Patterns of Tak: Ladders

Another fairly basic Tak shape is a ladder — two pieces with touching corners. A ladder isn’t fully connected yet, but there are two ways to do so. Thus, it is pseudo-connected because you are guaranteed an opportunity to fully connect. Ladders do not immediately extend in either direction, but open up an extra lane for expansion in both. Although a ladder may have a specific direction in mind, this is strictly a consequence of its surroundings — on its own, it is perfectly noncommittal. In this way, ladders are very difficult to defensively pin down; if your opponent defends one direction you can simply reroute along the other. The ladder effectively indicates that you are waiting to see what your opponent is up to and plan to react accordingly.

lanes_of_expansion

The bolder arrows indicate the ladder’s primary lanes for expansion. However, the thinner lines are still perfectly viable lanes; if developed, they would benefit from having a nearby off-lane piece providing (re)capture potential.

Since ladders are a “wait-and-see” shape, it’s worth talking about their follow ups. Obviously, if your opponent intrudes on one of the crucial points it is no longer a pseudo-connected shape, so you will want to play locally unless there is very high-value move elsewhere. Note that the presence of such a high-value move should be uncommon, as it would also shift your opponent’s priorities away from the ladder. Thus, ladder intrusion indicates that this area is now a point of contention and invites a local response. Unless you have other resources that you want to relate, finishing the connection (aka taking the other crucial point) is your best bet.

crucial_points

The highlighted squares are the crucial points of the original ladder. In this example, Black has intruded one of the crucial points and White has responded simply by taking the other, thus fully connecting her pieces.

You could also elect to create an extended ladder by adding more corner-touching pieces along the same diagonal. This continues your wait-and-see policy, but has diminishing returns in terms of expansion because it commits extra full-connection moves in the future; in other words, increasing your longest path along the diagonal is slower than along the vertical/horizontal because it takes more pieces. But despite the expansionary slowness, it firmly takes lanes of expansion away from your opponent — they will not be able to build through your ladder without it being a Pyrrhic victory.

extended_ladder_lanes

An extended ladder has many lanes to expand on. However, as with a regular ladder, not all of these lanes are as efficient; as such, the bolder lines indicate the more reasonable lanes. Having pre-existing pieces in each of these lanes is also beneficial for defensive purposes. Despite not wanting to focus on expanding in the weaker lanes, White’s presence may be blocking some of Black’s potential.

In contrast to a basic ladder, an extended ladder is not quite pseudo-connected; your opponent could cut the shape with multiple walls/caps and at least one capture. However, this would be a significant defensive investment. In this way, extended ladders are the first of a broad class of powerful shapes which I will refer to as strongly connected — requiring multiple walls/caps AND at least one capture to cut. Additionally, a cut ladder can shift it’s focus to a single direction without losing local tempo.

strongly_connected

There are many possible permutations whereby Black could cut an extended ladder. Inevitably it will require getting a wall in the middle of the ladder, however it will also require a second wall in order to prevent White from getting to crawl around the center wall with flats. In this example, White has matched Black’s intrusions on the critical points and has a fully connected shape; Black will need to capture the center with one of his walls to finish the cut.

A more direct follow-up to a ladder is simply adding partners. As per my discussion on partners, you primarily want to do this when you’re sure that this is an area of contention or have time to press the initiative. Unless the partner fully connects the ladder (more on that later), it constitutes a directional commitment that gives your opponent a heads up about where they can try to block you. Note that this is the transpositional equivalent of following up partners with a ladder, and though it has a directional focus it is not fully committed to a single lane in that direction.

adding_partners

White has added a partner to her ladder and is now focusing on a North-South path. Although the North-facing side of this shape is more committed to a single lane, the South-facing side is still quite flexible. And, while this is not doing as good a job in the East-West direction as an extended ladder, White still could still seek to turn back in that direction if Black overly defends the North. For instance, she might extend Northeast off her partners with a new ladder to add a lane to the North-South threat while planning for future East-West development.

As with partners, the edge of the board has a big impact on how ladders operate. One of the most powerful uses of a ladder is in developing out of a corner. By pseudo-connecting to the corner you immediately make it relevant to all your future plans. This isn’t as flexible as central partners because half of it’s development lanes are edge-bound, but by incorporating the corner you are being efficient with your pieces without committing to an edge-crawl. Additionally, the directionally ambivalent nature of ladders is well suited to the corner, where you have a preexisting edge connection in both directions simultaneously. Note that for quite the opposite reasons, a ladder that develops ‘around’ a corner (i.e. the only way to make a ladder where both pieces is on an edge) is quite weak — this is basically an edge-crawl that doesn’t gain any tempo (arguably the only thing that edge-crawl is good for in the first place).

corner_ladders

White has staged a nice entrance into the center of the board with a ladder off her starting H1 flat; this promises future development either North along the G-column or West along the 2nd-rank. Meanwhile, Black has a very disfunctional ladder; it doesn’t contest White’s initiative and its primary lanes for expansion (South along the A-column and West along the 8th-rank) are both edge-bound.

Ladders off the edge are not quite as intuitively powerful as ladders out of the corner. Although it is pseudo-connected to the edge, the directional flexibility isn’t particularly potent since some of your lanes of expansion would be edge-crawls. Moreover, partners arguably do a better job of extending off the edge because you don’t have to futz around with the minor tempo-distinction between fully and strongly connected. It is also a little bit easier to build through a ladder than it is to build through partners, and so it offers less of a defensive deterrent.

ladders_off_the_edge

Consider the difference between Black’s partners off the edge and White’s ladder off the edge. In both cases, the central piece has been flanked on both sides by opposing flats. However, the ladder is slightly easier to build through. Black could place on either H3 or F3 from which to eventually capture G3 (and thus connect G2/G4); whereas White can only develop a capture on B6 from C6 (and thus connect B5/B7).

A ladder with a capstone is extremely potent. In fact, a preexisting capstone arguably benefits far more from a ladder than a partner. One of a cap’s most important functions is to control an area of contention (an area through which both you and your opponent are trying to build). At least at first, your cap doesn’t really need a partner to fulfill this role; and more importantly, the ladder’s lack of directional commitment gives the cap more potential to play an active role. Moreover, caps move so strongly that you don’t necessarily need to respond to an intrusion by taking the other crucial point. The cap opens up a plethora of options that morph seamlessly into a local victory, even when doing so involves taking prisoners.

cap_controlling_crucial_points

The presence of a capstone in White’s ladder makes it more viable to consider responses to a ladder intrusion that don’t take the other crucial point. In this setup, instead of fully connecting her shape now, White has elected to place a flat which develops North-South more directly. Although there are other options, this position anticipates that her capstone will eventually capture Black’s flat in order to fully connect her pieces.

Patterns of Tak: Partners

Let’s imagine for a moment a game of Infinite Tak, with infinitely many pieces and played on an infinite board. What would happen? For starters, such a game would never end — the end conditions rely on either a finite board or finite pieces. Also, black starts at a comparably minuscule disadvantage as he literally has all the time in the world to catch up; indeed, this is true for either player when they fall behind in any way. But the lack of an achievable victory doesn’t makes this analysis futile, we just need to redefine the objective. The goals of this game can be stated fairly simply. At any given time, you are trying to: 1) have the longest connected path, and 2) have the highest flat count. Note that in order to match the finite game’s rules, the “length” of a path isn’t its Euclidean distance, but rather its width or its height (whichever is greater). In pursuit of these goals — or perhaps just out of sheer boredom — some interesting patterns will eventually emerge, and it’s an intuition for these patterns that I want to build. In this open-ended series of posts, I will be introducing various patterns as though they have arisen in the context of Infinite Tak, and then selectively delve into how this understanding extends to the finite game.

 


 

Beyond a solo flat, the most basic pattern you can make is a partnership — two touching pieces. A partnership is a fully connected shape and may thus add value to your longest connected path immediately. This is the most cooperative pattern of two pieces because they directly support one another. Although the partners only extend in one direction, they also provide orthogonal redundancy as a tempo-neutral recapture and by creating an extra lane for expansion. In fact, this redundancy is arguably more valuable than the extension, which stubbornly commits to a single lane and loses directional tempo when recapturing.

lanes_of_expansion

These partners extend in the East-West direction, but continued extensions have to follow the same unbroken lane. Meanwhile, they do not extend in the North-South direction, but have two lanes in each direction with which to do so in the future.

Partners are well suited to hotly-contested regions, where building local influence is vital. And if you can correctly anticipate competition in an area, adding partners there preemptively will be a fantastic asset. However, partners can also be an over-commitment of resources; in less important areas a looser shape might be more appropriate. Since they expand your influence so slowly, you only want to add partners away from the action when you have time to “press the initiative”. There are two common scenarios when this will be the case: 1) you have thoroughly dismantled a segment of your opponent’s path and want to build out your own, and 2) when you have thoroughly dominated an area of contention and want to increase the value of that victory by supportively extending away from the area.

partners_off_of_local_victories

White has a strangle-hold on the circled region, in large thanks to her capstone. She has a lot of East-West development coming out of the contested region and has chosen to add a partner to the East. This increases the value of her victory in the contested region. Or, if you prefer, it accentuates the irrelevance of Black’s pieces in the region.

Getting away from Infinite Tak, we find that edges introduce some caveats to the partner shape. Partners that both connect to the edge are a basic form of “edge-crawl”. This is not a particularly strong shape, offsetting the orthogonal redundancy benefits by foregoing potential influence. Your opponent can seek orthogonal partners in the path of your extension, which provides a relative benefit to both their tempo and influence. And if you block their edge partner, it creates a wall-able hole in your edge-crawl that will either devastate your tempo or draw your capstone out of position.

obstructions_along_edge

On each side of the board we see how the edge-crawling partners A2 and H2 might play out. In the West, White placed at B5 only to be given the opportunity to grab an edge-partner that Black will have a terrible time overcoming. In the East, White hasn’t allowed an edge-partner on H5, but has created a hole road which Black chose to fill with a wall. Edge-bound caps can be quite poor, so this effectively invalidates the H-column road. In both cases, the defender has needed relatively few pieces to invalidate their opponent’s edge-bound initiative.

In contrast to edge-crawling, it is actually quite valuable to give an existing edge piece a non-edge partner. Attachments to the edge are important because they are necessary to actually finish a road, and so you should prize your pre-existing edge pieces — having to re-attach to the edge can sometimes be tricky. Indeed, a preemptive center partner is invaluable because it will never need to recapture the edge; if your opponent develops an edge-bound attack, then you can back up the edge piece with another partner. Note that this is a unique feature of edge positions specifically because they have an odd number of neighboring positions.

parters_off_edge

E1 only has 3 neighboring locations. Now that White has E2, she can guarantee superior flat influnece on E1 (if Black takes either of the highlighted locations, White can respond by taking the other). In this way, she has shored up her connection to the edge without sacrificing any raw influence.

Partners near the edge can also be quite powerful. Although partners add an additional lane for orthogonal expansion, this strategic influence decays the farther away you get. In other words, once you start to develop orthogonally off of partners your path starts to look much narrower; alternately, your opponent can still effectively get in the way of both lanes if they start their defense far enough away from you. Thus, partners near the edge are an excellent way for ensuring an eventual attachment to the edge because their dual-lane flexibility has not decayed.

partners_near_edge_tinue

This is a very basic example of Tinue that White has found because of the partner on G4. Despite not being a compound tak (or a road threat), after blocking with a flat on H3, the only proper response to G4 would have been to capture G3. White will now win in at most three turns, and having had to play at most one more piece.

Back to our more abstract Infinite Tak reasoning, capstones are obviously an excellent partner for any solo flat. Consider the ultimate objective of the partners. If they are being created for extension, then the capstone is liable to remain a passive anchor for your position. If they are being used more for flexibility reasons, then you are anticipating a much more active cap whose function will be to reclaim captured segments of your road. As always, capstones are best played where the action is thickest, but they do not necessarily need to be active in order to achieve value — they will continue to pay off as long as they remain relevant.

capstone_partner

White’s capstone is not particularly interested in moving as long as she continues to develop in the East-West direction. However, it has several paths of interest to move as part of later developments in the North-South direction: 1) it might recapture future pieces directly North/South of its current location, or 2) it might recapture (or deputize) its current partner and then run North/South from there.

Strategy 106: The End Game

So you’ve gone toe to toe with your opponent, thwarting each other’s roads at every turn, and now it’s beginning to look as though you are competing for a flat win. First of all, congratulations on making it this far. The ability to get this deep into a game of Tak without either of you getting tricked onto the road to Tinuë means that you have both played a beautiful game. However, the tools that have gotten you to this point will no longer be sufficient to carry you to victory. The board is likely polluted with enough walls that the initiative has little or no meaning. Instead, you should be concerning yourself with each player’s current flat count and remaining piece count, and focusing intently on the flat-count differential of possible moves.

flat_count_differentials

In this example, White currently has a flat count lead of 2 (6 – 4). Also of importance, white has 7 remaining pieces to black’s 10. White looks to be able to make an important tak threat by placing at D1 or E2, but Black is prepared to defend with the +2 flat-count differential move 3E< which will fight his flat count deficit back to 1. After that exchange, White will need to be careful not to feed pieces to black’s walls at A2/B3. Despite having a companion each, neither of them can currently make a +2 flat count move. White will likely have to respond to black’s road threat after he plays on A3, but she should be able to do so without hurting her flat advantage by sliding her cap to the center (2C4-). Moreover, she always has the the +2 flat move 2D2< in her back pocket if it becomes necessary.

When you have the flat count advantage and have fewer remaining pieces, you are firmly in the driver’s seat. Simply playing additional flats continues your inexorable march to victory. This is doubly powerful when it also places your opponent in tak since the forced responses likely don’t help them catch up in flat count; moves of this nature maintain your lead and effectively run out the clock  on your opponent. However, despite your distinct advantage, you also need to be wary of your opponent finding high flat-count differential moves. Make sure to guard your prisoners tightly, either under or near walls/caps to restrict your opponent’s ability to release them. Also pay extra close attention to your opponent’t ability to put you in tak. If your opponent forces you to capture, they may be able to leverage those new prisoners. Well-placed flatstones, or even a wall that doesn’t lose your flat count advantage, will limit their ability to find an edge this way.

fewer_pieces_and_flat_advantage

White has a pretty sturdy flat count lead of 4 (10 – 6), and has fewer remaining pieces (5 to Black’s 6). Black has a +3 flat count differential move in 4E5-22, but doesn’t hold up well against White’s ability to flat E5 in response. White does need to be worried about tak threats that try to reclaim the prisoner on A2, but should have adequate responses. It is probably in White’s interest to simply lay a flat somewhere and force Black into an inadequate capture (he won’t be able to flat without losing immediately because the board is nearly full).

Conversely, when you are behind in flat count and have more remaining pieces than your opponent, you are in a tight spot. Putting your opponent in tak can be useful, but only if it makes them capture in ways that you are prepared to directly exploit. You should shift your focus away from road building, and instead concentrate your efforts on controlling and then running stacks to achieve flat count parity.

more_pieces_and_flat_disadvantage

This game is very close, Black is down by a single flat (8 – 7) and has more pieces left than White (9 to 6). However, he’s managed to find some useful stacks that give him some +2 flat differential options (2B4>, 2B4-, and 1D5>). He could capturing B1 or E1 to create a road threat and force White to take on another prisoner. 1D5> is probably Black’s best option for gaining the flat count advantage since he has his captstone nearby for support. After this, he will need to be careful about White’s tak potential but can otherwise start laying flats to try and catch back up in “played piece count”. 

Things are less clear cut when you have the flat count advantage but have more remaining pieces. This advantage is precarious because you have more prisoners than your opponent and are further from ending the game via playing all your pieces. You are still interested in guarding prisoners and placing your opponent it tak, but the goal is no longer to run out the clock as quickly as possible. Instead, you should focus on placing more pieces than your opponent, and on how to weather the storm when they inevitably find ways to release prisoners.

more_pieces_and_flat_advantage

Black has a slim flat count lead of 1 (7 – 6), but has more remaining pieces than White (10 to 6). It is a tenuous lead because he has so many prisoners under B4 and C3. He especially needs to be concerned about White finding a way to flatten his wall and reclaim all its prisoners. He will need to try to keep his pieces well coordinated, eventually forcing White to capture in response to played flats, and play keep-away with the wall-prisoners as long as possible (and find a way to mitigate the damage if White does manage to release them).

Walls and captstones are pivotal pieces in the end game. Although you should avoid over-walling in the midgame, having some pre-existing walls can be quite valuable when you transition to the end game. Similarly, the more prisoners your cap accrues in the midgame, the less valuable it will be in the endgame, so be extra sure that the prisoners it does take are productive exchanges. Finally, although placing new walls during the end game may seem like a losing proposition, be on the lookout for sequences that build up a tall/zebra stack only to be immediately attacked by a new wall. These kinds of exchanges either concede the stack, force it to run, or force it to be claimed by a pre-existing wall/cap. Depending on its surroundings, these may be extremely uncomfortable options for the winner of the stack.

walls_may_be_necessary

This is an incredibly tense game that is very near a conclusion. Despite a flat count lead of 1 (9 – 8), White is nervous about her prisoners on E4 and B5, and sees that Black has a +4 flat count differential move in 4A4-112. Moreover, her capstone is nearly frozen with the weight of all those prisoners. In fact, it might be fair to say that Black’s position looks much stronger. She probably wants to start with 3A3-12 to force Black’s cap to run to A1 (where it will be frozen for the remainder of the game, but will then need to fight back for flat count (probably starting with tak on A4, and then even consider if a wall on C2 to try and liberate the D2 prisoner might be viable). Whatever she does, she’ll need to do it quick, because after 4A4-112 Black only needs to find time to play 4 flats to win the game. 

Strategy 105: Walls and Capstones

You will no doubt have been wondering about the conspicuous absence of walls and capstones from my Strategy 101 posts thus far. Indeed, all of the topics I’ve covered thus far are dramatically altered by the presence of walls and caps. However, I feel that effective application of these powerful pieces is an additional layer of complexity that deserves its own post.


 

Both walls and capstones are able to disrupt your opponent’s progress towards a road more effectively than a flatstone. When your opponent tries to crawl around your obstruction, you will be able to capture along their road and shift focus toward an area where you have more influence. For the purpose of contesting the initiative, walls and capstones are nearly identical in their ability to slow your opponent’s progress. However, capstones should be reserved until they can serve a dual purpose — both slowing your opponent and being a formative part of your own road. Note that plugging holes in a unidirectional road provides a bigger tempo swing than walls/caps that merely block progress. You should exploit these weaknesses immediately (and avoid creating them yourself for the same reason).

initiative_cap_dual_purpose

After white has played on D3/D4, she is very single-minded about creating a North-South road. Knowing that he is terribly behind in tempo, black plays his capstone on D2. Although this may seem premature, D2 is both a weak point in white’s North-South road and can serve as a linch-pin for a developing East-West. Black can assuredly get one of the highlighted areas (E2 or E3). If he gets E3, then his capstone is in prime position to capture D3; or, if he can get E2 then the capstone will likely remain stationary for quite some time as black will angle towards linking up with A1.

wall_the_hole

After white begins with an edge-crawling E2, black takes D4. As we have seen in previous examples, it will be uncomfortable for her if black also gets E4, so she takes it herself. However, this creates a hole in white’s formation which black can powerfully fill with a wall.


 

Capturing with walls and caps is stronger than capturing with flats, but should still be avoided unless it serves a greater purpose. In addition to contesting the initiative, these pieces are extremely well suited to liberating captives because they will have an easier time controlling the prisoners you take in doing so. Indeed, their power to release prisoners is so strong that capturing with flatstones needs to account for the possibility that a new wall/cap may be placed in response.

bad_capture_followed_by_cap

White is considering capturing C3 or D4 (C4> looks particularly tempting). However, doing so would likely see black’s respond with his capstone in the vacated location. This would be terribly problematic for white, so she should not capture.

You will, however, want to be cautious about liberating too many captives with a single piece. Walls need to be careful not to let themselves get flattened with too many prisoners in tow. Similarly, your capstone will have a more difficult time flattening walls if it already has a lot of prisoners. As a general guideline, only use your cap to liberate prisoners if it puts your opponent in tak or solidifies the initiative — in other situations, a wall or flatstone will suffice.

cap_cant_flatten

Black’s capstone would be delighted to crush white’s D3 wall and liberate its captive, but this would be ill-advised because it would surrender an incredibly powerful stack of 3 white flats. These would immediately run West (or maybe North) and turn what was looking like a black-favored game on its head. Although in this case black has eked out a slight lead by taking these prisoners, the disadvantage of not being able to flatten walls later should still be taken to heart.


 

Stack mechanics are modified slightly when controlled by a wall or capstone. Throwing a wall-controlled stack may give you just enough reach to stop a remote tak theat or liberate a particularly soft stack. Throwing a cap-controlled stack is even better, since it can flatten walls. Moreover, a thrown cap that puts your opponent in tak may give you an opportunity to reinvigorate your cap via a sequence which transfers control of some of its prisoners to other pieces.

prisoner_transfer

White’s cap is starting to look a bit sluggish, having taken on 2 prisoners so far. However, white could actually seek to reduce this prisoner count by flattening C4. This would put black in tak and, since black can’t use the stack surrendered on C3 to escape tak, give white the chance to put her C2 wall in charge of the prisoners instead.

Conversely, a wall-controlled stack doesn’t run quite as potently as a normal stack because it can’t directly finish a road. Running a capstone-controlled stack is extremely powerful, although be careful not to run the cap out of position (it will not be particularly effective on the edge). More to the point, the ability to run over your opponent’s pieces can potentially be an existential threat. Don’t be afraid to let a centrally-located cap stack linger; your opponent will not have an easy time hemming it in (with walls or his own cap). Look for that special opportunity when it can either move with devastating effect or find an even better perch (or both!).

cap_stack_patience

White managed to snag a powerful stack on C3 with her cap. However, it is so well-positioned that black would not be able to hem it in easily. Her patience with this stack has been rewarded, having waited for the numbered moves to be played first. Now if she runs her cap West to A3 black will be in Tinuë!


 

Walls and caps are excellent at establishing or maintaining local influence. They serve as a strong deterrent against nearby captures, and shift your opponent’s focus elsewhere on the board because further material development in the area will have diminishing returns for them. Although playing a wall has a flat count opportunity cost, it should be treated as a long-term investment that just needs to eventually pay for itself. Having too many walls makes it difficult for all of these investments to pay off, but a few walls spread carefully across the board should be able to do so with dividends.

wall_investments

At first glance, black may appear to be in a tight spot; white has the initiative and is up by 2 in terms of flat count. However, his walls are poised to swing things drastically in his favor. After using his walls to liberate the B2 and E4 captives, he will not only take the flat count lead (after running to D2/E2 respectively), but also be in a far better position from which to create road threats.

Since capstones provide much stronger influence than walls and don’t sacrifice any tempo, you will typically want to get them into the fray before your first wall. However, it is also important to note that an edge-bound cap will not be able to live up to its full potential. It provides less raw influence and may even get trapped on the edge by an opposing wall/cap. As such, you will want to deploy your cap as centrally as possible so that it can exert and imply maximal influence. Conversely, walls are perfectly content on the fringes, especially defensively. The edges actually make them harder for your opponent to work around, and they can either avoid your opponent’s cap there or bait it out of position.

edge_wall_center_cap

Similar to the previous example, black has a wall poised to liberate a captive on E4. This was a good place to use a wall because the E4 stack likely would have just run away from an E5 cap. And unlike the previous example, black has found a central location for his cap which is also threatening to liberate a captive (on B3). White will be in dire straights once black’s capstone and wall have had a chance to act.


 

As a final note, flattening walls with your capstone can be tremendously powerful, but as with all forms of captures should be approached with caution. Don’t get lured into wall-flattening to score “style-points” — those don’t help you win the game! Pretend that the wall is just a flat that you’re thinking about capturing with your cap and ask yourself if that capture is really worthwhile. The most compelling reasons to flatten walls will be to release otherwise inaccessible captives, or if you can develop a beneficial sequence of moves that is only possible with a “leveled playing field”.

tempting_wall_flatten

Although wall-flattening looks cool, it would be premature for white to flatten black’s wall on E3 right now. Black would likely just respond on E4, maybe even with a wall. More over, it would develop an edge-bound cap that will not be as useful in the long run.

Grabbing a deputy, despite reducing your flat count, can be worthwhile if you anticipate that wall-flattening will eventually be desirable. As is so often the case, this is ideally done with a dual purpose in mind; for instance, threatening to run over an important part of your opponent’s road or restricting the movement of your opponent’s capstone.

worthwhile_deputy

Despite it temporarily reducing her flat count, this might be a good opportunity for white to grab a deputy on C3. She will likely want to leave the cap stack on C3 a few turns — just until she figures out whether she prefers a North-South threat (via flattening C4), or an East-West one (via capturing B3).

Strategy 104: Competing for Influence

As your strategies evolve, you will likely come to the conclusion that the center of the board is somehow more valuable than the edges (and the corners, eww!). There are several reasons for this, but the most basic is that pieces placed in the center exert influence on more places (4) than pieces placed on the edge (3; a measly 2 in the corners). Increasing your raw flat influence is not a worthwhile goal in and of itself, but it serves as a nice tie-breaker between otherwise equivalent moves that you are considering. This is an extremely long-term plan which intends to develop stack influence in more places on the board than your opponent, thereby increasing the diversity of road threats that you will eventually bring to bear.

raw_influence

In this example from the standard neighboring corners opening, white has played at D3, B4, and A4, to black’s A2, A3, and A5. Although black’s pieces seem more well-aligned, white still ostensibly has the initiative. It is white’s turn and she can make a road in 3 turns by playing on C4/D4/E4. Black looks to be 2 turns away from a road if he begins by capturing A4 (this puts white in tak), but white can simply play on the spot that black vacated to gain stack influence on A4. Thus, black is really 3 turns away from a road via playing on B3/B5 and moving it twice to get to A4. The primary difference between white and black’s positions is that each of white’s numbered pieces is exerting 1 more flat influence than its black counterpart, for a total of 3 extra flat influence.

From this perspective, all non-edge spaces may appear functionally equivalent, however this is not quite the case. This is true for solo flats, which only have a reach of 1, but as taller stacks develop, your more-central stacks have more room to run and thus exert more influence. Similar to how non-edge flats develop more influence than edge flats, by placing pieces more centrally than your opponent you are developing higher “quality” influence. When it comes time to convert your center influence into control of central stacks, your newfound control will exert its own influence more potently.

center_influence

White and black each have a hard stack with 2 companions exerting influence on a total of 8 spaces on the board. However, white’s stack can run out fully in all directions, whereas black’s can only run out fully south or east. This effectively gives white more options for using her stack than black has with his.

Capturing, especially when it liberates captives, in order to exert new influence actually applies to the entire board, not just the center. Stack influence is, in fact, so powerful that it makes sense to say that the options available to you after capturing constitute implied influence of your current position. We can begin to quantify the benefits of a central-leaning position, in that it develops more implied influence across the board.

implied_influence

In this example, white’s prospective capture of C3 implies more flat influence (on A3/B3/C1/C2/C4/C5/D3/E3) than does black’s prospective capture of A4 (implying only A2/A3/A5/B4/C4). Despite the fact that they currently have the same amount of raw influence (they each have 1 corner, 1 edge, and 1 center leader), after white captures C3 and black captures A4, white will have the more influential position. The reason for this discrepency is that black has played twice on the edge and gained an unholdable prisoner in the center, whereas white has played twice in the center and gained an unholdable prisoner on the edge.

So far, we’ve discussed focusing on center influence in order to create the most long term potential. However, local influence is often a more important consideration when trying to contest the initiative. Local influence is necessarily an imprecise term, however the concept is fairly straightforward — the player with more pieces in a particular area of the board is dominating the influence there. As such, this creates something of a “defender’s advantage” where the act of placing a piece anywhere in the open immediately dominates the local influence landscape. If the other player chooses to contest that local influence it becomes the initial placer’s prerogative to maintain their local advantage by continuing to play in the area. Especially in the early game, when much of the board is open space, contesting the initiative will ideally be done indirectly. This allows the “contestor” (usually black) to at least maintain a local influence advantage and make it that much harder for the tempo-advantaged player to maintain their lead. Although this means giving up on well-defined road options in the early game, a local advantage somewhere important to your opponent can eventually be extended elsewhere once things settle down at the point of contention.

local_influence

In this neighboring corners example, black has responded to white’s D2 flat with C4. This is an excellent response because it prepares a local advantage in both places that white may seek to build a road (either north along the D-column, or west via the 2nd rank).

early_game_local_influence

This is an example opening where both players are trying to diligently cultivate as much long-term potential as possible; 5 moves into the game there are no edge pieces and nearly all center positions are filled! Here is a logical narrative for this sequence. 1) White isn’t ready to commit to a direction for expansion but takes center influence while keeping her home corner relevant; black prepares a local advantage in both directions white might expand. 2) White is reticent about extending north because of C4 and wants to keep A1 isolated while grabbing some more center influence; black grabs the initiative while keeping D2/E1 relatively isolated. 3) White stomachs the lack of local influence and retakes the initiative (developing her road to the north and starting to incorporate D1/E1); black  cuts off the connection to D2 and reclaims the initiative by angling to capture D4. 4) White senses that D3 has become vital to her position and grabs the center to make multiple viable options with which to capture D3; black doesn’t feel ready to capture D4 or commit to the 4th rank east-bound road by playing on E3/E4 and so grabs the last central position which is of use to him (in this way he senses that C3 is vital to his position in much the same way that D3 is vital to white’s).

Strategy 103: Stack Basics

There isn’t a clearly defined boundary between the early-game and mid-game, but I think it’s conceptually useful to think of this transition as happening when two important conditions have been met: 1) a player has been placed in tak, and 2) a player has captured. In this sense, one of the hallmarks of the mid-game will be the arrival of stacks. The majority of this phase of the game will hinge heavily on creating, controlling, and manipulating stacks.

Stack movement can be broken down into three main categories. First, a stack may be run, whereby it moves to its greatest potential without surrendering any prisoners. This is by far the most powerful use of a stack, as you gain or maintain control of all of locations where it moves. Describing this kind of movement as “running” is apt in many situations. As part of racing across the map and consuming mostly open territory, you are running out the stack. As part of escaping with prisoners away from a location where your opponent has stack influence, you are running away from that influence. Or, as part of disrupting an area where your opponent has concentrated influence, you are running over their territory.

running_stack

White’s stack on D3 has two incredibly powerful options; it can run west over black’s A3/B3/C3 or it could run out south and claim D1/D2/D3.

Second, a stack may be thrown, whereby it travels farther than simply running, but is only able to do so by surrendering prisoners. Utilizing more of a stack’s reach in this way is somewhat haphazard, but may be appropriate if there is some value to be gained in the region to where the top of the stack is being thrown.

throwing_stack_tak

Revisiting an earlier example, black is in tak here because white can throw her stack on B3 east in order to claim D3 and finish her road.

Finally, a stack may be repositioned, whereby it moves less than it would if it were run or thrown. The strength of repositioning stacks is very situational, but will typically only be done to either create stronger running/throwing options elsewhere or as part of breaking apart a stack that exceeds the carry limit.

stack_repositioning

Black might consider repositioning his entire A3 stack south to A2 in order to threaten running the new stack over white’s pieces on B2/C2/D2. Note that this is merely an example of how a repositioning move might be motivated. In this case, playing on A4 is a much better move since it puts white in a compound tak. I’m holding off on examples where I think repositioning is the best possible move for now because they are more complex.

There are many different types of stacks, but there are some basic shapes/categories that will arise in nearly every game. Single-prisoner stacks are the most basic, and will almost always be the first to make an appearance in game. The only value that the prisoner adds is 1 extra reach (i.e. as part of throwing the stack). However, this is outweighed by the fact that the prisoner is a weakness that your opponent may seek to exploit. You should only choose to gain a single-prisoner stack when doing so realizes a clear positional advantage.

single_prisoner

Continuing from a previous example, black has captured C2 to escape tak and now has a single prisoner stack. He doesn’t even have stack influence on C2, so it probably doesn’t have any positive value for black (it will have value to white if/when she claims it). The only thing it can do that a solo flat can’t is throw the leader to C4 or E2 (or A2), but it’s hard to see any context that might arise in which doing so would be a good idea.

Soft stacks contain at least as many prisoners as pieces of the leader’s color. Note that single-prisoner stacks are a type of soft stack. The value of soft stacks diminishes greatly the more prisoners it contains. Additional prisoners provide extra reach, but they incrementally degrade the overall quality of the stack. The softer the stack, the greater the liability. Unless your opponent is unable or unlikely to gain influence on the soft stack, anything softer than a single-prisoner stack should be taken with the utmost caution.

soft_stack

Continuing from the previous example, white decided to leave the single prisoner stack on C2 alone and black has made the mistake of softening the stack further by taking C3. This stack is so soft that the extra stack-throwing reach isn’t even useful because the board is too small (if the board were bigger, the leader on C3 could get thrown to C6 for example).

Hard stacks contain at least as many companions as they do prisoners. In contrast to soft stacks, which will normally only run away, hard stacks are excellent for dramatically altering the landscape of the board when either run out into the open or run over your opponent’s flats. You will typically only gain hard stacks by capturing soft stacks from your opponent. Although it may occasionally be useful to jump on top of your own pieces to create a hard/harder stack, this reduces your flat count and thus should only be done with a clear objective in mind.

hard_stack

White had stack influence over black’s soft stack on C3 and immediately captured to create a hard stack of her own. Its most potent threat is being able to run to A3.

Zebra stacks alternate between white and black, and are either barely soft or barely hard depending on whether the bottom piece is a prisoner or a companion (respectively). These typically arise from a capture-recapture sequence which a player initiates despite lacking stack influence. Although this ostensibly sacrifices material, it may serve to regain the initiative. Additionally, the recapture may not even be immediately advisable if the prisoner would introduce too much liability.

zebra_stack

Black is in a compound tak and his only option is to capture B4 (for the second time this game, it appears). The zebra stack on B4 will probably grow even more, after white recaptures from A4 to prevent black from running the zebra stack over C4/D4. The one good thing that can be said for black’s position is that after the exchange on B4, he will temporarily have the initiative and be able to put white in tak by playing D1.

Tall stacks exceed the carry limit and therefore cannot run fully in a single turn. A minor caveat to this is when the bottom-most companion can be exactly unearthed by the carry limit. Although it is still a tall stack, it can fully convert its companions to flat count in a single move. Repositioning a tall stack can be a powerful way to make use of its full potential, as it may force your opponent to respond to the reposition and allow you a second turn with which to utilize the remaining portion of the stack.

tall_stack_1

Black has a tall stack on B3 and cannot make use of all of it in one turn. He will need to first reposition some of it; for instance, by moving 2 pieces south to B2.

tall_stack_2

B3 is still a tall stack, but its companions can be fully expanded to run north (note that white is in tak because this move is a road threat). In fact, white is on the road to Tinue because none of her options for dealing with this tak will help against black’s next move on E1 creating an unescapable compound tak.

Strategy 102: Capturing with Purpose

There is no better way to put yourself on a long road to Tinuë than capturing without purpose. First of all, let’s discuss why capturing is generally a bad idea. Flat count is an important metric with which to evaluate who is winning the game. Indeed, if neither player is liable to finish a road it is the most important metric because it exclusively determines the victor when the game ends in non-road fashion. Other considerations aside, you should be optimizing for flat count the entire game. In the context of flat count, a basic capture is functionally equivalent to placing a new piece. However, capturing has the side effect of increasing your prisoner count. Prisoners are a vulnerability because they can be leveraged against you if your opponent ever manages to reclaim them.

purposeless_capture

Despite having stack influence on C4, it is not in white’s best interest to capture from D4. It neither improves her flat count nor gets her any closer to finishing a road, but picks up a prisoner which will cause problems if surrendered later.

However, there are many situations in which capturing may be beneficial or downright necessary. Against a compound tak — when your opponent has multiple options with which to create a road — the only way to neutralize all possibilities is by capturing. You will often have several ways to escape the tak. Where possible, avoid options where your opponent can immediately renew tak, especially when they can do so by placing a new piece — this merely adds to your prisoner count without fixing your tempo deficit.

escape_tak

White has potential roads at both D5 and E4, so black must capture part of both taks to survive. He would prefer to use the D2 flat for this because using any of his other pieces would slow his own road (he has primarily been paving a North-South connection in the B-column). Capturing C2 and D3 both escape the tak, however D3 is not a very attractive option because white can renew tak by placing at C4. Capturing C2 is a better option because it prevents white from renewing tak.

In addition to escaping tak, capturing can be effective if it puts your opponent in tak. But tread carefully when doing this. If you can’t maintain control of the position, then your opponent can simply recapture and gain extra influence along your road. Also, a road threat is typically more difficult to deal with than a potential road — so if you can play a new piece and convert your potential capture into a road threat, you will instead force your opponent to capture out of tak.

bad_capture_for_tak

White could put black in tak by capturing D2 with her C2 flat. However, after black plays on D1 in response, white will not be able to maintain control over D2 and will eventually surrender the prisoner. Instead, it would be better for white to place on D1 and force black to capture to escape tak.

Creating and escaping tak are really just instances of competing for the initiative — albeit with quite a bit of urgency. But just because a capture doesn’t create or escape tak doesn’t mean that you should dismiss/defer the option. It might be the case that both players have mutually exclusive capture options that would seize the initiative. Evaluate how each player might eventually recapture, and capture preemptively when being captured would be more uncomfortable than taking on the prisoner(s).

preemptive_capture_for_initiative

In this position, white’s ability to capture from C2 to D2 and black’s ability to capture from C3 to C2 are mutually exclusive (only the player who acts first will get to cash in). It is white’s turn, but she should not be terribly concerned by black capturing on his turn; playing on D1 or E2 are stronger options.

preemptive_capture_for_initiative_2

Continuing from the previous example, white has placed on D1, leaving the tension on C2/D2. It is black’s turn and he should be quite concerned about white’s potential to capture D2 because it would put him in a compound tak. Flatting E2 is uncomfortable because white retains stack influence over D2; preemptively capturing C2 is probably a better option.

Strategy 101: Contesting the Initiative

At the start of every turn you should ask yourself two very important questions. 1) How can I build a road? And 2) How can I delay my opponent from building theirs? Ideally, you can answer both of these questions simultaneously, but most turns you will only be able to address one. The most important factor for getting your priorities straight is who currently has the initiative. With the initiative you should continue building your road, and without it you should look for ways to delay your opponent. The motivation is very simple: if you are “winning the race”, so to speak, just keeping running!

basic_block

White starts with the initiative and plays E2 to simply continue her road. Black, sensing that letting white continue unhindered would be problematic, answers with E3. This does little to build a road of his own, so white will maintain the initiative with D2 or D3. But this is still a small success for black because he has returned white to being 4 turns away from a road and now has some options to capture parts of white’s road.

However, sometimes moves that *directly* contribute to your road can in fact be brittle – easily delayed by a skillful opponent. While paving your road, be on the lookout for how your opponent might attempt to delay you and how you might choose to respond. If overcoming the obstruction would lose the initiative, then perhaps you need to consider how to build a more robust road. Although this may temporarily sacrifice the initiative, you will be better off in the long run by having a resilient position. Never forget that the devious obstruction you just preempted will also be available to you defensively if your opponent tries to maintain the iniative too stubbornly.

robust_road

Sensing that black will have an easier time thwarting E2, white chooses to first play on D3 to set up a more versatile north-south road. Black decides to maintain the initiative with A2, but white simply plays on A3 to start developing some east-west potential and reclaim the intiative.

Similarly, the best defense is a good offense. As you puzzle out how to delay your opponent’s road, consider how you might ultimately be building a road in its own right. It might not be part of your quickest route, but if your opponent isn’t careful you could easily snag the initiative based entirely on moves whose original intent was defensive.

defense_claims_the_intiative

Instead of responding to white’s E2 with E3, black plays the softer D4. Figuring that this does nothing to directly obstruct her road, white continues on E3. However, black can now seize the initiative with E4. Despite having abandoned his A1 flat for the time being, black has created the beginnings of an east-west road while simultaneously blocking white’s path to the north.

A final word of caution: as the board starts to fill up, you will rapidly approach the first tak of the game — when one of the players is a single turn away from completing a road and their opponent must respond. Although a developing move creates more long-term potential, it is typically preferable to issue the first tak of the game.

over_development

White and black have both started with the developing moves D3 and B3, respectively. However, white’s continuation on C4 will be uncomfortable for her because, after B4, black will almost assuredly issue the first tak of the game (or at the very least gain a positional edge if white takes drastic measures to avoid tak). In this way, C4 is too indirect; D4 (or possibly even B4) would have been better options for white.

Core Concepts

Before I dig too deeply into any strategies, let’s establish some basic terminology. The beta rules lay some groundwork in this regard. However, I will be diverging slightly from their descriptions when I feel that it facilitates clarity/brevity or evokes a more apt analogy. As such, these concepts will be critical for understanding all my future strategic discussions. For visual reference, I will always introduce what I deem to be core concepts in bold and secondary concepts in bold italics.

 

Notation and Cardinal Directions

Borrowing from chess notation, the community has developed board coordinates according to “rank and file” or “row and column”. However, Portable Tak Notation (PTN) is necessarily more complicated than chess notation because we need to encapsulate more than just a source and destination — as a stack moves it leaves a variable number of pieces behind on every space! The drawback of this complexity is that it often slows discussion; people don’t intuitively parse PTN. So, while I will at times present moves in PTN, I will also use cardinal directions for the sake of descriptive prose. Every diagram I present with be oriented with A1 in the lower left corner.

cardinal_directions

In this game, white and black are respectively starting in the northeast and southwest corners.

 

Initiative, Tak, and Tinuë

Perhaps the most important feature of the game at a given point in time is how many unhindered moves each player is away from finishing a road. The player who would be able to accomplish this first has the initiative — which I will interchangeably refer to as a tempo advantage. We quantify a tempo advantage by turn count.

initiative

The red path will complete black’s road in 2 turns, whereas the green path will complete white’s road in 4 turns. Even though it is currently white’s turn, black has the initiative with a 2 turn tempo advantage.

When your road is so near completion that you need only one additional turn to complete it, you have put your opponent in tak. This forces a response from your opponent because you are about to win the game! A road can be completed by either playing a new piece or by moving existing ones in to position. A location at which placing a new piece would complete a road is a potential road, whereas a move using existing pieces to complete a road is a road threat. This is an important distinction because a potential road can be dealt with by playing a flatstone (aka a “flat”), whereas a road threat cannot.

potential_road

White is in tak because black has a potential road at C1. White could deal with this by playing a flat on C1.

road_threat

White is again in tak, but this time black has a road threat moving south from C2. White’s only options here are to capture east or west with her C1 flat. Capturing east to D1 is likely her best option because it creates a potential road for her at D2!

When your opponent is in tak and cannot remove all road threats/potentials then they are in Tinuë, because you will inevitably finish a road on the very next turn. If you reach a point where you can guarantee a road victory, but it will take more than 1 turn, then you have put your opponent on the road to Tinuë. The term “in Tinuë” was first coined by Simmon (A.J. Hough) on playtak.com and is a reference to Patrick Rothfuss’ fictional world of Temerant, where it is believed that all roads eventually pass through the city of Tinuë if you travel long enough.

tinue

Black is in tak because white has potential roads at both D5 and E4. However, he is also on the road to Tinuë because, after he captures north from A3 and white recaptures south from A5, he will have arrived in Tinuë.

 

Control and Influence

A player has control over all stacks on the board where a piece of their color is on top. Transitively, control of a stack also implies control of its location on the board. All stacks on the board, even lowly stacks of a single flatstone, exert influence on their surroundings. Influence, broadly speaking, is the ability to move pieces on the board in order to obtain control. This video by Ben from TakStrategy provides a basic overview of influence, but there are several different varieties of influence that I would like to define more explicitly.

Each type of piece exerts its own form of influence on the board. Flat influence — the ability to move a flatstone somewhere — is additive because flatstones can be infinitely stacked on top of one another. Wall influence — the ability to move a wall somewhere — trumps flat influence and is not additive because walls cannot be stacked upon. Cap influence — the ability to move a capstone somewhere — trumps both flat influence and wall influence and, as with wall influence, is not additive. Note that, although cap influence trumps wall influence (a cap can “crush” a wall), it would have to leave the rest of its current stack behind in order to convert its influence into control.

There are also derived forms of influence. Positional influence means that you can gain control of a position, but does not promise any long term control there. This may provide defensive value if it allows you to escape or delay tak, and may have offensive value as a road threat. Positional influence may also be leveraged to create longer term potential by softening your opponent’s stacks, but that is an advanced topic which I will discuss later.

positional_influence_tak

Black is in tak because white is exerting positional influence on D3 with her B3 stack. If not for the road threat, black wouldn’t be concerned by white’s positional influence at D3 because he has the same amount of flat influence there as white and would eventually maintain control of both the position and stack.

Stack influence, in contrast, promises that you can gain (or currently have) control of a stack in such a way that you could (eventually) exhaust all of your opponent’s positional influence and retain control.

stack_influence

White has stack influence on C3 because she has more flat influence. If she captures from C4, black could recapture but then after white captures again (this time from D3), black would no longer have any positional influence and regardless of black’s next move, white would get to start her next turn with control of the C3 stack.

Note that stack influence may sometimes depend on turn order. That is, it may be the case that only the *active* player has stack influence. In this situation, control of the stack is disputed. Disputed control of a stack will not always be resolved immediately, and may indeed exist for a long time if control has little contextual value.

disputed_unimportant

White and black both have walls which only project stack influence on C2 on their respective turns, so control of C2 is disputed. However, it is of little importance because it is occupied by a singular flatstone and neither white nor black is anywhere near building an east-west road. Neither player will be interested in capturing C2 with their wall, and it will remain disputed for the time being.

disputed_important

However, after a few moves of exchanging control on C2 with flatstones, the stack at C2 has grown significantly and become much more valuable. It is black’s turn and he will likely capture C2 with his wall to prevent white from running the stack west.

As a final note on the topic of control and influence, a player’s influence may sometimes be so overwhelming that it really qualifies as pseudo-control. Specifically, undisputed influence that will remain undisputed  despite any possible move should be regarded as pseudo-control. Typically, pseudo-control will only apply to the position, but if the stack is pinned or otherwise trapped then the pseudo-control extends to the stack as well.

pseudo_control

In this example, white has cap influence on B3 (this is stack influence even without her surrounding flats). Additionally, she has pseudo-control of this position because black can’t get his capstone in position to dispute control (A3/B2/C3 are all occupied). Note that this doesn’t imply psuedo-control of black’s flat there because it is not pinned and could move away (for instance, east to C3). Conversely, she does *not* have pseudo-control at C4 because black could place his capstone on D4 to dispute control there.

 

Leaders, Prisoners, Captives, and Companions

As you’ll quickly discover, one of the richest and most complex dimensions of Tak arises from the movement of large stacks. So, we need an explicit vocabulary for discussing the contents of stacks. Cheapass Games’ rule book already gives us some basics. Soft stacks you control contain many of your opponent’s flatstones; conversely, hard stacks contain many of your own flatstones. But, the rules are imprecise about how to refer to the individual components of a stack. For the purpose of this blog, I will refer to the piece on top of a stack as the leader. Flatstones in a stack that don’t match the leader’s color, I will typically refer to as prisoners. However, when I want discuss a scenario from a specific player’s point of view, I will use the term captives to refer to flatstones that their opponent has captured. Similarly, when control of captured pieces changes hands back to their original player, prisoners are surrendered whereas captives are released. I’ve chosen these terms deliberately to evoke the analogy that your opponent’s captured pieces are miscreants justly in shackles, whereas your own captured pieces are innocent victims waiting to be liberated.

For flatstones that match the leader’s color, the rules suggest the term “reserves”, however I prefer the term companions. In contrast to games like Go and Chess, capturing pieces does *not* remove them from the board, so I don’t believe that analogies to war or battle are most appropriate to Tak. The victory conditions are only indirectly affected by how many prisoners you take or how many captives you free. Rather, the point of the game is to get there first or, barring that, to simply be more influential. This is better compared to a bustling economy than a chaotic battlefield! Playing Tak, I more readily identify as a traveling merchant trying to outwit my competition than as a general slaying my enemies. As such, I don’t think of pieces buried in my stacks as reserves ready to be deployed. Rather, they are traveling companions, following their leader until left behind to exert control and influence on their own.

Finally, the mechanics of  wall-flattening makes it important to articulate whether the piece directly below the capstone is a companion or a prisoner. If it is a companion, then this flatstone is the cap’s deputy.

deputy

Black is in tak because white’s capstone has a deputy. Additionally, black is not particularly close to making a road because his cap does *not* have a deputy and flattening white’s wall on A1 would leave white in control of A2.

Beginnings

Where to begin? If you’re reading this, then you’ve probably already heard that Tak is a beautiful game, so let’s start there. Tak is a beautiful game. It is beautiful because it is both simple and profoundly complex. It is beautiful because it inspires curiosity, and because it promises hidden depths wherein our curiosity will be rewarded — both with answers and with ever more questions. It is beautiful because every time you sit across an opponent you embark on a journey, and because learning and exploring Tak’s nuances is itself an even grander journey of discovery.

This journey is even more of a discovery for us than for Kvothe, because we have no Bredon – not yet, at least. Though we imagine a history of Tak in Patrick Rothfuss’ colorful world of Temerant, there isn’t a real history to this beautiful game. Not until we make one. I want to share with you here the process of developing Tak strategy, and in doing so we begin to write the history of Tak in *our* world.

If you’re here as a true beginner, then you’ll want to watch this wonderful video by James Ernest and the folks at Cheapass Games, and take a peek at the official beta rules. These may change in the final version of the game, but I expect that any such changes will be minor and not affect any of the core mechanics.

Welcome, fellow traveler! I look forward to exploring Tak with you.