We consider a two-person zero-sum game where the players alternate
their moves until each of them has made a total of $\, n$ moves.
A move of either player consists of instructing a referee to move
a chip either clockwise or counterclockwise to the next node around
a three-node board. These three nodes are arranged in a circle and
are labeled +1, +2 and -3. The main feature here is neither player
is informed of any of his opponent's past or current moves. Whenever
the chip visits a node there is an intermediate payoff equal to
the label on that node. The payoff is taken to be the sum of these
intermediate payoffs at termination. Each player can remember all
his own past moves and therefore may use a history of such moves
to decide his next move. This game is solved for all positive
integral values of $n$.