Saturday, January 22, 2011

Maximum Theoretical Score is 9080

Nathaniel Johnston from Guelph, Ontario, found the maximum score possible on our standard Entanglement solitaire board. Here's an excerpt from his analysis:
The standard Entanglement game board is made up of a hexagonal ring of 6 hexagons, surrounded by a hexagonal ring of 12 hexagons, surrounded by a hexagonal ring of 18 hexagons, for a total of 36 hexagons. In order to maximize our score, we want to maximize how much we increase the length of our path on our final move. Thus, we want to just extend our path by a length of one on each of our first 35 moves, and then score big on the 36th move....
Read the rest of Nathaniel's interesting and thorough analysis »


  1. You RAT BasTAR)
    How did you do that????

    Good job my Friend.

    I am, defeaattted.....

  2. Hello guys, I really love your game, but since I play it through Google Chrome online app, I cannot register my high scores when I want to login with my gmail account.

    I always get the "Request-URI Too Large" after entering my password and trying to login, very annoying as basically I cannot save my high scores...

    Am I the only one with this issue ?

    Profile: Chrome 9 Beta, Gmail account, Entanglement through Chrome App.

  3. Hi Guillaume, we have had one player report that this occurs when signed into multiple Google Accounts simultaneously. If this is true of your case, you might try logging out of each account and then sign into a single Google Account as a workaround until we are able to resolve this particular issue.

  4. I just logged out from all my computers and phones, but still, I cannot login to save my high scores...

    I really hope you'll be able to fix this issue, that would be great !

    And keep the good work, your game is great !

  5. yea, but thats not the maximum because the pieces do not work like that... they are random

  6. Hey, head of days ... I think you might have missed the point. This is the maximum *theoretical* score, meaning the highest possible score that could be obtained if the player always got the perfect tile and made perfect moves.

    The probability of this ever happening is extremely small, but it's possible - and it's the highest possible score. It's the kind of thing that gets mathematicians excited. ;-)

  7. 1. So, are the tiles generated randomly, really? Or is there a set of 36+ tiles that are randomly selected from? For example, I've yet to see a tile that has the u at each of the six sides (or at each of the six corners); but then I've only played about a hundred times or so. Has anybody counted the possible number of tiles? And, as importantly, are all possible tiles in the pool that the random selection is made from? This would help in determining the probability of a perfect score (perhaps it's impossible under the current implementation?)

    2. I think it would add some satisfaction and intrigue to the game if instead of just allowing rotational symmetries of the tile to be tested, that additionally we could try reflections of the tile about its vertical and horizontal lines of symmetry. This would lead to higher scores for sure; perhaps it should only be allowed once somebody has broken 300-400 or so (which seems to be a watershed of sorts, to me). In any event, it would probably allow for a shot at the perfect score, for somebody.

  8. Good questions, David - I hope Derek or Todd will shed some light on the actual mechanism used. I really doubt there's code to create the images for random tiles at game time, so I'm guessing they've created a set of available tiles to draw from, which is smaller than the set of all possible tiles.

    So - how big is that set, anyway? I started to work it out but realized that it's trickier than I'd thought (and more than I can think about while I'm at work ;-) ). I'd be curious to see the correct answer.

  9. Hi David and belliott4488,

    You might want to check out our case-study on In short, yes, tiles are randomly generated and drawn on-the-fly. And every possible combination is possible due to the way we are randomizing their generation. I'm not sure how many unique tiles there are, but you might enjoy the comments on this thread as well. All that to say Nathaniel's mock-up above is actually possible, but definitely not probable.

    Allowing tile reflections is an interesting idea. I might need to think more about that one.

  10. hey i can,t make score more than 200, what to do.........

  11. I love the game, I'm pretty addicted. One minor change I'd like to see - on the last play I'd like to see the "fireworks" from the last run complete before the final score box covers it.


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