storisende position I've often been able, from the very moment they had fully unfolded in my mind, to fairly accurately envision the behaviour of games that emerged inside out and displayed organicity. I'm talking about for instance Emergo, Symple, Sygo, Havannah, Starweb, Io and the like. These are all simple games with uniform material on a uniform board and with one specific behaviour. If you're reasonably well acquainted with the emergent complexity in such games by known examples like Go or Hex, then it isn't all that difficult to more or less predict their behaviour.

Storisende emerged the same way. It was conceived as a complete game and never changed. Yet I found it unexpectedly difficult to envision how endgames would look in balanced games. In visualising game behaviour you inherently presume balanced games because there's no alternative, but I couldn't quite see how things would pan out. The reason is the game's unique stucture. These considerations regarding its strategy are therefore based on that very structure that seems to divide the game in two intricately interwoven games, each of which has a different way to serve the actual territorial goal.
The game starts out on a hex grid of which every cell is 'virgin' territory (beige in the diagrams). A cell's virginity ends the moment it is vacated by a move, prior to which is obviously must have been occupied at some point. This action turns the virgin cell either into 'established' territory (green) or into a cell of 'the Wall'. In over-the-board play the pieces in this scenery are flat stackable checkers that may move either as singles or as like-coloured stacks. In this AiAi representation they are displayed as human figurines.

  • Singles move one step in one of the six main directions.
  • Stacks move exactly as far as they're high, or in this case as far as the number of figurines that are moved.
  • Stacks may split, or merge with like coloured pieces if they land on them.
  • Pieces capture by replacement, that is: the captured single or stack is removed and the captor takes its place.

In the endgame position above the division so far as the game went has fully evolved. Black's last move, splitting a double by moving one man to the left, is indicated. White resigned because he has no territory at all and his presence on the Wall equals Black's. There are fifteen wall cells, which is nearly half of the total playing area. The rest is either still virgin territory or it has become established territory.

The hot phase: growing while shaping the terrain
Both growth and shaping the terrain arise from piece movement. Virgin cells turn into established territory or into wall cells the moment they are vacated, irrespective of the height of the piece that vacated them. But what decides whether it will be one or the other? And where do all those men come from? These proceedings are based on two pillars:
  1. Only doubles can breed.
  2. Separated areas of established territory (green) never merge.
storisende positionA 'double' is a stack of two single men. The game starts out on a virgin board with both players placing one double. If a double vacates a virgin cell it leaves a new-born man behind, regardless of whether the cell turns into established territory or into a cell of the Wall.

White places first. The move options as one piece are indicated. The piece may also split and move one men one step, but in this stage that would be silly. The yellow spots indicate good cells for Black to reply.
storisende positionAfter Black's reply White has moved his double, thus vacating the virgin cell and turning it into established territory. In doing so he has left a new-born man behind. This man blocks Black's access to the northward cells, leaving only the options given by the green arrows.

If Black moves to the right then White is unlikely to move the direction of the yellow arrow because thereafter he would have no other option than to go back or jump to the bottom-left corner, leaving his singles wide apart. Both would mean slowing down the growth rate.

storisende positionSpeaking of which, making two cell jumps on a hex grid will grind to a halt at some point because the piece is bound to one of the four sub-grids displayed here.

storisende positionIf both players maximise growth, then after the first five moves we're in the diagram, at the end of an unobstructed growth route of both on their original sub-grids. Switching to other sub-grids is necessary for two reasons:
  1. To grow more men.
  2. To create new established territory or enlarge existing areas, or erect wall cells.

It is not necessary or even usual to wait with the occupation of a new sub-grid till all other options have gone. Making a double implies two non-growing moves anyway, whatever the timing. On larger boards there are more options to diversify and it usually starts long before the growing options on the original sub-grid have expired.

Between any small triangle of established cells there are three cells that belong to the other three sub-grids. The cell marked yellow belongs to White's sub-grid. Of the other two the brown sub-grid gives more options for a double to jump. How to proceed?
Up on the Wall and down in the trenches
Next to when and how fast to grow, an important question is on what kind of cell to grow. The origin of a wall cell lies in the fact that separate areas of established territory may never merge. So if a virgin cell is vacated that borders on seperate green areas, the cell becomes a part of the Wall. A quick check reveals that all virgin cells in the inner area of the board in the diagram above, will turn into wall cells if vacated. Cells of the western edges may turn one way or the other depending on the order in which they are vacated.

Erecting wall cells with new-born men is crucially important for reasons to be disclosed. If you want more of them, then make small established territories close together and erect wall cells between them. This is counter intuitive because it implies making small territories instead of large ones in the first place, and it also keeps your forces initially closer together than a territorial goal would suggest.

Why are pieces on the Wall so important?
Without them you can't move stacks from one area of territory to another. Pieces down in the trenches can never get up on the Wall. But stacks can jump over wall cells and to do so the cell(s) that are jumped over must be occupied by a like coloured piece. Of course these jumps must be according to the allotted distance of a stack and singles therefore cannot jump over the Wall. That's one thing you need pieces on the Wall for, to regroup pieces in the territories. But you don't need many for that. The reason you need many is to fight other pieces on the Wall!

The Fight on the Wall
Up on the Wall pieces also must move according to their allotted distance, but they have no obstacles. They may move over any cell, whether wall or territory, whether occupied or vacant, and land on any cell, again whether wall or territory, occupied or vacant. Once they move off the Wall however, they cannot move back up, so moving a piece off the Wall should only be done for very pressing reasons.
The fight on the Wall is an existential fight and it is more often than not primarily concerned with annihilation and not with 'territory'. Of course territory remains the formal goal so in the end these fights are about territory, but the action itself feels far more like playing Chess.

Down in the territories stacks usually have no reason to become very high because even if they switch territories, they operate locally. But stacks on the Wall may grow very high to enable long jumps across the board, thereby targeting far away pieces as easily as the ones that are close by. And they never have to worry about threats from below! It's also worth noting that larger stacks may threaten smaller ones without being threatened by them. Of course if such a smaller piece is defended, the larger one would think twice before capturing it, because it would then sacrifice itself in the process.

Win the Fight on the Wall and you win the Game!
That's not entirely true, but for beginners (I just promoted myself to 'beginner') it's a fairly dependable provisional signpost. And in any case, the fight on the Wall precedes the territorial fight because it starts long before territorial claims can be substantiated. Territorial claims become more clear towards the endgame, when forces on the Wall have dwindled to more surveyable numbers. Eventually the remaining pieces on the Wall, especially if you 'own' parts of it by dominance, may be used to capture opponent's pieces in small territories in order to claim them, or indeed to claim wholly vacant territories.

A good example of bad play
I must apologise to AiAi for exploiting its weakness for educational purposes. On smaller boards, with say 15 seconds per move at its strongest level, it plays a very good game. Over a million iterations at a six ply depth on a base-4 board provides a good balance between existential and territorial issues. But on a base-6 board it falls victim to the increased branch density and an understandable lack of long term planning. And Storisende lends itself excellently for long term planning!
storisende positionI started on a cell next to the centre and AiAi swapped, so I play White. Both have provisionally fenced off along the line that runs from the NW cell to the SE one. Let's have a look at the position after 21 moves by both.
  • White has 17 men, Black has 15.
  • Both have 3 doubles, but Black has two on the same sub-grid.
  • White has 5 men on the Wall, Black has 1.
  • White has created 10 green cells, Black 13.

Note that White needs three moves to capture the lone black man on the Wall. Not an immediate priority because breeding is still hot, but a priority nonetheless. White can always leave the cell should the forces be needed elsewhere, but so long as they're there White can immedialely capture any newborn that would emerge on adjacent wall cells. Kill 'm before they get a chance to grow up!
storisende positionThis is the position after 40 moves each. Let's have a look at the stats again:
  • White has 23 men, Black has 13.
  • Both have 3 doubles, but all White one can immediately breed.
  • White has 10 men on the Wall, Black has 5, two of which are still vulnarable for an attack with a stack of 3 or 4.
  • White has created 12 green cells, Black 13.
Already Black's position is completely lost! Territory is very provisional in the opening and middle game. But imagine you have NO men on the Wall:
  • You can't move stacks from one territory to the other anymore, every man is locked inside the patch he's in.
  • You can't claim empty territory, or capture lone occupants of small territories 'from above', or neutralise a patch if you can't conquer it.
In the diagram the priority of catching the lone men on the Wall has become more pressing, though breeding is still hot. If you win the Chess-like fight on the Wall, then the endgame, when territory really matters, may look all the better for it! A majority on the Wall may and usually will give some positive feedback. If you have three cooperative men, you can usually catch a lone one without exchanging it for another man. In exceptional cases even two men are enough. In my view any player should always keep an eye on isolated prey on the Wall!

This is a game between a beginner and a program that inherently has no long term plan or vision. So the position isn't interesting other than to illustrate the game's unique double edged strategy. The existential fight for and on the Wall and the territorial fight overall.

How will strategy evolve?
I can't quite see how AI might help in this particular case. Not that it couldn't, but it would require a lot more effort to make a program that would lead the way on larger boards where long term planning is crucial. But humans would of course focus on the importance of the fight on the Wall and they certainly wouldn't allow their opponents to create the kind of dominance that AiAi allowed me to have.
Thinking about evolving strategy means thinking about balanced games in which threats and counter threats progress to an ever increasing resolution in terms of details that matter. The need for a right balance between the existential fight on the Wall and the territorial fight down below is evident, but that balance has not yet been found. Tactics are varied and manifold and I'm sure I haven't seen more than the most elementary ones and that there's much more to discover. But the game needs human players for that.

March 2019,

christian freeling