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This paper answers a long-standing open question concerning the$1/e$-strategy for the problem of best choice. $N$ candidates for a job arriveat times independently uniformly distributed in $[0,1]$. The interviewer knowshow each candidate ranks relative to all others seen so far, and mustimmediately appoint or reject each candidate as they arrive. The aim is tochoose the best overall. The $1/e$ strategy is to follow the rule: `Do nothinguntil time $1/e$, then appoint the first candidate thereafter who is best sofar (if any).'  The question, first discussed with Larry Shepp in 1983, was to know whetherthe $1/e$-strategy is optimal if one has `no information about the total numberof options'. Quite what this might mean is open to various interpretations, butwe shall take the proportional-increment process formulation of \cite{BY}. Suchprocesses are shown to have a very rigid structure, being time-changed {\empure birth processes}, and this allows some precise distributionalcalculations, from which we deduce that the $1/e$-strategy is in fact notoptimal.

Answer to an open question concerning the $1/e$-strategy for best choice under no information