# Randomly but Evenly Distributing Tokens on a Board

I'm designing a board game where, as more sections of the board are added, tokens are randomly placed on the new board section. Each board section is 2'×1' (24"×12"), so we using dice to randomise coordinates: 4d6 for the X coordinate and 2d6 for the Y coordinate.

Note that the board is not in a grid; the dice results just correspond to inch measurements on the board.

For some reason this system doesn't seem to work very well, as tokens tend to be grouped together rather than spreading evenly. Are there better ways to distribute the tokens more evenly?

• 2 feet by 1 foot is a large thing, is your game field large like warhammer fields? May 27 '15 at 8:44
• the total length is 4 feet by 2 feet, tiles are added to the board as the game progresses. May 27 '15 at 8:45
• so there is a total of just 4 board sections? May 27 '15 at 8:50
• yes that is correct May 27 '15 at 8:51
• oh ok, so you add terrain "tokens" to the section right? is there a fixed amount of terrain tokens on each section? May 27 '15 at 8:52

The more dice you use to generate a single random value, the closer each random value will be to a certain average. You can see this happening in Catan: rolling two dice results in a lot more sevens than twos.

If you do this with 4 dice, almost everything will be centered around the 14th coordinate. If you don't mind some normalization, you could use 2d12 instead of 4d6.

You could give the players some say in where the pieces are placed. There are many ways in which you could do this, either before or after the dice are rolled.

If you want 'complete' randomness with dice, you'll need a 1d10 and a 1d20, or two decks of numbered cards.

So, after some discussion, this is the idea we're going with.

We will create 12 (not concrete yet) set layouts for tokens that can be applied to any given board section. These layouts will be drawn onto cards and shuffled together to make a deck. When the game is started and the Board is tiles are placed, a card is drawn for each section and tokens will be placed on the section as depicted by the card giving a semi-random placement.

I think freekvd explained rather well why your probability distribution is not flat, but if you want a flat distribution, you could do one of the following:

1. get a 24-sided and a 12-sided die and do basically the same thing you had already done.
2. make cards numbered 1-24 and draw two of them for each token placement. Those on the 12-inch side can either be divided by two or taken mod 12 (meaning that you subtract 12 from anything above 12, just like with time). You could also have a separate 1-12 deck.

3. If you only have 6 sided dice and only want to use dice, then you could roll two six sided dice for each side. The two dice are not interchangeable, so they'll have to either be different colors or be rolled one at a time. For this example, let's say you have a black and a white die.

• Roll both dice and subtract 1 from each roll.
• Multiply the roll of the white die by 1/6.

This will give you a total between 0 and 5 + 5/6. (You could then add 1/12 to that number if you're worried that two edges will have tokens and the other two won't.) For the 24-inch side, multiply that total by 4 inches and for the 12-inch side, multiply it by 2 inches.

1. Mark the edges of your board with number pairs from 1-1 to 6-6 which are evenly spaced. Forget about inches and just place the token on the corresponding part of the board.

2. Put walls around your board and then toss the tokens in from a few feet away. There's no guarantee that it'll be an even distribution, but it'd probably be more fun than rolling dozens of dice and making measurements just to set up your game.

If I understand your question correctly, you want a way to determine terrain on a X by Y grid such that a logical terrain layout is created.

You start with putting the upper left square first (for example a mountain). Next you determine the tile to the right (methods below). Continue until you reach the right end. Then use the same method to find the tiles below the first row. Continue until the board is filled.

There are two possible methods:

1. Use a table with probabilities using dice. For example, a mountain has 40% chance for another mountain, 30% for hills and so on. This method is a bit cumbersome.

2. Use several stacks of tiles one for each terrain type. So if you want a tile next to a mountain, use the mountain stack. If that is a hill, use the hill stack. This method is faster but requires more tiles.