Just to recap, you have found that using 1.618 as a multiplier suffices if the volunteer from the audience does 9, 10 or 11 calculations, but can be wrong if he does more than 11 or less than 9.  Using 1.618034 extends the upper range, but is still inaccurate if the volunteer does less than 9 calculations.

I guess the magician needs to insist that the volunteer does at least 9 calculations ...