Customs vs. Smuggler (player I and II, respectively)game 
where the amount of cargo is a random variable is discussed.  
II wants to cross the strait a motorboat carrying illegal 
cargo duringone of $n$ nights.  I wants to stop it, and can
patrol at most $k$ nights.  The amount $X_i$ of cargo in the 
$i$-th night is supposed to be $U_{[0, 1]}$-distributed 
random variable.  We suppose that the realized value of 
$X_i$ in each night is, by some information agent, 
communicated to I.  Payoff to I is $X_i (-X_i)$, 
if patrol-go (no=patrol-go) are chosen.  I (II) wants to 
maximize (minimize) the expected payoff to I.  
This game $G_k^n$ is formulated and solved by deriving 
the triangular recursion of values 
$V_k^n=\mbox{Val}(G_k^n), 1\leq k\leq n, n=1, 2, \cdots$.
It is shown that $V_k^n\downarrow -1$ as $n\to \infty$,
for every fixed $k$.