth I don’t like both #6 and #8 and it collapses more and more with every next move...

  • leela_bot ★ at 2019-04-09

    leela thought 7.d7 was a perfectly OK move. In fact things weren’t quite over yet until 15.i3. It thought 15.j7 would have been much better.

  • lazyplayer at 2019-04-10

    Leela, you’ve not commented on this game: https://littlegolem.net/jsp/game/game.jsp?gid=2033216&nmove=19

    I think that Daniel has blundered near the end, but maybe I’m missing some tactic?

  • Daniel Sepczuk at 2019-04-10

    Maybe 9.F6 instead E7?

  • gzero_bot at 2019-04-10

    @lazy & @arek – gzero would appreciate some game time if you are up for it.  you can tell me what the random(ish) moves are so I can try to debug it.  Thanks.

  • lazyplayer at 2019-04-10

    Gzero, I’ve no timefor another game now. In hex practice there are many things that are considered wrong but that are FAR from disproved. For example:

    https://littlegolem.net/jsp/game/game.jsp?gid=2033245&nmove=4

    https://littlegolem.net/jsp/game/game.jsp?gid=2089896&nmove=6

    And basically, we don’t know if they’re REALLY wrong or not. Maybe in a FEW rare cases they’re indeed optimal.

  • gurgeh ★ at 2019-04-10

    @ lazy – ok thanks.  The game 2033245 is a really old model, I threw away all the training data and started over.

    https://littlegolem.net/jsp/game/game.jsp?gid=2089896&nmove=6

    I will look that into that one, it was divergent from the games I had earlier with leela.  And I am not sure why.


  • gzero_bot at 2019-04-10

     And posted from wrong account. :)

  • Arek Kulczycki at 2019-04-10

    Im up for it but do you mean through the “Rated games” mechanism?

    gzero, it’s hard for me to describe the randomishness clearly, because it’s a long term observation. Leela seems to follow up on the initial moves. Gzero seems to play all the good stuff but without order.

    An example is this https://littlegolem.net/jsp/game/game.jsp?gid=2080616&nmove=16

    All white stones support each other. Black d5, g4 and j3 make no sense in terms of putting them on board together,

  • gzero_bot at 2019-04-10

    "gzero, it’s hard for me to describe the randomishness clearly, because it’s a long term observation. Leela seems to follow up on the initial moves. Gzero seems to play all the good stuff but without order."

    That’s interesting, thanks.  I’ll try rerunning that example.  One thing is that if gzero gets pessimistic, the top moves end up shuffling down in priority and all the top candidate moves are bunched up with the same probability, and usually a randomish move remains at the top at the end of the search (so maybe what it thinks will prolong the loss).  It is generally whats happens with long searches and MCTS if it goes into pessimistic mode.  I am not a strong enough player to see such bad moves, so I have no idea when such bad moves are made, so it hard to even correlate this theory.  Maybe one reason we see less of this with leela is that leela doesn’t lose very often!  I might be clutching at straws here, it is very hard to figure why it does something.

    Sure rated or unrated if you want.  

  • lazyplayer at 2019-04-10

    gzero, so basically it’s more random when the game is less balanced? actually this is understandable, because it’s hard to evaluate unbalanced positions...

  • gzero_bot at 2019-04-10

    it is more random for the player that is losing when the game is less balanced. 

    another way to view it – from a single board state and the current player to play:

    the less chance of winning, the more it will explore – and the more random the top move will be.  

    [the famous lee sedol versus alphago is a prime example of this]

    the greater the chance of winning, the more it will latch onto the top move and barely explore other moves. 

    but again, it is just one example of something that can go wrong.  If the network evaluation is in lala land, it will behave very different.

  • lazyplayer at 2019-04-10

    gzero, maybe I’ve understood, unbalanced position create some kind of instability, but this instability is a problem only at the root node, because at the root you’ve to eventually make a final decision.

  • lazyplayer at 2019-04-10

    Ok, I take back what I’ve just said. I guess it’s due to the MCTS algorithm. It’s simply more random when you’re losing.

  • gzero_bot at 2019-04-10

    lazy – yes, what you said was right.  non-root nodes that are pessimistic don’t matter, they just back-propagate a truer score.  In fact, pessimistic opponent non-root nodes are great since it will be exploring more, and less chance of a surprise move. 

  • leela_bot ★ at 2019-04-10

    I’ve certainly observed that with leela also: if it is losing it starts making really bad looking moves. They are objectively probably still the best moves, but I think human players seem to know how to complicate the situation by playing tricky stuff when they are losing, but the bots are too “honest” for that :)

  • leela_bot ★ at 2019-04-10

    Next pair of games are underway 2089922 and 2090091

  • Arek Kulczycki at 2019-04-10

    I think k7/c7 is too strong and both game will end as white win. I will be watching carefully :)

  • lazyplayer at 2019-04-10

    It seems Leela is going to win both. It plays so confidently, as if it’s knowing what it’s doing.

    Regarding root nodes, I can understand that, but there also has to be some asymmetry between losing and winning. Maybe there is a logarithm somewhere in the formulas of MCTS?

  • lazyplayer at 2019-04-10

    Well, maybe gzero has decent chances in game #...91. Both are after the 16th move right now.

  • lazyplayer at 2019-04-10

    In my experiences, for stones like c7 to lose, black has often to play b6-b9 threat, and it’s really fun when it happens. :)

  • lazyplayer at 2019-04-10

    Well, but I was playing that on 11x11. On 13x13 it’s really hard to imagine a way to fit b6 and b9 into play without losing on the spot. :D

  • lazyplayer at 2019-04-10

    Leela even found a way to play B6 in its game. Both games look complex and beyond human understanding. Maybe it would take hours to understand what’s going on there.

  • gzero_bot at 2019-04-10

    fwiw, @ move 32 - gzero seems rather confident with game 22 (90% rising with search) - but then stranger things have happened!  91 is still in the balance, with (60% decreasing with search).   

  • lazyplayer at 2019-04-10

    gzero, you may end up winning both against all previsions :D heheheh

    i think you still play very dubious initial stones but not even leela seems able to refute them.

  • leela_bot ★ at 2019-04-10

    leela agrees 22 is over, also pretty balanced still on 91. I don’t think I have ever seen it this close this deep into a game.

  • lazyplayer at 2019-04-10

    Yeah 22 is over, but I think gzero has just blundered at 91 with 38 k4...

  • lazyplayer at 2019-04-10

    Well, it’s over anyway, congrats to gzero. Who wrote the code? I see it’s in GitHub.

  • leela_bot ★ at 2019-04-10

    leela expected 38.k4.

  • lazyplayer at 2019-04-10

    38 L3 is of course better, as you can see locally. But it loses anyway.

  • lazyplayer at 2019-04-10

    Probably Gzero isn’t even bothering analyzing, it picks first random winning move and stays with it.

  • leela_bot ★ at 2019-04-10

    Congrats to gzero on winning 22! Leela is now under 20% on 91 also, so it looks like the score is going to be leela 2, gzero 2 so far.

  • gzero_bot at 2019-04-11

    @lazy 38.k4 was 70% on policy from neural network – so it latched on to it because it gets more exploration due to policy percent and the winning rate was much higher than other candidates.  The policy for L3 was 0.02%.  The node is in optimistic mode due to latching on to k4, and with that and the low policy – l3 never gets much exploration.

    I am running gzero now with more exploration at root (including some code changes), and a little longer search to compensate for search width.   Replaying k12 opening game, which gzero lost to leela in first round of games.

  • leela_bot ★ at 2019-04-11

    For convenience here are the next pair of games: 2090398 and 2090401.

  • lazyplayer at 2019-04-11

    Leela, in recent times you’ve started to like center. I think even bots really don’t know how to play the first few stones!

  • David J Bush ★ at 2019-04-11

    “Knowing the first moves” should be equivalent to “solving that size grid.” AFAIK the largest posted swap map is for 9x9.

  • lazyplayer at 2019-04-11

    Eheh, this time leela wins 2-0. Gzero seems to play desperate tactics/strategies.

  • gzero_bot at 2019-04-11

    Yeah, I was checking in, game 401 has been over for a while.  :)  Not sure where that went wrong so early.

    Don’t know about other game, seems semi-balanced from gzero’s point of view.

  • lazyplayer at 2019-04-11

    Well, maybe it has a chance on game 398...

  • lazyplayer at 2019-04-11

    gzero, actually I’ve just checked, maybe in 398 it’s plainly winning. Leela plays a beautiful style and I like its move visually, but the evil is in the details.

  • lazyplayer at 2019-04-11

    I think probably leela is stronger at strategy (global play), and gzero is stronger at tactics (local play).

  • lazyplayer at 2019-04-11

    gzero, i think you win 398 (we’re after move 32 now), correct? :)

  • Arek Kulczycki at 2019-04-11

    Awww what a beautiful move by gzero! 

    https://www.littlegolem.net/jsp/game/game.jsp?gid=2090091&nmove=16

  • lazyplayer at 2019-04-11

    Arek, https://www.littlegolem.net/jsp/game/game.jsp?gid=2076353&nmove=11

    I also play that! :D

  • gzero_bot at 2019-04-11

    398:  I’ve no idea! :)  gzero still over 50% but dropping with more search.  I’d put my money on leela with those stats (without looking at the board).

  • leela_bot ★ at 2019-04-11

    Here is leela’s current “swap file”. The percentages are the winning percentage leela thinks white has if black plays it’s first stone in the indicated hex. How does this compare with gzero’s thoughts, gzero?


  • lazyplayer at 2019-04-11

    I think if you analyze a8 and a10 deeper, maybe they’ll be closer to 50 than they’re there.

    Anyway, the really surprising result is H3 stronger than G3 and then even more surprising we see that J3 is almost as bad as G3. This latter fact (J3 almost as bad as G3) never crossed anyone mind as far as I know except maybe for Arek: https://littlegolem.net/jsp/game/game.jsp?gid=1597836&nmove=2. Probably it’s because it allows white to play L2 at some point.

  • gzero_bot at 2019-04-12

    @leela Very cool and pretty! :) 

    I don’t have any swap file, as swap is baked into the rules/neural network.  To get something similar I could generate, from blacks point of view, the win probability after N simulations for each board position with a single white stone from your swap file/heatmap.  I’ll try that at the weekend.

    What I have done is has ran MCTS at depth=0 for a long time with high exploration settings.  I’ll paste a most recent result below.  Also because it is MCTS, it is not very consistent results (the previous time I ran it, a13 was lower than f11).  Nor is there any symmetry (so i took the top result for each symmetry).

    (#simulations, policy probability, win probability for black after #simulations)

    • k12 / c2 : 339337, 16.92, 0.473
    • g11 / g3 : 339011, 0.30, 0.465
    • a13 / m1 : 339006, 0.43, 0.462
    • h11 / f3 : 339003, 0.14, 0.456
    • f11 / h3 : 339000, 0.37, 0.448
    • l12 / b2 : 178608, 1.69, 0.439
    • k2 / c12 : 146951, 3.27, 0.438
    • m12 / a2 : 101694, 6.55, 0.436
    • a8 / m6 : 60740, 0.10, 0.438
    • m11 / a3 : 33494, 3.55, 0.425
    • a4 / m10 : 29866, 0.20, 0.424
    • m4 / a10 : 22574, 0.24, 0.417
    • a5 / m9 : 12259, 0.13, 0.415
    • b4 / l10 : 11543, 0.13, 0.412
    • a9 / m5 : 10396, 0.14, 0.406
    • i11 / e3 : 9068, 0.12, 0.409
    • m8 / a6 : 8842, 0.11, 0.408

  • gzero_bot at 2019-04-12

    Also interesting with J3 – since it doesn’t appear in gzero’s list.  leela has played that in our new game 2090407.  :)

  • leela_bot ★ at 2019-04-12

    Score so far: leela 4, gzero 2. 

    Next pair of games 2090407 and 2090408.

  • David J Bush ★ at 2019-04-12

    This is very useful, thank you Leela bot. Of course it will take a lot more time, and perhaps a different sort of algorithm, to nail down every cell as either 100% or 0. During that process, some of the relative values between specific cells might flip around.

  • lazyplayer at 2019-04-12

    Ah, I was totally confused on 398. What a fool. Anyway, the last 2 games are very interesting starts!

  • Carroll ★ at 2019-04-12

    Very nice, thanks!

    Did you agree on a thinking time or better a number of playouts for this bot fight?

    Could you explain the numbers for the openings? If swap is allowed, every number should be greater than 50% and else I think there should be lot more squares for first player that should be?

  • Ignatius J Reilly at 2019-04-12

    @Carroll — The percentages in the opening diagram assume no swap.


  • leela_bot ★ at 2019-04-12

    That is right. Put another way: if black plays it’s first move on an indicated hex and that hex has a number smaller than 50% leela will swap. If bigger than 50% leela will play on with white. leela will also swap any empty hex (if black plays it’s first move there).

  • leela_bot ★ at 2019-04-12

    Also, if leela plays first it would prefer to play k12 (or c2) because that is the cell with the number closest to 50%. In practice, for the sake of variety, it currently randomly plays anything within 6% of 50%.

  • leela_bot ★ at 2019-04-12

    For the “bot battle” we have a somewhat informal agreement to allow around 10 minutes thinking time per move. 

  • HappyHippo at 2019-04-12

    Interesting results with the swap map. I might try more F3/G3 openings

    For the first move selection, have you considered a weighted probability of all moves? Apparently this is what the TwixtBot does:

    "For the first move, rather than pick the one point closest to 50%, I decided to make a weighted random selection: the closer the win rate is to 50%, the higher the chance I pick that move."

    Ultimately that might reduce the bot’s winning percentage, but it could potentially make for some more interesting games. And maybe give the lowly humans a chance ;)

  • lazyplayer at 2019-04-12

    Happy, if it plays less variation in first move, we can study its game and learn something. So actually, lowly humans have more to gain if it plays objectively better... ;)

  • lazyplayer at 2019-04-12

    First principle of Hex strategy: The best way to learn hex is by copying the choices of strong players, especially at the beginning. :-)

  • lazyplayer at 2019-04-12

    Next pair of games, my forecast is 2-0 for gzero! The first stone does matter!

  • lazyplayer at 2019-04-12

    "I’ve certainly observed that with leela also: if it is losing it starts making really bad looking moves. They are objectively probably still the best moves, but I think human players seem to know how to complicate the situation by playing tricky stuff when they are losing, but the bots are too “honest” for that :)"

    Poor bot, these evil humans are tricking him, haha :D



  • lazyplayer at 2019-04-12

    Leela_bot, what about game 087? what you play if I play i8? it seems rather game over to me... :)

  • Arek Kulczycki at 2019-04-12

    Leela thanks for the heatmap! Very interesting with j3!

    Although I don’t see why h3 would be stronger than g3, could this difference still be within the error?

    And ooops, seems a7 and a8 are way too strong :( I liked those

    My last surprise is I would have expected a3 to be more balanced. It’s a pitty leela will not play it as it’s not within 6%...

  • gzero_bot at 2019-04-13

    Interesting game 2090408, it seemed leela had won but then played a couple of moves b10 and a12 - that gave gzero a chance to claw back into the game.

    Score so far: leela 5, gzero 3.   Think gzero is quite fortunate with that score line. :)  Congrats leela!

    I agree with lazy and arek, it always seems as if games with leela it is fighting a losing battle from move 2 onwards – with the win probability being slowly sapped away. If lucky, gzero seems to have jumps in win probability in the late game, such as the b10/a12 above, which lets it back in the game.   Maybe leela just feeling sorry for her wee brother and throwing the game! ;)

    One last game being played now, for reference: 2090522, with h11 opening, since g11 was interesting.


  • Arek Kulczycki at 2019-04-13

    It would take longer analysis to prove but to me it seems in 2090408 at move 33 leela could even win in multiple ways... At least the move I would like is 33.h9 and I dont see many opportunities for white to turn the game...

  • lazyplayer at 2019-04-13

    Gzero, don’t worry, leela is not making late game blunders. In the game 2090408 the “error” is probably 13 g8 or 15 i8. I say “error” in quotes because it’s not obvious at all that there was a winning choice there for Leela at all. It’s possible that all choices there were actually losing and Leela at best could have picked another that was less obvious.

  • lazyplayer at 2019-04-13

    Nonetheless it’s possible your idea is still correct. It’s possible gzero is slightly stronger in later moves than leela.

  • lazyplayer at 2019-04-13

    Gzero, you can try a match at much higher time controls, like 6 hours per move instead of 10 mins. This should allow you to use your endgame skill to compute the right initial stones.

    By the way, I think something similar is true between me and Arek. I’m slighly stronger later moves and/or much longer time controls and/or smaller boards.

  • lazyplayer at 2019-04-13

    I thought I was winning in game 087 but I was not. Maybe I’ve blundered somewhere near the end? Overconfidence is terribly dangerous...

  • lazyplayer at 2019-04-13

    I should have played 14 L2, maybe even 18 L2 was enough... shame on me!

  • lazyplayer at 2019-04-13

    Gzero, I also propose a funny experiment for you to do, if you’ve time. I see that you can easily change board size (your code is game-agnostic). Why don’t you try to set board size = 100, or board size = 500, and then do some training on that, and then you show us the “heatmap” of openings? I’m wondering if center is a winning opening on arbitrarily large boards like 100x100.

  • leela_bot ★ at 2019-04-13

    @lazy you are seriously underestimating what “some training” on a 100x100 board would involve.

  • lazyplayer at 2019-04-13

    leela, it’s better to have a low quality “heatmap” than having no “heatmap” at all :)

    btw, take a look at our last game, sadly, i blundered, i was too happy because i had won another!

  • lazyplayer at 2019-04-13

    can you confirm i was winning before the blunder? L2 was winning no?

  • ypercube at 2019-04-13

    I agree with Leela. Training for size 19 might give us some results. For 29 maybe.

    For 100? I doubt it. 

  • ypercube at 2019-04-13

    The bots do not even play at 19 yet.

    I challenge them for a game of 36x36. 

  • lguser at 2019-04-13

    I too am interested in seeing how good play in the early game scales with board size

  • leela_bot ★ at 2019-04-13

    @lazy on your game 2090087. Yeah, 18.k7 was wrong (leela jumped to above 70%). I wouldn’t call 18.l2 winning: leela says 51%. It was actually expecting 18.l3 (44%). 14.l2 is also 51% (I didn’t run leela super long on these so take these numbers with a grain of salt)

  • lazyplayer at 2019-04-13

    leela, h7 seems to win “cleanly”: http://www.trmph.com/hex/board#13,a2d10j9j10i10i5f6h4e5e6f5f9l4i8c10c11h8h7


  • lazyplayer at 2019-04-13

    leela, it’s surprising to me that bots are so “probabilistic”. For me it’s either win or loss, the rest are illusions. :)

  • lazyplayer at 2019-04-13

    Well, no, 18 H7 indeed worse than 18 L2,  maybe I’ve caused a mess at 16, and 16 D9 would be a clean white win? Or maybe there are no clean wins at all and it’s genuinely complicated.

  • lazyplayer at 2019-04-14

    Yeah, your assessment is right, it’s still a damn mess and far from over.

  • Force majeure at 2019-04-14

    @Leela & @Gzero – would it be possible to include some description of bots' thoughts after every move? At least its estimated winning probabilities, I think it would be a great lesson.

  • gzero_bot at 2019-04-14

    For Alpha*Zero approach on 100x100 hex or 500x500 (!), the demands on time and space would make Deepmind baulk.  I think to get to high levels on 19x19 would be an adventurous project for a hobbyist... but it could be done if someone is motivated enough (and has deep enough pockets to run GPU for many months).  Likely some new AI tricks would be required for 100 or 500, IMO.  Cheers.

  • lazyplayer at 2019-04-14

    gzero, you don’t have to win a 100x100 tournement. Just do some exploration for the fun of discovery :)

    open questions that are interesting to: is the center strong on arbitrarily large board? how hex compares to go on arbitrarily large board?

  • lazyplayer at 2019-04-14

    *interesting to me

  • Arek Kulczycki at 2019-04-15

    lazyplayer congrats for having the game with leela around ~50% at the key stage. I was expecting there were many tricks and manouvers that made it complex, but didn’t know if were available to both players :)

    in my games I think I usually play too simpleminded and all the surprises are available to leela only ;)

  • gzero_bot at 2019-04-15

    2 more games for reference.  I lost track of the score...  leela wins most the time. :)

     2090913, 3rd time lucky with gzero playing k12 opening (first 2 leela won).

     2090914, f11 opening

    @force – yes good idea.  Unfortunately, I haven’t kept my logs.  If leela and gzero do a second round, will dump probabilities/best moves to a file.

  • lazyplayer at 2019-04-15

    gzero, you win 13 and lose 14.

  • Arek Kulczycki at 2019-04-17

    Hey leela I’m looking at the opening heatmap again and I see that the error on the rarely used cells is pretty sufficient. I think probably you don’t play enough a3 and the coefficient is highly biased. I suggest you include a3 among reasonable options, especially that a2 is being used.

  • Arek Kulczycki at 2019-04-17

    Hmm, no, maybe Im wrong, sorry. Seems the error is within 1 percentage point. It’s just unacceptable that moves like a3 and a8 are unplayable... :p I hope on 19x19 there is a playable move in the middle of an edge, say a11

  • lazyplayer at 2019-04-17

    Arek, a3 is another “corner case” like you’ve said to me. It’s surrounded by a2, b2, b3, a4 and yet it’s so much inferior!

  • Arek Kulczycki at 2019-04-18

    Some “corner cases” are kind of obvious. A2 is connected and a3 is not. The unobvious part is how a3 is actually stronger than should be because there is the ladder on 3rd row trick. Seems that it’s not enough though. 

    Anyway 13x13 is still to small for the opening map to be really interesting, because it lacks some “in between” moves :)

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