Let X
i
≥ 0 be independent, i = 1,…, n, with known distributions and let X
n
*= max(X
1,…,X
n
). The classical ‘ratio prophet inequality’ compares the return to a prophet, which is EX
n
*, to that of a mortal, who observes the X
i
s sequentially, and must resort to a stopping rule t. The mortal's return is V(X
1,…,X
n
) = max EX
t
, where the maximum is over all stopping rules. The classical inequality states that EX
n
* < 2V(X
1,…,X
n
). In the present paper the mortal is given k ≥ 1 chances to choose. If he uses stopping rules t
1,…,t
k
his return is E(max(X
t
1,…,X
t
k
)). Let t(b) be the ‘simple threshold stopping rule’ defined to be the smallest i for which X
i
≥ b, or n if there is no such i. We show that there always exists a proper choice of k thresholds, such that EX
n
* ≤ ((k+1)/k)Emax(X
t
1,…,X
t
k
)), where t
i
is of the form t(b
i
) with some added randomization. Actually the thresholds can be taken to be thej/(k+1) percentile points of the distribution of X
n
*, j = 1,…,k, and hence only knowledge of the distribution of X
n
* is needed.