Consider the setting where we have a numerical sample X1, . . . , Xn that is assumed iid from an unknown distribution. We want to assess whether the data are congruent with an underlying distribution that is symmetric about 0. The following is a well-known test based on random sign flipping. For a sign vector = (1, . . . , n) {1, +1}n, compute the sample mean of 1X1, . . . , nXn, denoted Y = n1 Pi iXi. Let Y denote the original sample mean. The two-sided version of the test returns the p-value P = #{:|Y||Y|} 2n (The denominator comes from the fact that there are that many possible sign flips of the data.) A. In practice there are too many sign vectors to compute this p-value exactly and