The Hotelling Game

Rules

Three players occupy distinct numbers on the line 1–10.

On a player's turn:

1. That player scores from the current board.
2. Each integer gives:
   • 2 points if it lies closer to the player's site than to any other player.
   • 1 point if it is exactly midway to a neighbour.
3. After scoring, the player must move to a different unoccupied number.
4. Play then passes to the next player.

This version supports human players, a greedy AI, a lookahead AI, and a nasty AI that tries to minimize the next player's score.

In Random from other two mode, the next player is chosen from the other two, with a bias toward the one who has had fewer turns:

• same number of turns: probability 1/2 each
• one fewer turn: probability 3/4 for the player with fewer turns
• two or more fewer turns: probability 1 for the player with fewer turns

Board