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Subject: Formula for tile mix in maze/path game rss

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Andrew Stackhouse
United States
Ohio
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I am looking for formulae for determining tile mixes for a game where players reveal NOT build a maze or path.
I've got an idea for a game where there is, let's say, a 7x7 grid of tiles face down, each tile is Carcassone-esque in that there is a road on it that goes in 4-, 3-, 2-, 1-directions or a dead end. As players move, they flip and align (rotate) tiles. Players are NOT placing tiles like Tsuro
Rather than start from scratch, it seems like there must be a formula to determine the tile mix I need to avoid players being routinely trapped (occassionally trapped is okay, as players will have the limited option to get past a barrier).
I presume I'll probably have 3 different tile types -- outer ring, middle ring, and inner ring tiles -- to allow different combos of tile types.
 
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Jeremy Lennert
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You should probably explain the details of your "flip and align" rules, and what it means for the players to be "trapped" (are they trying to reach the outer edge of the map? A specific edge? A specific location? To reveal a certain total number of tiles, regardless of position?)

One useful approach might be to look at the expected number of open (unexplored) doorways remaining at a given time.

My game Gem Rush uses a rule that players choose the rotation of a new tile but must have at least one doorway pointing back the way they came in. If you do something similar (rotate the new tile so that one door connects with the entrance you just walked through), then a room with 1 opening is a dead end, a room with 2 openings will create 1 new doorway to replace the one you just used, a room with 3 openings will create 2 new doorways, etc. So in order for players to avoid being trapped, at minimum you need the average number of doors on tiles they explore to be 2 or higher. (That's the average of the tiles they actually reveal; how that relates to the average in your deck as a whole may be more complex.)

However, some "new" openings will end up pointing back to rooms that have already been explored (depending on how many sides of the new room are already face-up) or off the edge of your grid, so your average number of doors may need to be higher to account for that.


How does the game start? In Gem Rush, you start with a random tile, which means the most likely way for you to get stuck is if you start in a dead-end and the next tile you reveal is also a dead-end, ending your exploration before it starts. You could dramatically reduce the odds of a quick end if you always start on a tile with 4 doors.
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Johnathan Ness
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Another idea is to have most or all the tiles be 4-directional, but have things like locked doors, iron fences, or some other roadblock that can be opened or knocked down if you have the right equipment. Then small tokens could be placed over the block to show that they have been dealt with.
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guy
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This is one where I'd break out the compiler and get the computer to crunch the numbers: Make a 2d array of integers where the integers indicate number and arrangement of paths.

Then have the program randomly generate arrangements until you get the playing field that looks right most often. Translate those probabilities into actual ratios to get the number of tiles of each type.

I think this is a rich game development strategy and you are onto something here. Now I want to play a game that uses this kind of tile set.

 
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