Enclose Horse

I took a screenshot of my solution and the optimal one - and then I could compare like this.

https://en.wikipedia.org/wiki/Angel_problem

[0] I'm assuming, possibly quite wrongly, that there's only one optimal solution per day.

I love Wordle but I found it unplayable when I used that Wordle archive site to play infinite games since there was no reason to think deeply about the 10th+ round I was playing in one sitting.

Note that traditional SAT and SMT solvers are quite inefficient at computing flood-fills.

The ASP specifications it uses to compute optimal solutions are surprisingly short and readable, and look like:

  #const budget=11.
  horse(4,4).
  cell(0,0).
  boundary(0,0).
  cell(0,1).
  boundary(0,1).
  % ...truncated for brevity...
  cell(3,1).
  water(3,1).
  % ...
  
  % Adjacent cells (4-way connectivity)
  adj(R,C, R+1,C) :- cell(R,C), cell(R+1,C).
  adj(R,C, R-1,C) :- cell(R,C), cell(R-1,C).
  adj(R,C, R,C+1) :- cell(R,C), cell(R,C+1).
  adj(R,C, R,C-1) :- cell(R,C), cell(R,C-1).
  
  % Walkable = not water
  walkable(R,C) :- cell(R,C), not water(R,C).
  
  % Choice: place wall on any walkable cell except horse and cherries
  { wall(R,C) } :- walkable(R,C), not horse(R,C), not cherry(R,C).
  
  % Budget constraint (native counting - no bit-blasting!)
  :- #count { R,C : wall(R,C) } > budget.
  
  % Reachability from horse (z = enclosed/reachable cells)
  z(R,C) :- horse(R,C).
  z(R2,C2) :- z(R1,C1), adj(R1,C1, R2,C2), walkable(R2,C2), not wall(  R2,C2).
  
  % Horse cannot reach boundary (would escape)
  :- z(R,C), boundary(R,C).
  
  % Maximize enclosed area (cherries worth +3 bonus = 4 total)
  #maximize { 4,R,C : z(R,C), cherry(R,C) ; 1,R,C : z(R,C), not cherry(  R,C) }.
  
  % Only output wall positions
  #show wall/2.

Great, now I've been double nerd-sniped - once for the thing itself and another for 'What would an optimiser for this look like? Graph cuts? SAT/SMT? [AC]SP?'

https://cs.stackexchange.com/questions/176005/how-to-remove-...

I think it should go up, otherwise it doesn't look like a wall. It would look like something the horse can step on and run over. For the water it makes sense to be flat flat and that the horse doesn't want to touch it: it is water-shy.

I also wonder if making it GPL and submitting to various *NIX distros would be best. Then it may need to be standalone with random maps created by ML or similar.

I hope they're not. Can't we have a few things in this world that are just fun without going and sticking surveillance on them?

I would have responded earlier, but I wanted to actually implement something you suggested: different walls. Alternative wall sprites, which don't occlude other tiles so much, are now live and can be adjusted in the settings.

Re: analytics, the only serious plans I had were to use the daily level histograms to adjust difficulty. The idea of taking some levels and releasing them as a standalone game is tempting, but I wonder if doing this type of puzzle over and over again might get tedious? That's one of the reasons I thought it would work better as a daily game. Let's see how it's doing in a few months.

I love the mechanic ideas. I think there are two big constraints on what kind of cool new features/gimmicks can be implemented though. First: if this is going to be a daily game, the new mechanics have to be intuitive enough to where somebody could figure them out their first time playing. I like the idea of cherries being misleading, and it's a fun troll-ish idea for a single player game, but it would be a mean trick if it were someone's first daily. (Then again, there's someone who's first Wordle game was probably MYRRH.) The other constraint is I have a solver that can guarantee the optimal solution is actually optimal. Some game mechanics might make this a lot harder, or even impossible.

> I don’t think the gates should animate up into the air. It breaks the visual logic of 2D for no benefit.

I also feel it would make more sense either for everything to be 2.5D or pure top down. Having appear / disappear animation is nice feedback to user though.

Other thing is that maybe the hitbox should change when the wall comes up. Now to remove it you need to press the grid, essentially the root of the wall. Unintuitive to me.

Thanks for the game, looking forward to when there is multiple horses or sheep to enclose.

1. lure the horse to an optimal point on the map.

2. trap it in a small circle of fences.

3. build part of your final wall with the remaining fences.

4. one by one, move the fences trapping the horse in place into position.

I agree! It feels off compared to the overall aesthetic of the game.

Awesome game though! Loved it.

I interpreted it as standard "top-down" RPG graphics, where the Y axis always doubles as the Z axis. As such, I didn't find it visually confusing - but it did made playing on mobile annoying, because you often end up targeting the wrong field.

This is a rather simple game to program. IMO, if you can program, take a few weekends to make your own game based on your ideas. If you can't program, your ideas will lead you to a wonderful learning project.

(jk)

I did originally try to measure the difficulty computationally by running the solver and timing it, but it didn't really line up with what humans would find difficult. Now I'm just eyeballing it.