  On-line chain partition is a two-player game between Spoiler and Algorithm.
Spoiler presents a partially ordered set, point by point. Algorithm assigns
incoming points (immediately and irrevocably) to the chains which constitute a
chain partition of the order. The value of the game for orders of width $w$ is
a minimum number $\fVal(w)$ such that Algorithm has a strategy using at most
$\fVal(w)$ chains on orders of width at most $w$. We analyze the chain
partition game for up-growing semi-orders. Surprisingly, the golden ratio comes
into play and the value of the game is $\lfloor\frac{1+\sqrt{5}}{2}\; w
\rfloor$.
