Basic Entanglement Strategy
I discovered a simple to learn puzzle game, gopherwood studio's "Entanglement"
while checking on Google's Chromium's "Web Store".
As a 1300+ player, with a record in the best 25 ever, I think I might have something to say about the basic strategy of the game.
First, the scoring is very simple: When you place a tile, you get an arithmetic progression of points per tile crossed (1 + 2 + 3 + ...). Since the total number of points progresses quadratically on the length of the paths, it makes all the sense in the world to prefer to play single-steps if that way you prepare very long paths that you hope to eventually traverse. The principle is this: let's say you have the option to place two tiles to make a path of 20 squares, either make two steps of 10 squares each, or a sequence of length 1 followed by length 19: the first case will give you 5*11*2 = 110 points, the second will give you 1 + 19*10 = 191. So, there you have it, it is most efficient to prepare one long path even while making 1-length extensions to your line. This is the cardinal rule. For the sake of example, consider a 4-tile sequence of total length 20 and individual lengths 1, 1, 1, 17: You would get 1 + 1 + 1 + 17*9 = 156 points; versus a sequence of 5, 5, 5, 5 = 4 * 5 * 3 = 60.
Whenever you have freedom to place any of your two tiles and many rotation options, chose the one that connects the longest two "free" paths [[ I call a path "free" when neither extreme is a wall ]] inbound to the square you are placing. This strategy also minimizes the total number of paths.
In the early stages, try to keep the tiles that when placed at the six corner positions would leave no standing non-free path (a corner position is one of those that have three walls). Since in the corners your options are reduced to the minimum it is worth keeping those tiles around.
Try to connect non-free paths together as soon as possible.
In the later stages, make sure you have an exit path when you get into an isolated hole. Obviously try to keep the option to go over all the hexagons, but if going to an hexagon and back would give you two short paths at the price of not joining two long paths you could traverse later, then it's preferable to forgo that hexagon altogether.
Lastly, this game is stochastic, if you aim for an absolute record, focus on joining the longest free paths and joining non-free paths and assume you will get the hexagon you need; I don't think you can reliably get 2000 points or more playing it safe, playing safe, with my current understanding of the game, I get around 500 points reliably but it is extremely hard to get more than 1000.
Fellow blogger Nathaniel Johnston blogs about the theoretical maximum score:
One non-related recommendation: For Christ's (or Alah's, Buddha's, etc) sake, please use Google's Chromium rather Google's Chrome, the fellow blogger "Manuel Jose" explains: http://www.techdrivein.com/2010/05/why-cant-we-all-use-chromium-instead-of.html
Wednesday, January 26, 2011
Basic Entanglement Strategy
Posted by Eddie at 9:20 AM