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Hex: A Strategy Guide

158 points by creata 5y ago

jkleiser 5y ago
Great! Thanks a lot.
grafs50 5y ago
Love this game! and its game theory underpinnings.
mrtweetyhack 5y ago
LugarOS 5y ago
That game looks cool
tromp 5y ago
This complements the 2019 book Hex - The Full Story by Ryan B. Hayward and Bjarne Toft https://webdocs.cs.ualberta.ca/~hayward/hexbook/hex.html https://webdocs.cs.ualberta.ca/~hayward/hexbook/hex.html
- JoeDaDude 5y ago
  I have not read it, but it likely complements another Hex strategy book: Hex Strategy: Making the Right Connections by Cameron Browne. [1]. https://www.google.com/books/edition/Hex_Strategy/tR7XkqeV31sC?hl=en https://www.google.com/books/edition/Hex_Strategy/tR7XkqeV31...
platz 5y ago
how is it guaranteed that games do not not end in a draw?
- tromp 5y ago
  The hexagonal diamond board topology is such that an east-west connection can only be prevented by a north-south connection. For more formal proofs, see https://sites.google.com/site/javhar1/hexcannotendinadraw https://sites.google.com/site/javhar1/hexcannotendinadraw
  - bo1024 5y ago
    Nice diagrams and proofs! This is one of those that can feel obvious, but needs a bit of deep math
- paxys 5y ago
  If you draw a hex board and try out some connections it will become immediately clear. There can never be a deadlock. No matter how you fill out all the tiles, either the white OR the black sides will connect.
- karmakaze 5y ago
  A square arrangement if we allow 8-way connections, we can end up with a cross-connection: ox xo If we only allow 4-way connections then a connected line won't permit another line to cross it. For hex 6-way connections, lets say a place ( ) is where lines cross, but it can only be a single color. How about making a cross connection like the 8-way square: (doesn't work) x x x o x o o o x x o x x x o x x x
  - shagie 5y ago
    If you put the constraint that an 'x' set of connections on a square board is not allowed - ox x. So that 'o' is prohibited from playing in the empty spot there because 'x' already has a connection - you get the game Crossway - https://boardgamegeek.com/boardgame/30517/crossway https://boardgamegeek.com/boardgame/30517/crossway // http://superdupergames.org/gameinfo.html?game=cross http://superdupergames.org/gameinfo.html?game=cross // http://www.marksteeregames.com/Crossway_rules.pdf http://www.marksteeregames.com/Crossway_rules.pdf
- kevinwang 5y ago
  My attempt at intuition: the very act of completely blocking your opponent from making a connection will make a connection for yourself.
- Syzygies 5y ago
  Wow. That takes me back. John Nash independently invented hex in grad school. A sequence of scenes involving hex were cut from the movie "A Beautiful Mind". The first day that Russell Crowe joined the production, he was occupied with hours of makeup tests for his aging progression. Ron Howard had me meet him during a break, to discuss the hex and go scenes to come. The first dozen of a crew that would be hundreds hadn't met him either, so they hovered nearby as we talked. To my surprise, Russell asked me what mathematical truths drew Nash to this game. Never underestimate people; I went for it. Rather than explaining the proof Nash liked that the first player could always win, I decided to explain why some player had to win. As I talked, Russell drew me in with fascinated, understanding facial expressions. When I was done he looked at Ron, "Can you get me the Parker Brothers rules? They're for 8 to 80, I didn't understand a word this guy just said!" Peals of laughter from the room. Months later we're filming a roomful of grad students playing hex, and Russell doesn't like what the script has him saying. He gets permission to ad lib. "Think of the black stones as water, the white stones as land. Either you can swim across this way, or there's a land bridge that way..." My longest day shooting, I woke at five, and was an actor in the pen ceremony that evening. Close to 24 hours awake, I found myself nodding off high at a party in Russell's room, everyone singing various national anthems. I learned much later that Russell had been kidded as a child for not knowing the New Zealand anthem. By the party he knew them all. He likes jokes only he gets, jokes with long fuses.
amenghra 5y ago
The site also has a ton of hex puzzles: http://www.mseymour.ca/hex_puzzle/hexpuzzle.html http://www.mseymour.ca/hex_puzzle/hexpuzzle.html
- SamBam 5y ago
  Those are very nice, and teach you the strategy very intuitively.
modeless 5y ago
Man, this brings back memories. In high school I made a version of this game for TI-89 BASIC. One of the first programs I ever released. I even made a silly AI for it just based on some basic heuristics because I had no idea how to make an AI back then. https://www.ticalc.org/archives/files/fileinfo/106/10660.html https://www.ticalc.org/archives/files/fileinfo/106/10660.htm...
ummwhat 5y ago
I thought this looked familiar so I checked my collection of 2 player abstracts and sure enough I own an octagonal variant called "pathagon". Haven't played it yet. Hard to find people interested in this genre (except for chess and go, grrr).
shagie 5y ago
Some other games in the immediate family: Y https://boardgamegeek.com/boardgame/5242/game-y https://boardgamegeek.com/boardgame/5242/game-y (from 1953) ConHex https://boardgamegeek.com/boardgame/10989/conhex https://boardgamegeek.com/boardgame/10989/conhex Away Across https://boardgamegeek.com/boardgame/30988/away-across https://boardgamegeek.com/boardgame/30988/away-across (Sid Sackson game from Calculate! - a set of math games) Lightning https://boardgamegeek.com/boardgame/35528/lightning https://boardgamegeek.com/boardgame/35528/lightning (from 1892 - possibly the first connection game - https://patents.google.com/patent/US471666A/en?oq=US471666 https://patents.google.com/patent/US471666A/en?oq=US471666) Thoughtwave https://boardgamegeek.com/boardgame/2395/thoughtwave https://boardgamegeek.com/boardgame/2395/thoughtwave (1974) a pipe's style. Tak https://boardgamegeek.com/boardgame/197405/tak https://boardgamegeek.com/boardgame/197405/tak (from The Wise Man's Fear) Twixt https://boardgamegeek.com/boardgame/949/twixt https://boardgamegeek.com/boardgame/949/twixt (1962, when 3M made games) (For more - https://boardgamegeek.com/boardgamefamily/7345/mechanism-connection https://boardgamegeek.com/boardgamefamily/7345/mechanism-con... and https://en.wikipedia.org/wiki/Connection_game https://en.wikipedia.org/wiki/Connection_game )
umvi 5y ago
Any quick links to play this online against a computer opponent? Looks fun.
- JoeDaDude 5y ago
  Here's one, though the AI is said to be pretty dumb: https://boardspace.net/english/about_hex.html https://boardspace.net/english/about_hex.html Last time I checked there were a couple of mobile games. Looks like these are still available: https://apps.apple.com/us/app/hex-ai-board-game/id1326484730 https://apps.apple.com/us/app/hex-ai-board-game/id1326484730 https://appadvice.com/app/hex-for-ipad/626696176 https://appadvice.com/app/hex-for-ipad/626696176
grimgrin 5y ago
Check this bit of info out, also the entire blog, and also their created games https://www.nickbentley.games/abstract-strategy-games-online-guide/ https://www.nickbentley.games/abstract-strategy-games-online...
jph00 5y ago
On Nintendo Switch, Clubhouse Games includes hex: https://www.nintendo.com/store/products/clubhouse-games-51-worldwide-classics-switch/ https://www.nintendo.com/store/products/clubhouse-games-51-w... (There's a lot of other really fun and interesting games there too BTW - it's been very popular in our family.)
derbOac 5y ago
I was interested in this game quite a bit for awhile when I was much younger, but then read an article or something stating that the first player has a strong advantage and that they have a guaranteed route to win simply by virtue of playing first. I'm not sure if this is correct or not but it was my understanding at the time, and it kinda dampened my enthusiasm.
- a1445c8b 5y ago
  That’s why there’s the “swap” rule.
  - JTBooth 5y ago
    After which the second player has a guaranteed route to win, but it's much harder to find! Last I checked the game tree was computed up to a 6x7 board, players usually use 13x13
    - hanche 5y ago
      I used to play it quite a bit with a friend back in my student days, on a 12×12 board. We were aware, in principle, that the first player had a winning strategy, but in practice, the advantage to the first player was small enough to hardly be detectable (though we did not compile any statistics on it). Perhaps this only serves to reveal that we weren't terribly good at it, though. We weren't aware of the swap rule at the time.
      - aidenn0 5y ago
        That's slightly surprising since playing in the middle of the board on your first move is such a large advantage. Beginner players do seem to think that playing near a black side is a good opening, but it's actually one of the weakest, but playing it "quite a bit" I would suspect you would stumble on playing near the middle by accident if nothing else?
        hanche 5y ago
deleted 5y ago
[deleted]
kqr 5y ago
I feel like I've missed something. This seems similar to go (yet different in several important ways, of course), which I do know. Is there a relationship?
- tromp 5y ago
  Both heavily feature stone connectivity. But where connecting your sides with a stone chain is the goal in Hex, connected stones sharing liberties is only used to define capture in Go, and the goal is instead to take the most territory.
  - bskrobisz 5y ago
    I think, if you're familiar with go, this is an uncharitable reading of the question. The victory condition in this game is very directly analogous to a not-uncommon source of (sometimes-game-deciding) violence in go--two nearby weak groups where connection means a decisive victory for whichever player achieves it. Having not played Hex, I can't say whether it's strategically similar (although just from the first couple of chapters, there are definitely similar concepts of important shapes and ladder breakers).
    - vintermann 5y ago
      There was a variant combining Hex and Go which was popular (as these things go) on online abstract games sites a few years ago. Square board, capturing like in Go, but the goal is to connect sides like in Hex. This game degenerated to "primitive Go" most of the time, because both sides blocking each other is easy on a square board, and at that point it's down to who has the most territory (most free moves to fill in their own areas without being captured. I've played both on a modest level. I'd say that Hex, at the sizes we typically play at, is a lot like one big Go fight. I find it easier to look far ahead in Hex since pieces are never removed, ladders are (even) more common, and since non-overlapping templates ("miai" in Go) always connect you can build them together into huge parts of the board where you know you can connect.
    - kqr 5y ago
vintermann 5y ago
I used to play this game quite a lot, back when Six was the strongest AI opponent. Managed to beat it at 11x11, no chance at 8x8. At 13x13 it completely fell apart (but you had to kind of hack the engine to even play at that size, so it might have been buggy). Now I guess the AlphaZero-variants win everything there as elsewhere. There was a kid from Poland who was insanely good. Maciej Celuch. Don't know what's become of him, but wouldn't be a kid any longer. He was the top player by a mile, won the Little Golem tournaments every year he participated. A bunch of people from the same town in Poland were also really, really good, I guess they had a bit of a community going. The other place there was a bit of community going was in Oslo, a bunch of guys associated with the defense research institute (FFI). I went to an offline tournament with them once, to my surprise I didn't finish quite last. I think it's a satisfying game, because it's quite easy to learn to look far ahead. Since the pieces stay put, it's much easier to reason about positions. M. Seymour's online book is great, too. I've heard good things about Ryan B. Hayward's book. Cameron Browne is a nice guy and has done a lot of other cool work in combinatorial games, but I can't recommend his old Hex book. The tactics advice is not good.
natufunu 5y ago
I wrote a hex AI with a couple of friends a few years back based on reinforcement learning. https://cleeff.github.io/hex/ https://cleeff.github.io/hex/ You move first and the ai might swap meaning that it steals your first move and you swap colors. This enforces you to pick an even opening. I'm very bad at hex but it still was an awesome experience to observe the ai surpass my performance.
- dematz 5y ago
  Thanks for making this! As a fellow very bad hex player I have had a lot of fun inevitably losing to the agent. You might be interested in this - the one time I won, it seemed like a bug? I was playing red and blue could have easily won, but threw the game? https://i.imgur.com/4uyipte.png https://i.imgur.com/4uyipte.png if blue goes on the other 6.4 spot blue probably wins, if not red wins. Honestly I was about to give up on the game because the ai plays "mean" as noted in the readme - it always does close out favorable positions but doesn't prioritize the simplest/quickest win. This time I was annoyed at it or something though and playing it out was really surprised at that move it made. This may or may not be relevant, but it's interesting that the agent rates both the correct move and the move it made at 6.4, maybe that was part of the problem?
JoeDaDude 5y ago
Way back in the day, I wrote an AI to play hex based on the Genetic Algorithm, for which I drew inspiration from Blondie24, a checkers AI. At the time I didn't realize how much broader the search tree for Hex was compared to checkers. The results were disappointing. I had to reduce the board size to get even modest performance. [1]. https://en.wikipedia.org/wiki/Blondie24 https://en.wikipedia.org/wiki/Blondie24
jacknews 5y ago
Is there a 3 player version of hex, and it is as deep? google is not being my friend today.

158 points by creata 5y ago

jkleiser 5y ago

Great! Thanks a lot.

grafs50 5y ago

Love this game! and its game theory underpinnings.

mrtweetyhack 5y ago

LugarOS 5y ago

That game looks cool

tromp 5y ago

This complements the 2019 book Hex - The Full Story by Ryan B. Hayward and Bjarne Toft https://webdocs.cs.ualberta.ca/~hayward/hexbook/hex.html https://webdocs.cs.ualberta.ca/~hayward/hexbook/hex.html

JoeDaDude 5y ago
I have not read it, but it likely complements another Hex strategy book: Hex Strategy: Making the Right Connections by Cameron Browne. [1]. https://www.google.com/books/edition/Hex_Strategy/tR7XkqeV31sC?hl=en https://www.google.com/books/edition/Hex_Strategy/tR7XkqeV31...

platz 5y ago

how is it guaranteed that games do not not end in a draw?

tromp 5y ago
The hexagonal diamond board topology is such that an east-west connection can only be prevented by a north-south connection. For more formal proofs, see https://sites.google.com/site/javhar1/hexcannotendinadraw https://sites.google.com/site/javhar1/hexcannotendinadraw
- bo1024 5y ago
  Nice diagrams and proofs! This is one of those that can feel obvious, but needs a bit of deep math
paxys 5y ago
If you draw a hex board and try out some connections it will become immediately clear. There can never be a deadlock. No matter how you fill out all the tiles, either the white OR the black sides will connect.
karmakaze 5y ago
A square arrangement if we allow 8-way connections, we can end up with a cross-connection: ox xo If we only allow 4-way connections then a connected line won't permit another line to cross it. For hex 6-way connections, lets say a place ( ) is where lines cross, but it can only be a single color. How about making a cross connection like the 8-way square: (doesn't work) x x x o x o o o x x o x x x o x x x
- shagie 5y ago
  If you put the constraint that an 'x' set of connections on a square board is not allowed - ox x. So that 'o' is prohibited from playing in the empty spot there because 'x' already has a connection - you get the game Crossway - https://boardgamegeek.com/boardgame/30517/crossway https://boardgamegeek.com/boardgame/30517/crossway // http://superdupergames.org/gameinfo.html?game=cross http://superdupergames.org/gameinfo.html?game=cross // http://www.marksteeregames.com/Crossway_rules.pdf http://www.marksteeregames.com/Crossway_rules.pdf
kevinwang 5y ago
My attempt at intuition: the very act of completely blocking your opponent from making a connection will make a connection for yourself.
Syzygies 5y ago
Wow. That takes me back. John Nash independently invented hex in grad school. A sequence of scenes involving hex were cut from the movie "A Beautiful Mind". The first day that Russell Crowe joined the production, he was occupied with hours of makeup tests for his aging progression. Ron Howard had me meet him during a break, to discuss the hex and go scenes to come. The first dozen of a crew that would be hundreds hadn't met him either, so they hovered nearby as we talked. To my surprise, Russell asked me what mathematical truths drew Nash to this game. Never underestimate people; I went for it. Rather than explaining the proof Nash liked that the first player could always win, I decided to explain why some player had to win. As I talked, Russell drew me in with fascinated, understanding facial expressions. When I was done he looked at Ron, "Can you get me the Parker Brothers rules? They're for 8 to 80, I didn't understand a word this guy just said!" Peals of laughter from the room. Months later we're filming a roomful of grad students playing hex, and Russell doesn't like what the script has him saying. He gets permission to ad lib. "Think of the black stones as water, the white stones as land. Either you can swim across this way, or there's a land bridge that way..." My longest day shooting, I woke at five, and was an actor in the pen ceremony that evening. Close to 24 hours awake, I found myself nodding off high at a party in Russell's room, everyone singing various national anthems. I learned much later that Russell had been kidded as a child for not knowing the New Zealand anthem. By the party he knew them all. He likes jokes only he gets, jokes with long fuses.

amenghra 5y ago

The site also has a ton of hex puzzles: http://www.mseymour.ca/hex_puzzle/hexpuzzle.html http://www.mseymour.ca/hex_puzzle/hexpuzzle.html

SamBam 5y ago
Those are very nice, and teach you the strategy very intuitively.

modeless 5y ago

Man, this brings back memories. In high school I made a version of this game for TI-89 BASIC. One of the first programs I ever released. I even made a silly AI for it just based on some basic heuristics because I had no idea how to make an AI back then. https://www.ticalc.org/archives/files/fileinfo/106/10660.html https://www.ticalc.org/archives/files/fileinfo/106/10660.htm...

ummwhat 5y ago

I thought this looked familiar so I checked my collection of 2 player abstracts and sure enough I own an octagonal variant called "pathagon". Haven't played it yet. Hard to find people interested in this genre (except for chess and go, grrr).

shagie 5y ago

Some other games in the immediate family: Y https://boardgamegeek.com/boardgame/5242/game-y https://boardgamegeek.com/boardgame/5242/game-y (from 1953) ConHex https://boardgamegeek.com/boardgame/10989/conhex https://boardgamegeek.com/boardgame/10989/conhex Away Across https://boardgamegeek.com/boardgame/30988/away-across https://boardgamegeek.com/boardgame/30988/away-across (Sid Sackson game from Calculate! - a set of math games) Lightning https://boardgamegeek.com/boardgame/35528/lightning https://boardgamegeek.com/boardgame/35528/lightning (from 1892 - possibly the first connection game - https://patents.google.com/patent/US471666A/en?oq=US471666 https://patents.google.com/patent/US471666A/en?oq=US471666) Thoughtwave https://boardgamegeek.com/boardgame/2395/thoughtwave https://boardgamegeek.com/boardgame/2395/thoughtwave (1974) a pipe's style. Tak https://boardgamegeek.com/boardgame/197405/tak https://boardgamegeek.com/boardgame/197405/tak (from The Wise Man's Fear) Twixt https://boardgamegeek.com/boardgame/949/twixt https://boardgamegeek.com/boardgame/949/twixt (1962, when 3M made games) (For more - https://boardgamegeek.com/boardgamefamily/7345/mechanism-connection https://boardgamegeek.com/boardgamefamily/7345/mechanism-con... and https://en.wikipedia.org/wiki/Connection_game https://en.wikipedia.org/wiki/Connection_game )

umvi 5y ago

Any quick links to play this online against a computer opponent? Looks fun.

JoeDaDude 5y ago
Here's one, though the AI is said to be pretty dumb: https://boardspace.net/english/about_hex.html https://boardspace.net/english/about_hex.html Last time I checked there were a couple of mobile games. Looks like these are still available: https://apps.apple.com/us/app/hex-ai-board-game/id1326484730 https://apps.apple.com/us/app/hex-ai-board-game/id1326484730 https://appadvice.com/app/hex-for-ipad/626696176 https://appadvice.com/app/hex-for-ipad/626696176

grimgrin 5y ago

Check this bit of info out, also the entire blog, and also their created games https://www.nickbentley.games/abstract-strategy-games-online-guide/ https://www.nickbentley.games/abstract-strategy-games-online...

jph00 5y ago

On Nintendo Switch, Clubhouse Games includes hex: https://www.nintendo.com/store/products/clubhouse-games-51-worldwide-classics-switch/ https://www.nintendo.com/store/products/clubhouse-games-51-w... (There's a lot of other really fun and interesting games there too BTW - it's been very popular in our family.)

derbOac 5y ago

I was interested in this game quite a bit for awhile when I was much younger, but then read an article or something stating that the first player has a strong advantage and that they have a guaranteed route to win simply by virtue of playing first. I'm not sure if this is correct or not but it was my understanding at the time, and it kinda dampened my enthusiasm.

a1445c8b 5y ago
That’s why there’s the “swap” rule.
- JTBooth 5y ago
  After which the second player has a guaranteed route to win, but it's much harder to find! Last I checked the game tree was computed up to a 6x7 board, players usually use 13x13
  - hanche 5y ago
    I used to play it quite a bit with a friend back in my student days, on a 12×12 board. We were aware, in principle, that the first player had a winning strategy, but in practice, the advantage to the first player was small enough to hardly be detectable (though we did not compile any statistics on it). Perhaps this only serves to reveal that we weren't terribly good at it, though. We weren't aware of the swap rule at the time.
    - aidenn0 5y ago
      That's slightly surprising since playing in the middle of the board on your first move is such a large advantage. Beginner players do seem to think that playing near a black side is a good opening, but it's actually one of the weakest, but playing it "quite a bit" I would suspect you would stumble on playing near the middle by accident if nothing else?
      - hanche 5y ago

deleted 5y ago

[deleted]

kqr 5y ago

I feel like I've missed something. This seems similar to go (yet different in several important ways, of course), which I do know. Is there a relationship?

tromp 5y ago
Both heavily feature stone connectivity. But where connecting your sides with a stone chain is the goal in Hex, connected stones sharing liberties is only used to define capture in Go, and the goal is instead to take the most territory.
- bskrobisz 5y ago
  I think, if you're familiar with go, this is an uncharitable reading of the question. The victory condition in this game is very directly analogous to a not-uncommon source of (sometimes-game-deciding) violence in go--two nearby weak groups where connection means a decisive victory for whichever player achieves it. Having not played Hex, I can't say whether it's strategically similar (although just from the first couple of chapters, there are definitely similar concepts of important shapes and ladder breakers).
  - vintermann 5y ago
    There was a variant combining Hex and Go which was popular (as these things go) on online abstract games sites a few years ago. Square board, capturing like in Go, but the goal is to connect sides like in Hex. This game degenerated to "primitive Go" most of the time, because both sides blocking each other is easy on a square board, and at that point it's down to who has the most territory (most free moves to fill in their own areas without being captured. I've played both on a modest level. I'd say that Hex, at the sizes we typically play at, is a lot like one big Go fight. I find it easier to look far ahead in Hex since pieces are never removed, ladders are (even) more common, and since non-overlapping templates ("miai" in Go) always connect you can build them together into huge parts of the board where you know you can connect.
  - kqr 5y ago

vintermann 5y ago

I used to play this game quite a lot, back when Six was the strongest AI opponent. Managed to beat it at 11x11, no chance at 8x8. At 13x13 it completely fell apart (but you had to kind of hack the engine to even play at that size, so it might have been buggy). Now I guess the AlphaZero-variants win everything there as elsewhere. There was a kid from Poland who was insanely good. Maciej Celuch. Don't know what's become of him, but wouldn't be a kid any longer. He was the top player by a mile, won the Little Golem tournaments every year he participated. A bunch of people from the same town in Poland were also really, really good, I guess they had a bit of a community going. The other place there was a bit of community going was in Oslo, a bunch of guys associated with the defense research institute (FFI). I went to an offline tournament with them once, to my surprise I didn't finish quite last. I think it's a satisfying game, because it's quite easy to learn to look far ahead. Since the pieces stay put, it's much easier to reason about positions. M. Seymour's online book is great, too. I've heard good things about Ryan B. Hayward's book. Cameron Browne is a nice guy and has done a lot of other cool work in combinatorial games, but I can't recommend his old Hex book. The tactics advice is not good.

natufunu 5y ago

I wrote a hex AI with a couple of friends a few years back based on reinforcement learning. https://cleeff.github.io/hex/ https://cleeff.github.io/hex/ You move first and the ai might swap meaning that it steals your first move and you swap colors. This enforces you to pick an even opening. I'm very bad at hex but it still was an awesome experience to observe the ai surpass my performance.

dematz 5y ago
Thanks for making this! As a fellow very bad hex player I have had a lot of fun inevitably losing to the agent. You might be interested in this - the one time I won, it seemed like a bug? I was playing red and blue could have easily won, but threw the game? https://i.imgur.com/4uyipte.png https://i.imgur.com/4uyipte.png if blue goes on the other 6.4 spot blue probably wins, if not red wins. Honestly I was about to give up on the game because the ai plays "mean" as noted in the readme - it always does close out favorable positions but doesn't prioritize the simplest/quickest win. This time I was annoyed at it or something though and playing it out was really surprised at that move it made. This may or may not be relevant, but it's interesting that the agent rates both the correct move and the move it made at 6.4, maybe that was part of the problem?

JoeDaDude 5y ago

Way back in the day, I wrote an AI to play hex based on the Genetic Algorithm, for which I drew inspiration from Blondie24, a checkers AI. At the time I didn't realize how much broader the search tree for Hex was compared to checkers. The results were disappointing. I had to reduce the board size to get even modest performance. [1]. https://en.wikipedia.org/wiki/Blondie24 https://en.wikipedia.org/wiki/Blondie24

jacknews 5y ago

Is there a 3 player version of hex, and it is as deep? google is not being my friend today.