Coin Strip
Coinstrip is a game that I first heard discussed in connection with "On Numbers and Games" by John Conway. The game is played by two opponents which take turns moving one and only one coin at a time along a strip. The strip is slotted such that each slot can accommodate at most one coin at a time, and coins can be moved in only one direction. A player chooses a coin to move and moves it from its current location towards the front of the strip. He may choose to move it any number of slots, but may not jump over any coins. Since the strip is not infinitely long, coins begin accumulating at the front. The player that can no longer move a coin because they are all blocked, looses. The initial number and positions of the coins is chosen randomly, within some reasonable limits.
For example, a player can choose to move either coin in the following example:
If he chooses to move the first coin (the one closest to the front), then he can only move it forward one slot. But if he chooses to move the second, he can move it forward one, two or three slots, but no further because the first coin blocks it.
Now suppose the play progresses until the strip reaches the following state:
The current player is now faced with a situation in which no coin can be moved and looses the game.