A Game With Coins

The applet below is a simulation of a two-person game that could be played on a table top with a sufficient supply of coins. The coins of various denominations are arranged in a chain (e.g., a row, a semicircle) with two "end points" and the others each having two neighbors. A move consists in removing an end coin, whereby the coin's immediate (and the only) neighbor becomes naturally an end coin available for the removal on successive moves. When all the coins have been removed, the game ends, and the players count their bounties. The player with the larger amount wins.

The applet allows some variations. First, the coin can be arranged in a loop, in which case the first player is allowed to remove any coin. After that the game continues as before. The applet uses 4 US coins: a penny (1 cent), a nickel (5 cents), a dime (10 cents) and a quarter (25 cents), but, in addition, it can also display a sequence of small random numbers.

At the outset, you can force the computer to make the first move by pressing the "Make Move" button.

Can the first player always guarantee a win or at least a draw?

Discussion

Copyright © 1996-2008 Alexander Bogomolny