  We analyze a simple random process in which a token is moved in the interval
$A=\{0,...,n\$: Fix a probability distribution $\mu$ over $\{1,...,n\$.
Initially, the token is placed in a random position in $A$. In round $t$, a
random value $d$ is chosen according to $\mu$. If the token is in position
$a\geq d$, then it is moved to position $a-d$. Otherwise it stays put. Let $T$
be the number of rounds until the token reaches position 0. We show tight
bounds for the expectation of $T$ for the optimal distribution $\mu$. More
precisely, we show that $\min_\mu\{E_\mu(T)\=\Theta((\log n)^2)$. For the
proof, a novel potential function argument is introduced. The research is
motivated by the problem of approximating the minimum of a continuous function
over $[0,1]$ with a ``blind'' optimization strategy.
