I am working with a clinician and need her to randomly assign patients into one of two groups with the goal of having roughly equal numbers in both groups. The clinician does not have access to a random number generator and it would be inappropriate for her to flip a coin before the allocation. We initially decided upon using the second hand on a clock and splitting on the top/bottom half of the minute, but the exam room does not have a clock and she does not wear a watch.
We are thinking of splitting on the first letter of the first name which is on the patient's chart. We would then flip every couple of weeks whether the first half of the alphabet was in group A or group B. Is this a reasonable approach? Is there a better one? If we go this way, what letter do we split on to give roughly equal sizes?