Survivor on a Hexagonal Island
First task. Design the board above on poster board or paper or card stock. It should be rather large-- start with a circle with radius 9 cm. The side of a "small triangle" should be 3 cm long. (It is better than 1 inch.) The six directions should be indicated by arrows in the six corners of a big hexagon and marked with the numbers 1 to 6. A good pairing of opposite directions is (1, 6), (2, 5), and (3, 4), the same as on a die.
Second task. The game.
Two to six players play on one board. Each person has a different colored token (a penny, a colored plastic disc, etc.) Players choose initial positions on the board, which can be any of the six vertices closest to the center of the circle, and place their tokens on their chosen position.
Players begin by rolling one die, and the person with the lowest number plays first. Play proceeds clockwise.
Players roll one die in turn. The number on the die tells the direction that the token moves: up (1), down (6), northeast (4), southwest (3), northwest (5), southeast (2). A token makes a one-step move in the specified direction. You stay on the island until the die roll forces you to leave.
The object of the game is to be the last one to leave the island.
You may add this condition to the rules: If you move on a position occupied by another player's piece, his/her piece is out and he/she loses. (This makes the game faster and more interesting.)
Survivors are ranked in order of their leaving the board
A LONGER stay on the board is better. We call it "Survivor on a Hexagonal Island".
(3) We did some computations but did not have time to recheck them.
The expected time to exit the board by a single player starting in "basic position" is 16.5 moves, so the game is rather slow.
Percent of chance of exiting within some number of moves:
| 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |
| 10% | 31% | 49% | 62% | 72% | 79% | 84% | 88% | 91% | 93% |
So you may have very long-living survivors. I would suggest an extra rule: When more than one person survives (e.g) 40 moves, the game is a draw.