I am pondering a random tile set-up similar to Catan, but with squares instead of hexes. If anyone has any thoughts on how to determine some things mathematically, that would be swell!

There are 36 tiles, which will be arranged in a 6x6 square. Each tile has up to four (and as few as two) Connectors, which are centered on the sides of each tile. (A tile could have connectors on the North, South, East and/or West side.) When the Connectors of two tiles are placed next to each other (a North placed next to a South, or an East placed next to a West) a Link is formed. Connectors on the edge of the 6x6 square can not form a Link (since it is impossible for them to be next to another tile).

Here is the breakdown of how many tiles have how many Connectors.

12 tiles have 4 Connectors each.

20 tiles have 3 Connectors each.

4 tiles have 2 Connectors each.

I am trying to determine 3 things, based on these tiles being placed randomly in a 6x6 square;

1- What is the maximum number of links that can occur?

2- What is the minimum number of links that can occur?

3- What is the average number of links that will occur?

By drawing a grid out, I came-up with the following:

-There are 60 tile-side to tile-side edges where a Link could possibly form.

-The 20 tiles with 3 Connectors means there are up to 20 Links that can not be formed.

-The 4 tiles with 2 Connectors means there are up to 8 Links that can not be formed.

-Subtracting 20+8 from 60, leaves you with a Minimum of 32 Links that will be formed by any random placement.

Am I anywhere close?

Rick-Holzgrafe wrote:Great stuff Rick!

(Forgive me for jumping into the conversation)

I can use the same math for my dungeon tile laying game. I've been using a 5 by 5 grid, with the starting tile being in position 3 from the left. (The southmost edge of the board). I had an issue with too many deadends, and your analysis of what CaptainBob's situation helps me as well.

Thanks a million!

Falloutfan.