ravenblack.net : Elementals

The game of Elementals bears a distinct resemblance to Scissors, Stone, Paper.
The rules are very flexible, and hence difficult to explain. The elements can be named, but I prefer to refer to them by numbers for clarity.
The three variables in the rules are number, range and distance.

Number is how many elements exist in the game. This can be anything three or higher. It is normal for this value to be an odd number.

Range is how near each other elements have to be in order to fight. The maximum value for this follows the formula (number-1)/2 rounded down. It is normal for this value to be set to its maximum.

Distance is how many times an element has to win a battle to win the game. This can be anything, but three to five is normal.

The example game has Number 5, Range 2, Distance 3.

---1---
---2---
---3---  The game begins with all the elements in the middle.
---4---
---5---

The range works as follows... A higher number beats a lower number if it is within range. If a number is low enough that its range would extend below 0, it loops around to the high number. In the case of this example, then,
5 beats 4 and 3,
4 beats 3 and 2,
3 beats 2 and 1,
2 beats 1 and 5 and
1 beats 5 and 4

Player one is the left side, player 2 the right.
At the beginning of a round, both players choose their element simultaneously, as with Scissors, Stone, Paper.

---1---  Player one picks 5. Player two picks 2. 2 beats 5, so 2 moves one
--2----  square towards Player one.
---3---
---4---
---5---

---1---  Player one picks 1. Player two picks 2. 2 beats 1, so 2 moves one
-2-----  square towards Player one. Player one can't afford to be beaten
---3---  by a 2 again.
---4---
---5---

---1---  Player one picks 2, in an attempt to pull it back. Player two picks 3.
-2-----  3 beats 2, so 3 moves one square towards Player 1.
--3----
---4---
---5---

---1---  Player one picks 3. Player twp picks 2. 3 beats 2, so 3 moves one
-2-----  square back towards player 2. Some of the pressure is off player 1,
---3---  but he is still losing quite badly.
---4---
---5---

---1---  Player one picks 5, expecting a 3 or 4. Player two picks 2, however,
2------  which beats 5. 2 moves towards player 1, and reaches the edge of the
---3---  board. Player 2 is the winner.
---4---
---5---


Diagram of the board  -----1----- \
                      -----2-----  \
        Range -   /   -----3-----   \
       2 in this <    -----4-----    > Number - 7 in this case
          case    \   -----5-----   /
                      -----6-----  /
                      -----7----- /
                      \   /
                       \ /
                    Distance - 5 in this case (count the dashes)

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