Ruling: Final Table Seating

 
Looks like we have been doing it wrong all this while. There is an additional step to determine the order of play after the seating arrangements have been determined.

3.1.3. Final Round Seating

Table positions are not assigned in the final round. Instead each of the finalists is given an index card (or reasonable substitute) with his or her name on it. Starting with the lowest qualifier, each qualifier places his or her index card faceup in a row on the table. When placing his or her card, each player must choose to position his or her card at either end of the row (one end of the row is equivalent to the other) or may create a space between two cards already placed. After all cards have been placed, they are read from left to right to determine seating positions in the final round. The judge will then determine randomly which player will play first.