Dr Eric Silverman

I promised last time to cover two of my favourite connection games, Unlur and Side Stitch , but you may notice the title of this post only mentions Unlur.  I should clarify that my plans haven’t changed as a whole, I’ve just decided to devote an entire post to Unlur instead of covering both games at once.  Unlur is a deep and challenging game, so it deserves a bit of explanation — and if I cover Side Stitch separately as well, I can also cover a couple of related games by the same designer (Craig Duncan).

Unlur came about as a result of a game design contest in the Abstract Games magazine back in 2002 — the Unequal Forces Design Competition.  The competition challenged designers to create games where the two sides are asymmetric — having different goals and/or different tools with which to achieve the game’s win condition. Designer Jorge Gomez Arrausi won by creating Unlur, a game that took on a very difficult design challenge: how do you create a connection game where the players have unequal goals, yet the game remains balanced?

The Rules

As with most connection games, the rules of Unlur are appealingly simple, but the elegant rules enable remarkable complexity to emerge in play.  The first phase of the game, the contract phase, is particularly unique in Unlur, so after introducing the concept here I’ll illustrate how it works in practice with some brief discussion of several real games.

A game of Unlur is played on a hexagonal board tesselated with hexagons —  the classic ‘hexhex’ board we’ve seen a few times now.  The designer originally recommended playing on a hexhex-6 board, but hexhex-8 is more common — for a deeper and more subtle contest, try hexhex-10 or larger.   The game works like this:

1. Two players, Black and White, compete to form connections between different sides of the board:
   • White wins if they connect two opposite sides of the board
   • Black wins if they connect three non-adjacent sides (corner cells are considered part of both sides to which they are adjacent)
   • If either player achieves the other player’s goal without simultaneously achieving their own, they lose the game immediately
2. Black’s goal to connect three sides is significantly harder than White’s goal, so a game of Unlur is structured so that the players balance the game themselves before they start playing in earnest.  At the start of the game, players are not assigned colours — instead they begin with the contract phase.  In this phase, the two players take it in turns to place a single black stone on any empty hex that is not on the outer edge of the board.  When one player judges that Black has enough stones in the right positions on the board to give them an equal chance against White, they may pass their turn — from that point they play Black, and the other player is White.
3. White then makes the next move by placing a White stone on any empty hex, and the players then take it in turns to place a single stone of their colour on the board.

Here’s the final position for a real game of Unlur on a hexhex-8 board played on Richard’s PBEM Server:

Black won this game by resignation — White gave up because Black’s three stones on the bottom right of the board completely cut off White’s attempt to connect the top and bottom sides, and also ensure an unstoppable connection for Black.  Ultimately Black will win by connecting the bottom right corner and top left corner to the bottom left side — remember that corner cells count as part of both sides they’re adjacent to, so Black will achieve their goal of connecting three non-adjacent sides.

The genius of Unlur lies in the contract phase.  Essentially the contract is somewhat like an extended form of the pie rule used in many other games, except here players are not assigned colours initially and have complete freedom to decide at what point Black has equal chances.  Since neither player has chosen a side at this point, both are invested in making sure that the board is equal at the start, so both will add stones in such a way as to ensure whoever elects to pass and take Black will be competitive but not dominant.  The contract phase is of course hugely important to the ultimate outcome of the game, and the completely open nature of it means that opening play in Unlur is both unusual and extremely varied.

The rule enforcing a loss if either player achieves the other’s win condition serves to ensure that draws are impossible in Unlur.  In practice this rule affects Black more than White — after all, White’s goal is more economical in terms of stone placement, so it’s less likely they will end up forming Black’s more difficult connective goal before achieving their own.

The contract phase in action

The contract phase is not only ingenious, it’s also complex — how do we decide when Black as equal chances?  What sort of moves for Black should we play to ensure equal chances without unbalancing the game?

There are basic rules of thumb we can infer from our experiences with other connection games: the centre of the board is very valuable, so central stones for Black are strong in the contract phase; and conversely, stones closer to the edges of the board are weaker.  So as a starting point, we can say that a contract with several central stones for Black would be quite strong, while a contract consisting only of stones close to the edge would require more stones to be placed before we’d consider passing.

The designer adds to this that stones that are widely dispersed are more powerful than stones placed closely together.  This often leads to players cautiously adding more stones for Black adjacent to already-placed stones — this still increases Black’s chances but changes the position less drastically than placing stones elsewhere.

Even with these basic ideas in place, judging when to pass in Unlur is difficult, and our decision will have to change depending on the size of the board — on larger boards, Black would need a larger contract to have equal winning chances.  Let’s take a look at a few example games on different board sizes, and see how different players have addressed the contract phase in actual play.

First we’ll look at a tournament game played on a hexhex-8 board in 2006 on Richard’s PBEM Server.  Black ultimately won this game, and the contract certainly proved important in this case — here’s the game position when the winning player chose to pass and take Black:

In this game the contract consists of just six moves for Black — given that the designer’s analysis on the smaller hexhex-6 board suggested that up to ten stones for Black could still constitute a fair contract, we might conclude that Black’s contract was too weak here.  However, remember our rules of thumb — Black’s stones are close to the edge, but also widely dispersed, so they provide a framework for later connections across the board.  The stones are also close to several corners, which count as part of either side they’re adjacent to, which again is helpful for Black.

Black’s win in this game made very good use of these contract stones, as we can see:

Note that all of the contract stones save the stone on H11 played an important role in subsequent play.  The two stones in the bottom left were ultimately blocked by White, but Black nevertheless slipped through the centre to connect the contract stones on the left and upper right with the bottom of the board.  So in this case Black’s judgement of the contract proved correct — the number of stones was small, but they formed a framework for connection that Black could exploit well enough to take the win.

Now let’s jump up to a hexhex-9 game and see how the contract phase evolved:

Now this contract seems even more risky than the last one!  The winning player took the contract after just three moves — this despite playing on a hexhex-9 board which has 217 hexes, far more than the 169 in the hexhex-8 board of the previous game.  Given our rules of thumb we can see that these moves are quite powerful for Black, however; two of them are quite central, and while the stones aren’t widely dispersed they do provide good coverage of the top and top-right of the board.

As it happens, Black was able to construct a nice win here:

Note that the two central stones from the contract phase formed a crucial part of the winning player’s connection — in fact the winning Y-shaped configuration spreads out directly from those two stones.  Clearly more centrally-placed stones are quite powerful for Black, and can enable Black to form a strong core for a board-spanning connection.

I’d argue though that taking this contract after just 3 moves was still quite a risky play — after all, the board is large and there was still ample room for White to manoeuvre and possibly isolate those stones.  We should remember though that the contract is only the first stage of the game, and skilful play can still make up for a less-powerful contract.

In that sense the contract phase in Unlur could also function as an interesting way to balance the game between two players of very different skill levels.  I suspect with some detailed analysis we’d be able to develop a reasonably granular system for constructing contracts that help bridge skill gaps between players — perhaps by constructing some pre-set contract placements tailored for different skill levels, or by giving one player additional stones to place in the contract phase.  As far as I know this hasn’t really been investigated in detail, but I’d be interested to see some testing of possible handicap play rules.

So far we’ve seen a couple of relatively small contracts — let’s take a look at some more generous ones.  First we’ll jump up in size again to this game on a hexhex-10 board, where Black takes a contract four times larger than the last one we studied:

Here Black took the contract after 12 moves.  The distribution of stones suggests both players were playing carefully, looking for a balanced and relatively straightforward position — all 12 stones are placed near to the edge of the board, and we see two large clusters of adjacent stones, which as we know are less impactful on the position than more widely-scattered ones.  Given the size of the board — 271 hexes, much bigger than the previous game’s 217 — 12 stones in this kind of configuration seems a reasonably fair contract, giving Black a strong framework around the edges but leaving the centre open.  We might expect play to focus on that open centre as Black seeks to connect these disparate islands of stones, and White tries to wind their way through the maze to build their own connection.

This ends up being pretty accurate, as we can see in the final position:

Black ends up building several strong walls around the centre, blocking White from easily connecting through the middle of the board.  White resigned at this point, as it’s clear Black can stop them from connecting to the top, while Black’s structure ensures unstoppable connection between the bottom, right and top sides.  In the end Black played cleverly here and utilised the strong points of this contract well — the contract stones helped restrict White’s playable territory along the edges, and Black’s subsequent play largely blocked them out of the centre.

Finally let’s take a look at another well-balanced contract, this time on a rather gargantuan hexhex-11 board (331 hexes):

Here Black took the contract after 15 stones were placed.  Note again how many of the stones are clustered together, reducing the overall impact of each placement on the position.  However in this case we have a stone placed right in the centre of the board, which is certainly helpful for Black.  Given the size of the board and the fact that there’s just one central stone, 15 stones seems like a reasonably fair contract for Black.

The resulting game, another Black win, develops in an interesting way.  In issue 12 of Abstract Games, the designer of Unlur explores this kind of opening position and a resulting position called the arrow opening, which we can see in supersized form in this game after the above contract:

In this arrow game, White is in quite an unfortunate bind — their long wedge of stones on the bottom-right is completely hemmed in.  If we were speaking in Hex terms, we’d say that nearly all of White’s stones are dead — unable to take part in any winning connection.  Black has blocked the corner at U11 and constructed a vast wall as well, making a White connection between the lower-left side and the upper-right completely impossible.  White’s attempt to snake around the right side to connect to the top is easily stymied by Black using the group of stones on and around D14, so White’s position is utterly hopeless.  Black can easily win by connecting to the upper-right side — note this also forms a line, but since Black already connected the bottom (using the corner cell) and the upper-left, Black’s stones would form a 3-way Y connection at the same time, securing the win.

Hopefully these few examples can serve as a useful preview of what a sound contract for Black can look like in Unlur on some of the possible board sizes.   The number of possible contracts on any given board size is absolutely enormous — contract length can vary a lot, as we’ve seen, as well as the positions of the stones.  In the face of all this variability,  a few rules of thumb and experience are the best we can hope for; there are so many ways the contract phase can evolve that set opening sequences are not particularly useful.  Besides, your set opening can easily go awry if your opponent decides to go another way — after all, you’re building the contract together, not separately!

After the contract phase, you’ll find yourself using some of the same basic concepts you might use in other connection games like Hex or Y — bridges and so forth.  However Unlur is significantly different in one very important aspect: your own stones are never a liability in Hex or Y, but they definitely can be in Unlur!  You lose the game if you form the opponent’s connection before your own, so having poorly-placed stones scattered around the board can make this outcome more likely.

During the middle- and end-game of Unlur, it’s also worth keeping in mind some key configurations that ensure a win for one player or the other:

In the above pattern, Black completely controls three sides of the board.  In this configuration White cannot win — White would need to connect to one of the sides controlled by Black.  White will lose either when Black successfully connects or when they are eventually forced to make a foreign connection.

When White completely controls two opposite sides, Black is completely lost.  In order to connect three non-adjacent sides, Black would need to use one of White’s controlled sides, which is impossible.  Meanwhile, White still has several different ways to make a winning connection.

This pattern is another one that hands a certain win to White.  White can still connect to the top to form a winning line, but Black can’t break through — he can only form a losing line in the attempt.

During the game, watch out for your opponent working toward these configurations — don’t let them get away with it!  We can easily forget the ‘foreign connection’ rule and end up in a situation where we’ve unwittingly entered a board position where the foreign connection is the only one available to us.

Resources and where to play

Despite being a relatively well-known connection game and widely respected for its elegance and uniqueness, strategic advice on Unlur is rather hard to come by.  Your first stop should be issues 11 and 12 of Abstract Games — the game is introduced in issue 11, and the designer provides some background on his design decisions and some strategic advice in issue 12.  Note that he only covers hexhex-6 boards, as he felt that larger boards were too complex:

“…Unlur over a board with eight cells per side becomes very complex and difficult to understand, so now we prefer to play on a board with six cells per side.”

However, since those articles were published many players have come to prefer larger sizes, because there is greater scope for strategic intrigue.  I personally prefer larger boards as well, partially because the contract phase takes up a bit less of the overall play time on a larger board, which to me feels a bit better balanced in terms of the playing experience.

From there, you can check the archived version of the designer’s website for further tips, but unfortunately none of the images appear to work anymore.  Other than that I can’t really find any detailed strategic discussion anywhere, which is quite a shame.

That being the case, the best way to learn is to try playing some games.  Unlur is well-known enough that there are a few options for online play: Gorrion (supports hexhex-8, 10 and 12), Richard’s PBM Server (supports from hexhex-4 all the way up to 13!), igGameCenter (supports hexhex-8 and 10), and Ludoteka (supports hexhex-6 and 8).  Unfortunately all these servers are somewhat lacking in Unlur activity, but I’m sure you could rustle up a game or two via BoardGameGeek… or simply contact me if you want to arrange a few!

If you want to play in real life, I’ve made some Unlur boards in a range of sizes — hexhex-6, 7, 8, 10 and 12 — which are directly derived from the original Unlur hexhex-6 board offered in Abstract Games magazine.  I posted them on BoardGameGeek with permission from Kerry Handscomb of Abstract Games.  There are two versions — one with the original muted bronze board colour and grey background, the other with a white background and lighter board colour.  Both are in PDF format and look great printed out on a gaming mat — you can see my own neoprene-printed version below!

Summing up

Unlur is a game of genuine ingenuity, and it offers unique wrinkles you won’t find in any other connection game.  The contract phase is a fantastic addition, artfully accomplishing the difficult design goal of a balanced asymmetric connection game.  Finally, it’s fun — the contract phase is tense, forcing you to constantly second-guess your opponent and think carefully about each stone and how it will affect the coming game; and the subsequent connection battle feels even more consequential than in other games, given that your own misplaced stones can come back to bite you, potentially forcing you to make your opponent’s connection and lose the game.  I give this game my highest recommendation and hope some of you might consider giving it a try.

Related Games

Before I move on I’d be remiss not to mention Cross, Cameron Browne’s connection game inspired by Unlur.   Cross is also a connection game played on a hexhex board, but here there is no contract phase — instead, players both are striving to connect three non-adjacent sides of the board, and either player will lose if they make a line connecting two opposite sides of the board.  The game plays very differently than Unlur, but the shared element of the Y-connection wins/line connection loses dynamic leads to some tense situations, much like the middle/late-game of Unlur.

Conveniently, you can buy a physical Cross set with a hexhex-7 board from Nestor Games — and the components are generic you can play Unlur on that set too if you want!  Nestor also offers hexhex-8 and hexhex-10 boards via the games Iqishiqi and Omega respectively, if you want to play larger games.  Cross is also playable on Richard’s PBEM Server.

While I’m here I should also mention Coil — an intriguing game by Nick Bentley that adopts Unlur’s contract phase mechanism.   In Coil, players start with a contract phase as in Unlur, except the board starts with black stones in each corner cell, and stones placed during this phase cannot be placed adjacent to one another.  Once someone passes and takes the contract as Black, that player must then try to form a loop of Black stones (a loop being defined here the same way as in Havannah), while White tries to prevent the loop from being formed.  If Black forms a loop, they win; if the board fills up without a Black loop, White wins.  Coil is an interesting take on the asymmetric connection game, and ends up feeling quite different from Unlur.  Again it’s playable on any hexhex board with black and white stones, so definitely give it a try after your Unlur games!

Nick Bentley also designed another game with a loop-formation win condition and an Unlur-esque contract phase — Bobina, where players bid not with the black stones but instead with grey neutral stones that can help either player form a winning loop.  The concept is very clever but a bit hard to explain briefly here — I’d recommend you go have a read of Nick’s blog post to get a clear picture of it.  This is another interesting take on the contract phase, and definitely worth a try if that aspect of Unlur appeals to you.  I have to say I slightly prefer Coil due to the simplicity of that game and the asymmetric aspect, but Bobina does offer a unique twist with the neutral stone element.

That’s it for our in-depth look at Unlur — next time I’ll cover Side Stitch and sister games Exo-Hex and Iris.